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cellects.image_analysis.morphological_operations

cellects.image_analysis.morphological_operations

This module provides methods to analyze and modify shapes in binary images. It includes functions for comparing neighboring pixels, generating shape descriptors, and performing morphological operations like expanding shapes and filling holes.

Classes:

Name Description
CompareNeighborsWithValue : Class to compare neighboring pixels to a specified value

Functions:

Name Description
cc : Sort connected components according to size
make_gravity_field : Create a gradient field around shapes
find_median_shape : Generate median shape from multiple inputs
make_numbered_rays : Create numbered rays for analysis
CompareNeighborsWithFocal : Compare neighboring pixels to focal values
ShapeDescriptors : Generate shape descriptors using provided functions
get_radius_distance_against_time : Calculate radius distances over time
expand_until_one : Expand shapes until a single connected component remains
expand_and_rate_until_one : Expand and rate shapes until one remains
expand_until_overlap : Expand shapes until overlap occurs
dynamically_expand_to_fill_holes : Dynamically expand to fill holes in shapes
expand_smalls_toward_biggest : Expand smaller shapes toward largest component
change_thresh_until_one : Change threshold until one connected component remains
create_ellipse : Generate ellipse shape descriptors
get_rolling_window_coordinates_list : Get coordinates for rolling window operations

CompareNeighborsWithValue

CompareNeighborsWithValue class to summarize each pixel by comparing its neighbors to a value.

This class analyzes pixels in a 2D array, comparing each pixel's neighbors to a specified value. The comparison can be equality, superiority, or inferiority, and neighbors can be the 4 or 8 nearest pixels based on the connectivity parameter.

Source code in src/cellects/image_analysis/morphological_operations.py 
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class CompareNeighborsWithValue:
    """
    CompareNeighborsWithValue class to summarize each pixel by comparing its neighbors to a value.

    This class analyzes pixels in a 2D array, comparing each pixel's neighbors
    to a specified value. The comparison can be equality, superiority,
    or inferiority, and neighbors can be the 4 or 8 nearest pixels based on
    the connectivity parameter.
    """
    def __init__(self, array: np.ndarray, connectivity: int=None, data_type: np.dtype=np.int8):
        """
        Initialize a class for array connectivity processing.

        This class processes arrays based on given connectivities, creating
        windows around the original data for both 1D and 2D arrays. Depending on
        the connectivity value (4 or 8), it creates different windows with borders.

        Parameters
        ----------
        array : ndarray
            Input array to process, can be 1D or 2D.
        connectivity : int, optional
            Connectivity type for processing (4 or 8), by default None.
        data_type : dtype, optional
            Data type for the array elements, by default np.int8.

        Attributes
        ----------
        array : ndarray
            The processed array based on the given data type.
        connectivity : int
            Connectivity value used for processing.
        on_the_right : ndarray
            Array with shifted elements to the right.
        on_the_left : ndarray
            Array with shifted elements to the left.
        on_the_bot : ndarray, optional
            Array with shifted elements to the bottom (for 2D arrays).
        on_the_top : ndarray, optional
            Array with shifted elements to the top (for 2D arrays).
        on_the_topleft : ndarray, optional
            Array with shifted elements to the top left (for 2D arrays).
        on_the_topright : ndarray, optional
            Array with shifted elements to the top right (for 2D arrays).
        on_the_botleft : ndarray, optional
            Array with shifted elements to the bottom left (for 2D arrays).
        on_the_botright : ndarray, optional
            Array with shifted elements to the bottom right (for 2D arrays).
        """
        array = array.astype(data_type)
        self.array = array
        self.connectivity = connectivity
        if len(self.array.shape) == 1:
            self.on_the_right = np.append(array[1:], array[-1])
            self.on_the_left = np.append(array[0], array[:-1])
        else:
            # Build 4 window of the original array, each missing one of the four borders
            # Grow each window with a copy of the last border at the opposite of the side a border have been deleted
            if self.connectivity == 4 or self.connectivity == 8:
                self.on_the_right = np.column_stack((array[:, 1:], array[:, -1]))
                self.on_the_left = np.column_stack((array[:, 0], array[:, :-1]))
                self.on_the_bot = np.vstack((array[1:, :], array[-1, :]))
                self.on_the_top = np.vstack((array[0, :], array[:-1, :]))
            if self.connectivity != 4:
                self.on_the_topleft = array[:-1, :-1]
                self.on_the_topright = array[:-1, 1:]
                self.on_the_botleft = array[1:, :-1]
                self.on_the_botright = array[1:, 1:]

                self.on_the_topleft = np.vstack((self.on_the_topleft[0, :], self.on_the_topleft))
                self.on_the_topleft = np.column_stack((self.on_the_topleft[:, 0], self.on_the_topleft))

                self.on_the_topright = np.vstack((self.on_the_topright[0, :], self.on_the_topright))
                self.on_the_topright = np.column_stack((self.on_the_topright, self.on_the_topright[:, -1]))

                self.on_the_botleft = np.vstack((self.on_the_botleft, self.on_the_botleft[-1, :]))
                self.on_the_botleft = np.column_stack((self.on_the_botleft[:, 0], self.on_the_botleft))

                self.on_the_botright = np.vstack((self.on_the_botright, self.on_the_botright[-1, :]))
                self.on_the_botright = np.column_stack((self.on_the_botright, self.on_the_botright[:, -1]))

    def is_equal(self, value, and_itself: bool=False):
        """
        Check equality of neighboring values in an array.

        This method compares the neighbors of each element in `self.array` to a given value.
        Depending on the dimensionality and connectivity settings, it checks different neighboring
        elements.

        Parameters
        ----------
        value : int or float
            The value to check equality with neighboring elements.
        and_itself : bool, optional
            If True, also check equality with the element itself. Defaults to False.

        Returns
        -------
        None

        Attributes (not standard Qt properties)
        --------------------------------------
        equal_neighbor_nb : ndarray of uint8
            Array that holds the number of equal neighbors for each element.

        Examples
        --------
        >>> matrix = np.array([[9, 0, 4, 6], [4, 9, 1, 3], [7, 2, 1, 4], [9, 0, 8, 5]], dtype=np.int8)
        >>> compare = CompareNeighborsWithValue(matrix, connectivity=4)
        >>> compare.is_equal(1)
        >>> print(compare.equal_neighbor_nb)
        [[0 0 1 0]
        [0 1 1 1]
        [0 1 1 1]
        [0 0 1 0]]
        """

        if len(self.array.shape) == 1:
            self.equal_neighbor_nb = np.sum((np.equal(self.on_the_right, value), np.equal(self.on_the_left, value)), axis=0)
        else:
            if self.connectivity == 4:
                self.equal_neighbor_nb =  np.dstack((np.equal(self.on_the_right, value), np.equal(self.on_the_left, value),
                                                 np.equal(self.on_the_bot, value), np.equal(self.on_the_top, value)))
            elif self.connectivity == 8:
                self.equal_neighbor_nb =  np.dstack(
                    (np.equal(self.on_the_right, value), np.equal(self.on_the_left, value),
                     np.equal(self.on_the_bot, value), np.equal(self.on_the_top, value),
                     np.equal(self.on_the_topleft, value), np.equal(self.on_the_topright, value),
                     np.equal(self.on_the_botleft, value), np.equal(self.on_the_botright, value)))
            else:
                self.equal_neighbor_nb =  np.dstack(
                    (np.equal(self.on_the_topleft, value), np.equal(self.on_the_topright, value),
                     np.equal(self.on_the_botleft, value), np.equal(self.on_the_botright, value)))
            self.equal_neighbor_nb = np.sum(self.equal_neighbor_nb, 2, dtype=np.uint8)

        if and_itself:
            self.equal_neighbor_nb[np.not_equal(self.array, value)] = 0

    def is_sup(self, value, and_itself=False):
        """
        Determine if pixels have more neighbors with higher values than a given threshold.

        This method computes the number of neighboring pixels that have values greater
        than a specified `value` for each pixel in the array. Optionally, it can exclude
        the pixel itself if its value is less than or equal to `value`.

        Parameters
        ----------
        value : int
            The threshold value used to determine if a neighboring pixel's value is greater.
        and_itself : bool, optional
            If True, exclude the pixel itself if its value is less than or equal to `value`.
            Defaults to False.

        Examples
        --------
        >>> matrix = np.array([[9, 0, 4, 6], [4, 9, 1, 3], [7, 2, 1, 4], [9, 0, 8, 5]], dtype=np.int8)
        >>> compare = CompareNeighborsWithValue(matrix, connectivity=4)
        >>> compare.is_sup(1)
        >>> print(compare.sup_neighbor_nb)
        [[3 3 2 4]
         [4 2 3 3]
         [4 2 3 3]
         [3 3 2 4]]
        """
        if len(self.array.shape) == 1:
            self.sup_neighbor_nb = (self.on_the_right > value).astype(self.array.dtype) + (self.on_the_left > value).astype(self.array.dtype)
        else:
            if self.connectivity == 4:
                self.sup_neighbor_nb =  np.dstack((self.on_the_right > value, self.on_the_left > value,
                                               self.on_the_bot > value, self.on_the_top > value))
            elif self.connectivity == 8:
                self.sup_neighbor_nb =  np.dstack((self.on_the_right > value, self.on_the_left > value,
                                               self.on_the_bot > value, self.on_the_top > value,
                                               self.on_the_topleft > value, self.on_the_topright > value,
                                               self.on_the_botleft > value, self.on_the_botright > value))
            else:
                self.sup_neighbor_nb =  np.dstack((self.on_the_topleft > value, self.on_the_topright > value,
                                               self.on_the_botleft > value, self.on_the_botright > value))

            self.sup_neighbor_nb = np.sum(self.sup_neighbor_nb, 2, dtype=np.uint8)
        if and_itself:
            self.sup_neighbor_nb[np.less_equal(self.array, value)] = 0

    def is_inf(self, value, and_itself=False):
        """
        is_inf(value and_itself=False)

        Determine the number of neighbors that are infinitely small relative to a given value,
        considering optional connectivity and exclusion of the element itself.

        Parameters
        ----------
        value : numeric
            The value to compare neighbor elements against.
        and_itself : bool, optional
            If True, excludes the element itself from being counted. Default is False.

        Examples
        --------
        >>> matrix = np.array([[9, 0, 4, 6], [4, 9, 1, 3], [7, 2, 1, 4], [9, 0, 8, 5]], dtype=np.int8)
        >>> compare = CompareNeighborsWithValue(matrix, connectivity=4)
        >>> compare.is_inf(1)
        >>> print(compare.inf_neighbor_nb)
        [[1 1 1 0]
         [0 1 0 0]
         [0 1 0 0]
         [1 1 1 0]]
        """
        if len(self.array.shape) == 1:
            self.inf_neighbor_nb = (self.on_the_right < value).astype(self.array.dtype) + (self.on_the_left < value).astype(self.array.dtype)
        else:
            if self.connectivity == 4:
                self.inf_neighbor_nb =  np.dstack((self.on_the_right < value, self.on_the_left < value,
                                               self.on_the_bot < value, self.on_the_top < value))
            elif self.connectivity == 8:
                self.inf_neighbor_nb =  np.dstack((self.on_the_right < value, self.on_the_left < value,
                                               self.on_the_bot < value, self.on_the_top < value,
                                               self.on_the_topleft < value, self.on_the_topright < value,
                                               self.on_the_botleft < value, self.on_the_botright < value))
            else:
                self.inf_neighbor_nb =  np.dstack((self.on_the_topleft < value, self.on_the_topright < value,
                                               self.on_the_botleft < value, self.on_the_botright < value))

            self.inf_neighbor_nb = np.sum(self.inf_neighbor_nb, 2, dtype=np.uint8)
        if and_itself:
            self.inf_neighbor_nb[np.greater_equal(self.array, value)] = 0

__init__(array, connectivity=None, data_type=np.int8)

Initialize a class for array connectivity processing.

This class processes arrays based on given connectivities, creating windows around the original data for both 1D and 2D arrays. Depending on the connectivity value (4 or 8), it creates different windows with borders.

Parameters:

Name Type Description Default
array ndarray

Input array to process, can be 1D or 2D.

 required
connectivity int

Connectivity type for processing (4 or 8), by default None.

 None
data_type dtype

Data type for the array elements, by default np.int8.

 int8

Attributes:

Name Type Description
array ndarray

The processed array based on the given data type.
connectivity int

Connectivity value used for processing.
on_the_right ndarray

Array with shifted elements to the right.
on_the_left ndarray

Array with shifted elements to the left.
on_the_bot (ndarray, optional)

Array with shifted elements to the bottom (for 2D arrays).
on_the_top (ndarray, optional)

Array with shifted elements to the top (for 2D arrays).
on_the_topleft (ndarray, optional)

Array with shifted elements to the top left (for 2D arrays).
on_the_topright (ndarray, optional)

Array with shifted elements to the top right (for 2D arrays).
on_the_botleft (ndarray, optional)

Array with shifted elements to the bottom left (for 2D arrays).
on_the_botright (ndarray, optional)

Array with shifted elements to the bottom right (for 2D arrays).
Source code in src/cellects/image_analysis/morphological_operations.py 
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def __init__(self, array: np.ndarray, connectivity: int=None, data_type: np.dtype=np.int8):
    """
    Initialize a class for array connectivity processing.

    This class processes arrays based on given connectivities, creating
    windows around the original data for both 1D and 2D arrays. Depending on
    the connectivity value (4 or 8), it creates different windows with borders.

    Parameters
    ----------
    array : ndarray
        Input array to process, can be 1D or 2D.
    connectivity : int, optional
        Connectivity type for processing (4 or 8), by default None.
    data_type : dtype, optional
        Data type for the array elements, by default np.int8.

    Attributes
    ----------
    array : ndarray
        The processed array based on the given data type.
    connectivity : int
        Connectivity value used for processing.
    on_the_right : ndarray
        Array with shifted elements to the right.
    on_the_left : ndarray
        Array with shifted elements to the left.
    on_the_bot : ndarray, optional
        Array with shifted elements to the bottom (for 2D arrays).
    on_the_top : ndarray, optional
        Array with shifted elements to the top (for 2D arrays).
    on_the_topleft : ndarray, optional
        Array with shifted elements to the top left (for 2D arrays).
    on_the_topright : ndarray, optional
        Array with shifted elements to the top right (for 2D arrays).
    on_the_botleft : ndarray, optional
        Array with shifted elements to the bottom left (for 2D arrays).
    on_the_botright : ndarray, optional
        Array with shifted elements to the bottom right (for 2D arrays).
    """
    array = array.astype(data_type)
    self.array = array
    self.connectivity = connectivity
    if len(self.array.shape) == 1:
        self.on_the_right = np.append(array[1:], array[-1])
        self.on_the_left = np.append(array[0], array[:-1])
    else:
        # Build 4 window of the original array, each missing one of the four borders
        # Grow each window with a copy of the last border at the opposite of the side a border have been deleted
        if self.connectivity == 4 or self.connectivity == 8:
            self.on_the_right = np.column_stack((array[:, 1:], array[:, -1]))
            self.on_the_left = np.column_stack((array[:, 0], array[:, :-1]))
            self.on_the_bot = np.vstack((array[1:, :], array[-1, :]))
            self.on_the_top = np.vstack((array[0, :], array[:-1, :]))
        if self.connectivity != 4:
            self.on_the_topleft = array[:-1, :-1]
            self.on_the_topright = array[:-1, 1:]
            self.on_the_botleft = array[1:, :-1]
            self.on_the_botright = array[1:, 1:]

            self.on_the_topleft = np.vstack((self.on_the_topleft[0, :], self.on_the_topleft))
            self.on_the_topleft = np.column_stack((self.on_the_topleft[:, 0], self.on_the_topleft))

            self.on_the_topright = np.vstack((self.on_the_topright[0, :], self.on_the_topright))
            self.on_the_topright = np.column_stack((self.on_the_topright, self.on_the_topright[:, -1]))

            self.on_the_botleft = np.vstack((self.on_the_botleft, self.on_the_botleft[-1, :]))
            self.on_the_botleft = np.column_stack((self.on_the_botleft[:, 0], self.on_the_botleft))

            self.on_the_botright = np.vstack((self.on_the_botright, self.on_the_botright[-1, :]))
            self.on_the_botright = np.column_stack((self.on_the_botright, self.on_the_botright[:, -1]))

is_equal(value, and_itself=False)

Check equality of neighboring values in an array.

This method compares the neighbors of each element in self.array to a given value. Depending on the dimensionality and connectivity settings, it checks different neighboring elements.

Parameters:

Name Type Description Default
value int or float

The value to check equality with neighboring elements.

 required
and_itself bool

If True, also check equality with the element itself. Defaults to False.

 False

Returns:

Type Description
None
Attributes (not standard Qt properties)

equal_neighbor_nb : ndarray of uint8 Array that holds the number of equal neighbors for each element.

Examples:

>>> matrix = np.array([[9, 0, 4, 6], [4, 9, 1, 3], [7, 2, 1, 4], [9, 0, 8, 5]], dtype=np.int8)
>>> compare = CompareNeighborsWithValue(matrix, connectivity=4)
>>> compare.is_equal(1)
>>> print(compare.equal_neighbor_nb)
[[0 0 1 0]
[0 1 1 1]
[0 1 1 1]
[0 0 1 0]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def is_equal(self, value, and_itself: bool=False):
    """
    Check equality of neighboring values in an array.

    This method compares the neighbors of each element in `self.array` to a given value.
    Depending on the dimensionality and connectivity settings, it checks different neighboring
    elements.

    Parameters
    ----------
    value : int or float
        The value to check equality with neighboring elements.
    and_itself : bool, optional
        If True, also check equality with the element itself. Defaults to False.

    Returns
    -------
    None

    Attributes (not standard Qt properties)
    --------------------------------------
    equal_neighbor_nb : ndarray of uint8
        Array that holds the number of equal neighbors for each element.

    Examples
    --------
    >>> matrix = np.array([[9, 0, 4, 6], [4, 9, 1, 3], [7, 2, 1, 4], [9, 0, 8, 5]], dtype=np.int8)
    >>> compare = CompareNeighborsWithValue(matrix, connectivity=4)
    >>> compare.is_equal(1)
    >>> print(compare.equal_neighbor_nb)
    [[0 0 1 0]
    [0 1 1 1]
    [0 1 1 1]
    [0 0 1 0]]
    """

    if len(self.array.shape) == 1:
        self.equal_neighbor_nb = np.sum((np.equal(self.on_the_right, value), np.equal(self.on_the_left, value)), axis=0)
    else:
        if self.connectivity == 4:
            self.equal_neighbor_nb =  np.dstack((np.equal(self.on_the_right, value), np.equal(self.on_the_left, value),
                                             np.equal(self.on_the_bot, value), np.equal(self.on_the_top, value)))
        elif self.connectivity == 8:
            self.equal_neighbor_nb =  np.dstack(
                (np.equal(self.on_the_right, value), np.equal(self.on_the_left, value),
                 np.equal(self.on_the_bot, value), np.equal(self.on_the_top, value),
                 np.equal(self.on_the_topleft, value), np.equal(self.on_the_topright, value),
                 np.equal(self.on_the_botleft, value), np.equal(self.on_the_botright, value)))
        else:
            self.equal_neighbor_nb =  np.dstack(
                (np.equal(self.on_the_topleft, value), np.equal(self.on_the_topright, value),
                 np.equal(self.on_the_botleft, value), np.equal(self.on_the_botright, value)))
        self.equal_neighbor_nb = np.sum(self.equal_neighbor_nb, 2, dtype=np.uint8)

    if and_itself:
        self.equal_neighbor_nb[np.not_equal(self.array, value)] = 0

is_inf(value, and_itself=False)

is_inf(value and_itself=False)

Determine the number of neighbors that are infinitely small relative to a given value, considering optional connectivity and exclusion of the element itself.

Parameters:

Name Type Description Default
value numeric

The value to compare neighbor elements against.

 required
and_itself bool

If True, excludes the element itself from being counted. Default is False.

 False

Examples:

>>> matrix = np.array([[9, 0, 4, 6], [4, 9, 1, 3], [7, 2, 1, 4], [9, 0, 8, 5]], dtype=np.int8)
>>> compare = CompareNeighborsWithValue(matrix, connectivity=4)
>>> compare.is_inf(1)
>>> print(compare.inf_neighbor_nb)
[[1 1 1 0]
 [0 1 0 0]
 [0 1 0 0]
 [1 1 1 0]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def is_inf(self, value, and_itself=False):
    """
    is_inf(value and_itself=False)

    Determine the number of neighbors that are infinitely small relative to a given value,
    considering optional connectivity and exclusion of the element itself.

    Parameters
    ----------
    value : numeric
        The value to compare neighbor elements against.
    and_itself : bool, optional
        If True, excludes the element itself from being counted. Default is False.

    Examples
    --------
    >>> matrix = np.array([[9, 0, 4, 6], [4, 9, 1, 3], [7, 2, 1, 4], [9, 0, 8, 5]], dtype=np.int8)
    >>> compare = CompareNeighborsWithValue(matrix, connectivity=4)
    >>> compare.is_inf(1)
    >>> print(compare.inf_neighbor_nb)
    [[1 1 1 0]
     [0 1 0 0]
     [0 1 0 0]
     [1 1 1 0]]
    """
    if len(self.array.shape) == 1:
        self.inf_neighbor_nb = (self.on_the_right < value).astype(self.array.dtype) + (self.on_the_left < value).astype(self.array.dtype)
    else:
        if self.connectivity == 4:
            self.inf_neighbor_nb =  np.dstack((self.on_the_right < value, self.on_the_left < value,
                                           self.on_the_bot < value, self.on_the_top < value))
        elif self.connectivity == 8:
            self.inf_neighbor_nb =  np.dstack((self.on_the_right < value, self.on_the_left < value,
                                           self.on_the_bot < value, self.on_the_top < value,
                                           self.on_the_topleft < value, self.on_the_topright < value,
                                           self.on_the_botleft < value, self.on_the_botright < value))
        else:
            self.inf_neighbor_nb =  np.dstack((self.on_the_topleft < value, self.on_the_topright < value,
                                           self.on_the_botleft < value, self.on_the_botright < value))

        self.inf_neighbor_nb = np.sum(self.inf_neighbor_nb, 2, dtype=np.uint8)
    if and_itself:
        self.inf_neighbor_nb[np.greater_equal(self.array, value)] = 0

is_sup(value, and_itself=False)

Determine if pixels have more neighbors with higher values than a given threshold.

This method computes the number of neighboring pixels that have values greater than a specified value for each pixel in the array. Optionally, it can exclude the pixel itself if its value is less than or equal to value.

Parameters:

Name Type Description Default
value int

The threshold value used to determine if a neighboring pixel's value is greater.

 required
and_itself bool

If True, exclude the pixel itself if its value is less than or equal to value. Defaults to False.

 False

Examples:

>>> matrix = np.array([[9, 0, 4, 6], [4, 9, 1, 3], [7, 2, 1, 4], [9, 0, 8, 5]], dtype=np.int8)
>>> compare = CompareNeighborsWithValue(matrix, connectivity=4)
>>> compare.is_sup(1)
>>> print(compare.sup_neighbor_nb)
[[3 3 2 4]
 [4 2 3 3]
 [4 2 3 3]
 [3 3 2 4]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def is_sup(self, value, and_itself=False):
    """
    Determine if pixels have more neighbors with higher values than a given threshold.

    This method computes the number of neighboring pixels that have values greater
    than a specified `value` for each pixel in the array. Optionally, it can exclude
    the pixel itself if its value is less than or equal to `value`.

    Parameters
    ----------
    value : int
        The threshold value used to determine if a neighboring pixel's value is greater.
    and_itself : bool, optional
        If True, exclude the pixel itself if its value is less than or equal to `value`.
        Defaults to False.

    Examples
    --------
    >>> matrix = np.array([[9, 0, 4, 6], [4, 9, 1, 3], [7, 2, 1, 4], [9, 0, 8, 5]], dtype=np.int8)
    >>> compare = CompareNeighborsWithValue(matrix, connectivity=4)
    >>> compare.is_sup(1)
    >>> print(compare.sup_neighbor_nb)
    [[3 3 2 4]
     [4 2 3 3]
     [4 2 3 3]
     [3 3 2 4]]
    """
    if len(self.array.shape) == 1:
        self.sup_neighbor_nb = (self.on_the_right > value).astype(self.array.dtype) + (self.on_the_left > value).astype(self.array.dtype)
    else:
        if self.connectivity == 4:
            self.sup_neighbor_nb =  np.dstack((self.on_the_right > value, self.on_the_left > value,
                                           self.on_the_bot > value, self.on_the_top > value))
        elif self.connectivity == 8:
            self.sup_neighbor_nb =  np.dstack((self.on_the_right > value, self.on_the_left > value,
                                           self.on_the_bot > value, self.on_the_top > value,
                                           self.on_the_topleft > value, self.on_the_topright > value,
                                           self.on_the_botleft > value, self.on_the_botright > value))
        else:
            self.sup_neighbor_nb =  np.dstack((self.on_the_topleft > value, self.on_the_topright > value,
                                           self.on_the_botleft > value, self.on_the_botright > value))

        self.sup_neighbor_nb = np.sum(self.sup_neighbor_nb, 2, dtype=np.uint8)
    if and_itself:
        self.sup_neighbor_nb[np.less_equal(self.array, value)] = 0

box_counting_dimension(zoomed_binary, side_lengths, display=False)

Box counting dimension calculation.

This function calculates the box-counting dimension of a binary image by analyzing the number of boxes (of varying sizes) that contain at least one pixel of the image. The function also provides the R-squared value from linear regression and the number of boxes used.

Parameters:

Name Type Description Default
zoomed_binary NDArray[uint8]

Binary image (0 or 255 values) for which the box-counting dimension is calculated.

 required
side_lengths NDArray

Array of side lengths for the boxes used in the box-counting calculation.

 required
display bool

If True, displays a scatter plot of the log-transformed box counts and diameters, along with the linear regression fit. Default is False.

 False

Returns:

Name Type Description
out Tuple[float, float, float]

A tuple containing the calculated box-counting dimension (d), R-squared value (r_value), and the number of boxes used (box_nb).

Examples:

>>> binary_image = np.zeros((10, 10), dtype=np.uint8)
>>> binary_image[2:4, 2:6] = 1
>>> binary_image[7:9, 4:7] = 1
>>> binary_image[4:7, 5] = 1
>>> zoomed_binary, side_lengths = prepare_box_counting(binary_image, min_im_side=2, min_mesh_side=2)
>>> dimension, r_value, box_nb = box_counting_dimension(zoomed_binary, side_lengths)
>>> print(dimension, r_value, box_nb)
(np.float64(1.1699250014423126), np.float64(0.9999999999999998), 2)
Source code in src/cellects/image_analysis/morphological_operations.py 
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def box_counting_dimension(zoomed_binary: NDArray[np.uint8], side_lengths: NDArray, display: bool=False) -> Tuple[float, float, float]:
    """
    Box counting dimension calculation.

    This function calculates the box-counting dimension of a binary image by analyzing the number
    of boxes (of varying sizes) that contain at least one pixel of the image. The function also
    provides the R-squared value from linear regression and the number of boxes used.

    Parameters
    ----------
    zoomed_binary : NDArray[np.uint8]
        Binary image (0 or 255 values) for which the box-counting dimension is calculated.
    side_lengths : NDArray
        Array of side lengths for the boxes used in the box-counting calculation.
    display : bool, optional
        If True, displays a scatter plot of the log-transformed box counts and diameters,
        along with the linear regression fit. Default is False.

    Returns
    -------
    out : Tuple[float, float, float]
        A tuple containing the calculated box-counting dimension (`d`), R-squared value (`r_value`),
        and the number of boxes used (`box_nb`).

    Examples
    --------
    >>> binary_image = np.zeros((10, 10), dtype=np.uint8)
    >>> binary_image[2:4, 2:6] = 1
    >>> binary_image[7:9, 4:7] = 1
    >>> binary_image[4:7, 5] = 1
    >>> zoomed_binary, side_lengths = prepare_box_counting(binary_image, min_im_side=2, min_mesh_side=2)
    >>> dimension, r_value, box_nb = box_counting_dimension(zoomed_binary, side_lengths)
    >>> print(dimension, r_value, box_nb)
    (np.float64(1.1699250014423126), np.float64(0.9999999999999998), 2)
    """
    dimension:float = 0.
    r_value:float = 0.
    box_nb:float = 0.
    if side_lengths is not None:
        box_counts = np.zeros(len(side_lengths), dtype=np.uint64)
        # Loop through side_lengths and compute block counts
        for idx, side_length in enumerate(side_lengths):
            S = np.add.reduceat(
                np.add.reduceat(zoomed_binary, np.arange(0, zoomed_binary.shape[0], side_length), axis=0),
                np.arange(0, zoomed_binary.shape[1], side_length),
                axis=1
            )
            box_counts[idx] = len(np.where(S > 0)[0])

        valid_indices = box_counts > 0
        if valid_indices.sum() >= 2:
            log_box_counts = np.log(box_counts)
            log_reciprocal_lengths = np.log(1 / side_lengths)
            slope, intercept, r_value, p_value, stderr = linregress(log_reciprocal_lengths, log_box_counts)
            # coefficients = np.polyfit(log_reciprocal_lengths, log_box_counts, 1)
            dimension = slope
            box_nb = len(side_lengths)
            if display:
                plt.scatter(log_reciprocal_lengths, log_box_counts, label="Box counting")
                plt.plot([0, log_reciprocal_lengths.min()], [intercept, intercept + slope * log_reciprocal_lengths.min()], label="Linear regression")
                plt.plot([], [], ' ', label=f"D = {slope:.2f}")
                plt.plot([], [], ' ', label=f"R2 = {r_value:.6f}")
                plt.plot([], [], ' ', label=f"p-value = {p_value:.2e}")
                plt.legend(loc='best')
                plt.xlabel(f"log(1/Diameter) | Diameter ⊆ [{side_lengths[0]}:{side_lengths[-1]}] (n={box_nb})")
                plt.ylabel(f"log(Box number) | Box number ⊆ [{box_counts[0]}:{box_counts[-1]}]")
                plt.show()
                # plt.close()

    return dimension, r_value, box_nb

cc(binary_img)

Processes a binary image to reorder and label connected components.

This function takes a binary image, analyses the connected components, reorders them by size, ensures background is correctly labeled as 0, and returns the new ordered labels along with their statistics and centers.

Parameters:

Name Type Description Default
binary_img ndarray of uint8

Input binary image with connected components.

 required

Returns:

Name Type Description
new_order ndarray of uint8, uint16 or uint32

Image with reordered labels for connected components.
stats ndarray of ints

Statistics for each component (x, y, width, height, area).
centers ndarray of floats

Centers for each component (x, y).

Examples:

>>> binary_img = np.array([[0, 1, 0], [0, 1, 0]], dtype=np.uint8)
>>> new_order, stats, centers = cc(binary_img)
>>> print(stats)
array([[0, 0, 3, 2, 4],
   [1, 0, 2, 2, 2]], dtype=int32)
Source code in src/cellects/image_analysis/morphological_operations.py 
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def cc(binary_img: NDArray[np.uint8]) -> Tuple[NDArray, NDArray, NDArray]:
    """
    Processes a binary image to reorder and label connected components.

    This function takes a binary image, analyses the connected components,
    reorders them by size, ensures background is correctly labeled as 0,
    and returns the new ordered labels along with their statistics and centers.

    Parameters
    ----------
    binary_img : ndarray of uint8
        Input binary image with connected components.

    Returns
    -------
    new_order : ndarray of uint8, uint16 or uint32
        Image with reordered labels for connected components.
    stats : ndarray of ints
        Statistics for each component (x, y, width, height, area).
    centers : ndarray of floats
        Centers for each component (x, y).

    Examples
    --------
    >>> binary_img = np.array([[0, 1, 0], [0, 1, 0]], dtype=np.uint8)
    >>> new_order, stats, centers = cc(binary_img)
    >>> print(stats)
    array([[0, 0, 3, 2, 4],
       [1, 0, 2, 2, 2]], dtype=int32)
    """
    number, img, stats, centers = cv2.connectedComponentsWithStats(binary_img, ltype=cv2.CV_16U)
    if number > 255:
        img_dtype = np.uint16
        if number > 65535:
            img_dtype = np.uint32
    else:
        img_dtype = np.uint8
    stats[:, 2] = stats[:, 0] + stats[:, 2]
    stats[:, 3] = stats[:, 1] + stats[:, 3]
    sorted_idx = np.argsort(stats[:, 4])[::-1]

    # Make sure that the first connected component (labelled 0) is the background and not the main shape
    size_ranked_stats = stats[sorted_idx, :]
    background = (size_ranked_stats[:, 0] == 0).astype(np.uint8) + (size_ranked_stats[:, 1] == 0).astype(np.uint8) + (
            size_ranked_stats[:, 2] == img.shape[1]).astype(np.uint8) + (
                         size_ranked_stats[:, 3] == img.shape[0]).astype(np.uint8)

    # background = ((size_ranked_stats[:, 0] == 0) & (size_ranked_stats[:, 1] == 0) & (size_ranked_stats[:, 2] == img.shape[1]) & (size_ranked_stats[:, 3] == img.shape[0]))

    touch_borders = np.nonzero(background > 2)[0]
    # if not isinstance(touch_borders, np.int64):
    #     touch_borders = touch_borders[0]
    # Most of the time, the background should be the largest shape and therefore has the index 0,
    # Then, if there is at least one shape touching more than 2 borders and having not the index 0, solve:
    if np.any(touch_borders != 0):
        # If there is only one shape touching borders, it means that background is not at its right position (i.e. 0)
        if len(touch_borders) == 1:
            # Then exchange that shape position with background position
            shape = sorted_idx[0]  # Store shape position in the first place
            back = sorted_idx[touch_borders[0]]  # Store back position in the first place
            sorted_idx[touch_borders[0]] = shape  # Put shape position at the previous place of back and conversely
            sorted_idx[0] = back
        # If there are two shapes, it means that the main shape grew sufficiently to reach at least 3 borders
        # We assume that it grew larger than background
        else:
            shape = sorted_idx[0]
            back = sorted_idx[1]
            sorted_idx[1] = shape
            sorted_idx[0] = back
            # Put shape position at the previous place of back and conversely


    stats = stats[sorted_idx, :]
    centers = centers[sorted_idx, :]

    new_order = np.zeros_like(binary_img, dtype=img_dtype)

    for i, val in enumerate(sorted_idx):
        new_order[img == val] = i
    return new_order, stats, centers

close_holes(binary_img)

Close holes in a binary image using connected components analysis.

This function identifies and closes small holes within the foreground objects of a binary image. It uses connected component analysis to find and fill holes that are smaller than the main object.

Parameters:

Name Type Description Default
binary_img ndarray of uint8

Binary input image where holes need to be closed.

 required

Returns:

Name Type Description
out ndarray of uint8

Binary image with closed holes.

Examples:

>>> binary_img = np.zeros((10, 10), dtype=np.uint8)
>>> binary_img[2:8, 2:8] = 1
>>> binary_img[4:6, 4:6] = 0  # Creating a hole
>>> result = close_holes(binary_img)
>>> print(result)
[[0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0]
 [0 0 1 1 1 1 1 1 0 0]
 [0 0 1 1 1 1 1 1 0 0]
 [0 0 1 1 1 1 1 1 0 0]
 [0 0 1 1 1 1 1 1 0 0]
 [0 0 1 1 1 1 1 1 0 0]
 [0 0 1 1 1 1 1 1 0 0]
 [0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def close_holes(binary_img: NDArray[np.uint8]) -> NDArray[np.uint8]:
    """
    Close holes in a binary image using connected components analysis.

    This function identifies and closes small holes within the foreground objects of a binary image. It uses connected component analysis to find and fill holes that are smaller than the main object.

    Parameters
    ----------
    binary_img : ndarray of uint8
        Binary input image where holes need to be closed.

    Returns
    -------
    out : ndarray of uint8
        Binary image with closed holes.

    Examples
    --------
    >>> binary_img = np.zeros((10, 10), dtype=np.uint8)
    >>> binary_img[2:8, 2:8] = 1
    >>> binary_img[4:6, 4:6] = 0  # Creating a hole
    >>> result = close_holes(binary_img)
    >>> print(result)
    [[0 0 0 0 0 0 0 0 0 0]
     [0 0 0 0 0 0 0 0 0 0]
     [0 0 1 1 1 1 1 1 0 0]
     [0 0 1 1 1 1 1 1 0 0]
     [0 0 1 1 1 1 1 1 0 0]
     [0 0 1 1 1 1 1 1 0 0]
     [0 0 1 1 1 1 1 1 0 0]
     [0 0 1 1 1 1 1 1 0 0]
     [0 0 0 0 0 0 0 0 0 0]
     [0 0 0 0 0 0 0 0 0 0]]
    """
    if binary_img.dtype != np.uint8:
        binary_img = binary_img.astype(np.uint8)
    nb, new_order = cv2.connectedComponents(1 - binary_img)
    if nb > 2:
        binary_img[new_order > 1] = 1
    return binary_img

create_ellipse(vsize, hsize, min_size=0)

Create a 2D array representing an ellipse with given vertical and horizontal sizes.

This function generates a NumPy boolean array where each element is True if the point lies within or on the boundary of an ellipse defined by its vertical and horizontal radii. The ellipse is centered at the center of the array, which corresponds to the midpoint of the given dimensions.

Parameters:

Name Type Description Default
vsize int

Vertical size (number of rows) in the output 2D array.

 required
hsize int

Horizontal size (number of columns) in the output 2D array.

 required

Returns:

Type Description
NDArray[bool]

A boolean NumPy array of shape (vsize, hsize) where True indicates that a pixel lies within or on the boundary of an ellipse centered at the image's center with radii determined by half of the dimensions.
Source code in src/cellects/image_analysis/morphological_operations.py 
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@njit()
def create_ellipse(vsize: int, hsize: int, min_size: int=0) -> NDArray[np.uint8]:
    """
    Create a 2D array representing an ellipse with given vertical and horizontal sizes.

    This function generates a NumPy boolean array where each element is `True` if the point lies within or on
    the boundary of an ellipse defined by its vertical and horizontal radii. The ellipse is centered at the center
    of the array, which corresponds to the midpoint of the given dimensions.

    Parameters
    ----------
    vsize : int
        Vertical size (number of rows) in the output 2D array.
    hsize : int
        Horizontal size (number of columns) in the output 2D array.

    Returns
    -------
    NDArray[bool]
        A boolean NumPy array of shape `(vsize, hsize)` where `True` indicates that a pixel lies within or on
        the boundary of an ellipse centered at the image's center with radii determined by half of the dimensions.
    """
    # Use default values if input sizes are zero
    vsize = min_size if vsize == 0 else vsize
    hsize = min_size if hsize == 0 else hsize

    # Compute radii (half of each size)
    vr = hsize // 2
    hr = vsize // 2

    result = np.empty((vsize, hsize), dtype=np.bool_)
    if vr > 0 and hr > 0:
        for i in range(vsize):
            for j in range(hsize):
                x = i
                y = j
                lhs = ((x - hr) ** 2 / (hr ** 2)) + ((y - vr) ** 2 / (vr ** 2))
                result[i, j] = lhs <= 1
    else:
        result[hr, vr] = True
    return result

create_mask(dims, minmax, shape)

Create a boolean mask based on given dimensions and min/max coordinates.

Parameters:

Name Type Description Default
dims Tuple[int, int]

The dimensions of the mask (height and width).

 required
minmax Tuple[int, int, int, int]

The minimum and maximum coordinates for the mask (x_min, x_max, y_min, y_max).

 required
shape str

The shape of the mask. Should be either 'circle' or any other value for a rectangular mask.

 required

Returns:

Type Description
ndarray[bool]

A boolean NumPy array with the same dimensions as dims, initialized to False, where the specified region (or circle) is set to True.

Raises:

Type Description
ValueError

If the shape is 'circle' and the ellipse creation fails.
Notes

If shape is not 'circle', a rectangular mask will be created. The ellipse creation method used may have specific performance considerations.

Examples:

>>> mask = create_mask((5, 6), (0, 5, 1, 5), 'circle')
>>> print(mask)
[[False False False  True False False]
 [False False  True  True  True False]
 [False  True  True  True  True False]
 [False False  True  True  True False]
 [False False False  True False False]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def create_mask(dims: Tuple, minmax: Tuple, shape: str):
    """

    Create a boolean mask based on given dimensions and min/max coordinates.

    Parameters
    ----------
    dims : Tuple[int, int]
        The dimensions of the mask (height and width).
    minmax : Tuple[int, int, int, int]
        The minimum and maximum coordinates for the mask (x_min, x_max,
        y_min, y_max).
    shape : str
        The shape of the mask. Should be either 'circle' or any other value for a rectangular mask.

    Returns
    -------
    np.ndarray[bool]
        A boolean NumPy array with the same dimensions as `dims`, initialized to False,
        where the specified region (or circle) is set to True.

    Raises
    ------
    ValueError
        If the shape is 'circle' and the ellipse creation fails.

    Notes
    -----
    If `shape` is not 'circle', a rectangular mask will be created. The ellipse
    creation method used may have specific performance considerations.

    Examples
    --------
    >>> mask = create_mask((5, 6), (0, 5, 1, 5), 'circle')
    >>> print(mask)
    [[False False False  True False False]
     [False False  True  True  True False]
     [False  True  True  True  True False]
     [False False  True  True  True False]
     [False False False  True False False]]
     """
    mask = np.zeros(dims[:2], dtype=bool)
    if shape == 'circle':
        ellipse = create_ellipse(minmax[1] - minmax[0], minmax[3] - minmax[2])
        mask[minmax[0]:minmax[1], minmax[2]:minmax[3], ...] = ellipse
    else:
        mask[minmax[0]:minmax[1], minmax[2]:minmax[3]] = 1
    return mask

draw_img_with_mask(img, dims, minmax, shape, drawing, only_contours=False, dilate_mask=0)

Draw an image with a mask and optional contours.

Draws a subregion of the input image using a specified shape (circle or rectangle), which can be dilated. The mask can be limited to contours only, and an optional drawing (overlay) can be applied within the masked region.

Parameters:

Name Type Description Default
img NDArray

The input image to draw on.

 required
dims Tuple[int, int]

Dimensions of the subregion (width, height).

 required
minmax Tuple[int, int, int, int]

Coordinates of the subregion (x_start, x_end, y_start, y_end).

 required
shape str

Shape of the mask to draw ('circle' or 'rectangle').

 required
drawing Tuple[NDArray, NDArray, NDArray]

Optional drawing (overlay) to apply within the masked region.

 required
only_contours bool

If True, draw only the contours of the shape. Default is False.

 False
dilate_mask int

Number of iterations for dilating the mask. Default is 0.

 0

Returns:

Type Description
NDArray

The modified image with the applied mask and drawing.
Notes

This function assumes that the input image is in BGR format (OpenCV style).

Examples:

>>> dim = (100, 100, 3)
>>> img = np.zeros(dim)
>>> result = draw_img_with_mask(img, dim, (50, 75, 50, 75), 'circle', (0, 255, 0))
>>> print((result == 255).sum())
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Source code in src/cellects/image_analysis/morphological_operations.py 
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def draw_img_with_mask(img:NDArray, dims: Tuple, minmax: Tuple, shape: str, drawing: Tuple, only_contours: bool=False,
                       dilate_mask: int=0) -> NDArray:
    """

    Draw an image with a mask and optional contours.

    Draws a subregion of the input image using a specified shape (circle or rectangle),
    which can be dilated. The mask can be limited to contours only, and an optional
    drawing (overlay) can be applied within the masked region.

    Parameters
    ----------
    img : NDArray
        The input image to draw on.
    dims : Tuple[int, int]
        Dimensions of the subregion (width, height).
    minmax : Tuple[int, int, int, int]
        Coordinates of the subregion (x_start, x_end, y_start, y_end).
    shape : str
        Shape of the mask to draw ('circle' or 'rectangle').
    drawing : Tuple[NDArray, NDArray, NDArray]
        Optional drawing (overlay) to apply within the masked region.
    only_contours : bool, optional
        If True, draw only the contours of the shape. Default is False.
    dilate_mask : int, optional
        Number of iterations for dilating the mask. Default is 0.

    Returns
    -------
    NDArray
        The modified image with the applied mask and drawing.

    Notes
    -----
    This function assumes that the input image is in BGR format (OpenCV style).

    Examples
    --------
    >>> dim = (100, 100, 3)
    >>> img = np.zeros(dim)
    >>> result = draw_img_with_mask(img, dim, (50, 75, 50, 75), 'circle', (0, 255, 0))
    >>> print((result == 255).sum())
    441
    """
    if shape == 'circle':
        mask = create_ellipse(minmax[1] - minmax[0], minmax[3] - minmax[2]).astype(np.uint8)
        if only_contours:
            mask = get_contours(mask)
    else:
        if only_contours:
            mask = 1 - image_borders((minmax[1] - minmax[0], minmax[3] - minmax[2]))
        else:
            mask = np.ones((minmax[1] - minmax[0], minmax[3] - minmax[2]), np.uint8)
    if dilate_mask:
        mask = cv2.dilate(mask, kernel=cross_33, iterations=dilate_mask)
    anti_mask = 1 - mask
    img[minmax[0]:minmax[1], minmax[2]:minmax[3], 0] *= anti_mask
    img[minmax[0]:minmax[1], minmax[2]:minmax[3], 1] *= anti_mask
    img[minmax[0]:minmax[1], minmax[2]:minmax[3], 2] *= anti_mask
    if isinstance(drawing, np.ndarray):
        if drawing.dtype != np.uint8:
            drawing = bracket_to_uint8_image_contrast(drawing)
        drawing = [drawing[:, :, 0], drawing[:, :, 1], drawing[:, :, 2]]
    img[minmax[0]:minmax[1], minmax[2]:minmax[3], 0] += mask * drawing[0]
    img[minmax[0]:minmax[1], minmax[2]:minmax[3], 1] += mask * drawing[1]
    img[minmax[0]:minmax[1], minmax[2]:minmax[3], 2] += mask * drawing[2]
    return img

draw_me_a_sun(main_shape, ray_length_coef=4)

Draw a sun-shaped pattern on an image based on the main shape and ray length coefficient.

This function takes an input binary image (main_shape) and draws sun rays from the perimeter of that shape. The length of the rays is controlled by a coefficient. The function ensures that rays do not extend beyond the image borders.

Parameters:

Name Type Description Default
main_shape ndarray of bool or int

Binary input image where the main shape is defined.

 required
ray_length_coef float

Coefficient to control the length of sun rays. Defaults to 2.

 4

Returns:

Name Type Description
rays ndarray

Indices of the rays drawn.
sun ndarray

Image with sun rays drawn on it.

Examples:

>>> main_shape = np.zeros((10, 10), dtype=np.uint8)
>>> main_shape[4:7, 3:6] = 1
>>> rays, sun = draw_me_a_sun(main_shape)
>>> print(sun)
Source code in src/cellects/image_analysis/morphological_operations.py 
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def draw_me_a_sun(main_shape: NDArray, ray_length_coef: int=4) -> Tuple[NDArray, NDArray]:
    """
    Draw a sun-shaped pattern on an image based on the main shape and ray length coefficient.

    This function takes an input binary image (main_shape) and draws sun rays
    from the perimeter of that shape. The length of the rays is controlled by a coefficient.
    The function ensures that rays do not extend beyond the image borders.

    Parameters
    ----------
    main_shape : ndarray of bool or int
        Binary input image where the main shape is defined.
    ray_length_coef : float, optional
        Coefficient to control the length of sun rays. Defaults to 2.

    Returns
    -------
    rays : ndarray
        Indices of the rays drawn.
    sun : ndarray
        Image with sun rays drawn on it.

    Examples
    --------
    >>> main_shape = np.zeros((10, 10), dtype=np.uint8)
    >>> main_shape[4:7, 3:6] = 1
    >>> rays, sun = draw_me_a_sun(main_shape)
    >>> print(sun)

    """
    nb, shapes, stats, center = cv2.connectedComponentsWithStats(main_shape)
    sun = np.zeros(main_shape.shape, np.uint32)
    rays = []
    r = 0
    for i in range(1, nb):
        shape_i = cv2.dilate((shapes == i).astype(np.uint8), kernel=cross_33)
        # shape_i = (shapes == i).astype(np.uint8)
        contours = get_contours(shape_i)
        first_ring_idx = np.nonzero(contours)
        centroid = np.round((center[i, 1], center[i, 0])).astype(np.int64)
        second_ring_y = centroid[0] + ((first_ring_idx[0] - centroid[0]) * ray_length_coef)
        second_ring_x = centroid[1] + ((first_ring_idx[1] - centroid[1]) * ray_length_coef)

        second_ring_y[second_ring_y < 0] = 0
        second_ring_x[second_ring_x < 0] = 0

        second_ring_y[second_ring_y > main_shape.shape[0] - 1] = main_shape.shape[0] - 1
        second_ring_x[second_ring_x > main_shape.shape[1] - 1] = main_shape.shape[1] - 1
        for j in range(len(second_ring_y)):
            r += 1
            fy, fx, sy, sx = first_ring_idx[0][j], first_ring_idx[1][j], second_ring_y[j], second_ring_x[j]
            line = get_line_points((fy, fx), (sy, sx))
            sun[line[:, 0], line[:, 1]] = r
            rays.append(r)
    return np.array(rays), sun

dynamically_expand_to_fill_holes(binary_video, holes)

Fill the holes in a binary video by progressively expanding the shape made of ones.

Parameters:

Name Type Description Default
binary_video ndarray of uint8

The binary video where holes need to be filled.

 required
holes ndarray of uint8

Array representing the holes in the binary video.

 required

Returns:

Name Type Description
out tuple of ndarray of uint8, int, and ndarray of float32

The modified binary video with filled holes, the end time when all holes are filled, and an array of distances against time used to fill the holes.

Examples:

>>> binary_video = np.zeros((10, 640, 480), dtype=np.uint8)
>>> binary_video[:, 300:400, 220:240] = 1
>>> holes = np.zeros((640, 480), dtype=np.uint8)
>>> holes[340:360, 228:232] = 1
>>> filled_video, end_time, distances = dynamically_expand_to_fill_holes(binary_video, holes)
>>> print(filled_video.shape)  # Should print (10, 640, 480)
(10, 640, 480)
Source code in src/cellects/image_analysis/morphological_operations.py 
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def dynamically_expand_to_fill_holes(binary_video: NDArray[np.uint8], holes: NDArray[np.uint8]) -> Tuple[NDArray[np.uint8], int, NDArray[np.float32]]:
    """
    Fill the holes in a binary video by progressively expanding the shape made of ones.

    Parameters
    ----------
    binary_video : ndarray of uint8
        The binary video where holes need to be filled.
    holes : ndarray of uint8
        Array representing the holes in the binary video.

    Returns
    -------
    out : tuple of ndarray of uint8, int, and ndarray of float32
        The modified binary video with filled holes,
        the end time when all holes are filled, and
        an array of distances against time used to fill the holes.

    Examples
    --------
    >>> binary_video = np.zeros((10, 640, 480), dtype=np.uint8)
    >>> binary_video[:, 300:400, 220:240] = 1
    >>> holes = np.zeros((640, 480), dtype=np.uint8)
    >>> holes[340:360, 228:232] = 1
    >>> filled_video, end_time, distances = dynamically_expand_to_fill_holes(binary_video, holes)
    >>> print(filled_video.shape)  # Should print (10, 640, 480)
    (10, 640, 480)
    """
    #first move should be the time at wich the first pixel hole could have been covered
    #it should ask how much time the shape made to cross a distance long enough to overlap all holes
    holes_contours = cv2.dilate(holes, cross_33, borderType=cv2.BORDER_CONSTANT, borderValue=0)
    field = rounded_inverted_distance_transform(binary_video[0, :, :], (binary_video.shape[0] - 1))
    field2 = inverted_distance_transform(binary_video[0, :, :], (binary_video.shape[0] - 1))
    holes_contours = holes_contours * field * binary_video[- 1, :, :]
    holes[np.nonzero(holes)] = field[np.nonzero(holes)]
    if np.any(holes_contours):
        # Find the relationship between distance and time
        distance_against_time, holes_time_start, holes_time_end = get_radius_distance_against_time(binary_video, holes_contours)
        # Use that vector to progressively fill holes at the same speed as shape grows
        for t in np.arange(len(distance_against_time)):
            new_order, stats, centers = cc((holes >= distance_against_time[t]).astype(np.uint8))
            for comp_i in np.arange(1, stats.shape[0]):
                past_image = binary_video[holes_time_start + t, :, :].copy()
                with_new_comp = new_order == comp_i
                past_image[with_new_comp] = 1
                nb_comp, image_garbage = cv2.connectedComponents(past_image)
                if nb_comp == 2:
                    binary_video[holes_time_start + t, :, :][with_new_comp] = 1
        # Make sure that holes remain filled from holes_time_end to the end of the video
        for t in np.arange((holes_time_end + 1), binary_video.shape[0]):
            past_image = binary_video[t, :, :]
            past_image[holes >= distance_against_time[-1]] = 1
            binary_video[t, :, :] = past_image
    else:
        holes_time_end = None
        distance_against_time = np.array([1, 2], dtype=np.float32)

    return binary_video, holes_time_end, distance_against_time

expand_until_neighbor_center_gets_nearer_than_own(shape_to_expand, without_shape_i, shape_original_centroid, ref_centroids, kernel)

Expand a shape until its neighbor's centroid is closer than its own.

This function takes in several numpy arrays representing shapes and their centroids, and expands the input shape until the distance to the nearest neighboring centroid is less than or equal to the distance between the shape's contour and its own centroid.

Parameters:

Name Type Description Default
shape_to_expand ndarray of uint8

The binary shape to be expanded.

 required
without_shape_i ndarray of uint8

A binary array representing the area without the shape.

 required
shape_original_centroid ndarray

The centroid of the original shape.

 required
ref_centroids ndarray

Reference centroids to compare distances with.

 required
kernel ndarray

The kernel for dilation operation.

 required

Returns:

Type Description
ndarray of uint8

The expanded shape.
Source code in src/cellects/image_analysis/morphological_operations.py 
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def expand_until_neighbor_center_gets_nearer_than_own(shape_to_expand: NDArray[np.uint8], without_shape_i: NDArray[np.uint8],
                                                      shape_original_centroid: NDArray,
                                                      ref_centroids: NDArray, kernel: NDArray) -> NDArray[np.uint8]:
    """
    Expand a shape until its neighbor's centroid is closer than its own.

    This function takes in several numpy arrays representing shapes and their
    centroids, and expands the input shape until the distance to the nearest
    neighboring centroid is less than or equal to the distance between the shape's
    contour and its own centroid.

    Parameters
    ----------
    shape_to_expand : ndarray of uint8
        The binary shape to be expanded.
    without_shape_i : ndarray of uint8
        A binary array representing the area without the shape.
    shape_original_centroid : ndarray
        The centroid of the original shape.
    ref_centroids : ndarray
        Reference centroids to compare distances with.
    kernel : ndarray
        The kernel for dilation operation.

    Returns
    -------
    ndarray of uint8
        The expanded shape.
    """
    previous_shape_to_expand = shape_to_expand.copy()
    if shape_to_expand.any():
        without_shape = without_shape_i.copy()
        if ref_centroids.shape[0] > 1:
            # Calculate the distance between the focal shape centroid and its 10% nearest neighbor centroids
            centroid_distances = np.sqrt(np.square(ref_centroids[1:, 0] - shape_original_centroid[0]) + np.square(
                ref_centroids[1:, 1] - shape_original_centroid[1]))
            nearest_shapes = np.where(np.greater_equal(np.quantile(centroid_distances, 0.1), centroid_distances))[0]

            # Use the nearest neighbor distance as a maximal reference to get the minimal distance between the border of the shape and the neighboring centroids
            neighbor_mindist = np.min(centroid_distances)
            idx = np.nonzero(shape_to_expand)
            for shape_j in nearest_shapes:
                neighbor_mindist = np.minimum(neighbor_mindist, np.min(
                    np.sqrt(np.square(ref_centroids[shape_j, 0] - idx[1]) + np.square(ref_centroids[shape_j, 1] - idx[0]))))
            neighbor_mindist *= 0.5
            # Get the maximal distance of the focal shape between its contour and its centroids
            itself_maxdist = np.max(
                np.sqrt(np.square(shape_original_centroid[0] - idx[1]) + np.square(shape_original_centroid[1] - idx[0])))
        else:
            itself_maxdist = np.max(shape_to_expand.shape)
            neighbor_mindist = itself_maxdist
            nearest_shapes = []
        # Put 1 at the border of the reference image in order to be able to stop the while loop once border reached
        without_shape[0, :] = 1
        without_shape[:, 0] = 1
        without_shape[without_shape.shape[0] - 1, :] = 1
        without_shape[:, without_shape.shape[1] - 1] = 1

        # Compare the distance between the contour of the shape and its centroid with this contour with the centroids of neighbors
        # Continue as the distance made by the shape (from its centroid) keeps being smaller than its distance with the nearest centroid.
        while np.logical_and(np.any(np.less_equal(itself_maxdist, neighbor_mindist)),
                             np.count_nonzero(shape_to_expand * without_shape) == 0):
            previous_shape_to_expand = shape_to_expand.copy()
            # Dilate the shape by the kernel size
            shape_to_expand = cv2.dilate(shape_to_expand, kernel, iterations=1,
                                         borderType=cv2.BORDER_CONSTANT | cv2.BORDER_ISOLATED)
            # Extract the new connected component
            shape_nb, shape_to_expand = cv2.connectedComponents(shape_to_expand, ltype=cv2.CV_16U)
            shape_to_expand = shape_to_expand.astype(np.uint8)
            # Use the nex shape coordinates to calculate the new distances of the shape with its centroid and with neighboring centroids
            idx = np.nonzero(shape_to_expand)
            for shape_j in nearest_shapes:
                neighbor_mindist = np.minimum(neighbor_mindist, np.min(
                    np.sqrt(np.square(ref_centroids[shape_j, 0] - idx[1]) + np.square(ref_centroids[shape_j, 1] - idx[0]))))
            itself_maxdist = np.max(
                np.sqrt(np.square(shape_original_centroid[0] - idx[1]) + np.square(shape_original_centroid[1] - idx[0])))
    return previous_shape_to_expand

find_major_incline(vector, natural_noise)

Find the major incline section in a vector.

This function identifies the segment of a vector that exhibits the most significant change in values, considering a specified natural noise level. It returns the left and right indices that define this segment.

Parameters:

Name Type Description Default
vector ndarray of float64

Input data vector where the incline needs to be detected.

 required
natural_noise float

The acceptable noise level for determining the incline.

 required

Returns:

Type Description
Tuple[int, int]

A tuple containing two integers: the left and right indices of the major incline section in the vector.

Examples:

>>> vector = np.array([3, 5, 7, 9, 10])
>>> natural_noise = 2.5
>>> left, right = find_major_incline(vector, natural_noise)
>>> (left, right)
(0, 1)
Source code in src/cellects/image_analysis/morphological_operations.py 
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def find_major_incline(vector: NDArray, natural_noise: float) -> Tuple[int, int]:
    """
    Find the major incline section in a vector.

    This function identifies the segment of a vector that exhibits
    the most significant change in values, considering a specified
    natural noise level. It returns the left and right indices that
    define this segment.

    Parameters
    ----------
    vector : ndarray of float64
        Input data vector where the incline needs to be detected.
    natural_noise : float
        The acceptable noise level for determining the incline.

    Returns
    -------
    Tuple[int, int]
        A tuple containing two integers: the left and right indices
        of the major incline section in the vector.

    Examples
    --------
    >>> vector = np.array([3, 5, 7, 9, 10])
    >>> natural_noise = 2.5
    >>> left, right = find_major_incline(vector, natural_noise)
    >>> (left, right)
    (0, 1)
    """
    left = 0
    right = 1
    ref_length = np.max((5, 2 * natural_noise))
    vector = moving_average(vector, 5)
    ref_extent = np.ptp(vector)
    extent = ref_extent
    # Find the left limit:
    while len(vector) > ref_length and extent > (ref_extent - (natural_noise / 4)):
        vector = vector[1:]
        extent = np.ptp(vector)
        left += 1
    # And the right one:
    extent = ref_extent
    while len(vector) > ref_length and extent > (ref_extent - natural_noise / 2):
        vector = vector[:-1]
        extent = np.ptp(vector)
        right += 1
    # And the left again, with stronger stringency:
    extent = ref_extent
    while len(vector) > ref_length and extent > (ref_extent - natural_noise):
        vector = vector[1:]
        extent = np.ptp(vector)
        left += 1
    # When there is no incline, put back left and right to 0
    if len(vector) <= ref_length:
        left = 0
        right = 1
    return left, right

find_median_shape(binary_3d_matrix)

Find the median shape from a binary 3D matrix.

This function computes the median 2D slice of a binary (0/1) 3D matrix by finding which voxels appear in at least half of the slices.

Parameters:

Name Type Description Default
binary_3d_matrix ndarray of uint8

Input 3D binary matrix where each slice is a 2D array.

 required

Returns:

Type Description
ndarray of uint8

Median shape as a 2D binary matrix where the same voxels that appear in at least half of the input slices are set to 1.

Examples:

>>> binary_3d_matrix = np.random.randint(0, 2, (10, 5, 5), dtype=np.uint8)
>>> median_shape = find_median_shape(binary_3d_matrix)
>>> print(median_shape)
Source code in src/cellects/image_analysis/morphological_operations.py 
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def find_median_shape(binary_3d_matrix: NDArray[np.uint8]) -> NDArray[np.uint8]:
    """
    Find the median shape from a binary 3D matrix.

    This function computes the median 2D slice of a binary (0/1) 3D matrix
    by finding which voxels appear in at least half of the slices.

    Parameters
    ----------
    binary_3d_matrix : ndarray of uint8
        Input 3D binary matrix where each slice is a 2D array.

    Returns
    -------
    ndarray of uint8
        Median shape as a 2D binary matrix where the same voxels
        that appear in at least half of the input slices are set to 1.

    Examples
    --------
    >>> binary_3d_matrix = np.random.randint(0, 2, (10, 5, 5), dtype=np.uint8)
    >>> median_shape = find_median_shape(binary_3d_matrix)
    >>> print(median_shape)
    """
    binary_2d_matrix = np.apply_along_axis(np.sum, 0, binary_3d_matrix)
    median_shape = np.zeros(binary_2d_matrix.shape, dtype=np.uint8)
    median_shape[np.greater_equal(binary_2d_matrix, binary_3d_matrix.shape[0] // 2)] = 1
    return median_shape

get_all_line_coordinates(start_point, end_points)

Get all line coordinates between start point and end points.

This function computes the coordinates of lines connecting a start point to multiple end points, converting input arrays to float if necessary before processing.

Parameters:

Name Type Description Default
start_point NDArray[float]

Starting coordinate point for the lines. Can be of any numeric type, will be converted to float if needed.

 required
end_points NDArray[float]

Array of end coordinate points for the lines. Can be of any numeric type, will be converted to float if needed.

 required

Returns:

Name Type Description
out List[NDArray[int]]

A list of numpy arrays containing the coordinates of each line as integer values.

Examples:

>>> start_point = np.array([0, 0])
>>> end_points = np.array([[1, 2], [3, 4]])
>>> get_all_line_coordinates(start_point, end_points)
[array([[0, 0],
   [0, 1],
   [1, 2]], dtype=uint64), array([[0, 0],
   [1, 1],
   [1, 2],
   [2, 3],
   [3, 4]], dtype=uint64)]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def get_all_line_coordinates(start_point: NDArray[int], end_points: NDArray[int]) -> NDArray[int]:
    """
    Get all line coordinates between start point and end points.

    This function computes the coordinates of lines connecting a
    start point to multiple end points, converting input arrays to float
    if necessary before processing.

    Parameters
    ----------
    start_point : NDArray[float]
        Starting coordinate point for the lines. Can be of any numeric type,
        will be converted to float if needed.
    end_points : NDArray[float]
        Array of end coordinate points for the lines. Can be of any
        numeric type, will be converted to float if needed.

    Returns
    -------
    out : List[NDArray[int]]
        A list of numpy arrays containing the coordinates of each line
        as integer values.

    Examples
    --------
    >>> start_point = np.array([0, 0])
    >>> end_points = np.array([[1, 2], [3, 4]])
    >>> get_all_line_coordinates(start_point, end_points)
    [array([[0, 0],
       [0, 1],
       [1, 2]], dtype=uint64), array([[0, 0],
       [1, 1],
       [1, 2],
       [2, 3],
       [3, 4]], dtype=uint64)]
    """
    lines = []
    for end_point in end_points:
        line_coords = get_line_points(start_point, end_point)
        lines.append(np.array(line_coords, dtype=np.uint64))
    return lines

get_bb_with_moving_centers(motion_list, all_specimens_have_same_direction, original_shape_hsize, binary_image, y_boundaries)

Get the bounding boxes with moving centers.

Parameters:

Name Type Description Default
motion_list list

List of binary images representing the motion frames.

 required
all_specimens_have_same_direction bool

Boolean indicating if all specimens move in the same direction.

 required
original_shape_hsize int or None

Original height size of the shape. If None, a default kernel size is used.

 required
binary_image NDArray

Binary image of the initial frame.

 required
y_boundaries NDArray

Array defining the y-boundaries for ranking shapes.

 required

Returns:

Type Description
tuple

A tuple containing: - top : NDArray Array of top coordinates for each bounding box. - bot : NDArray Array of bottom coordinates for each bounding box. - left : NDArray Array of left coordinates for each bounding box. - right : NDArray Array of right coordinates for each bounding box. - ordered_image_i : NDArray Updated binary image with the final ranked shapes.
Notes

This function processes each frame to expand and confirm shapes, updating centroids if necessary. It uses morphological operations like dilation to detect shape changes over frames.

Examples:

>>> top, bot, left, right, ordered_image = _get_bb_with_moving_centers(motion_frames, True, None, binary_img, y_bounds)
>>> print("Top coordinates:", top)
>>> print("Bottom coordinates:", bot)
Source code in src/cellects/image_analysis/morphological_operations.py 
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def get_bb_with_moving_centers(motion_list: list, all_specimens_have_same_direction: bool,
                                original_shape_hsize: int, binary_image: NDArray,
                                y_boundaries: NDArray):
    """
    Get the bounding boxes with moving centers.

    Parameters
    ----------
    motion_list : list
        List of binary images representing the motion frames.
    all_specimens_have_same_direction : bool
        Boolean indicating if all specimens move in the same direction.
    original_shape_hsize : int or None
        Original height size of the shape. If `None`, a default kernel size is used.
    binary_image : NDArray
        Binary image of the initial frame.
    y_boundaries : NDArray
        Array defining the y-boundaries for ranking shapes.

    Returns
    -------
    tuple
        A tuple containing:
        - top : NDArray
            Array of top coordinates for each bounding box.
        - bot : NDArray
            Array of bottom coordinates for each bounding box.
        - left : NDArray
            Array of left coordinates for each bounding box.
        - right : NDArray
            Array of right coordinates for each bounding box.
        - ordered_image_i : NDArray
            Updated binary image with the final ranked shapes.

    Notes
    -----
    This function processes each frame to expand and confirm shapes, updating centroids if necessary.
    It uses morphological operations like dilation to detect shape changes over frames.

    Examples
    --------
    >>> top, bot, left, right, ordered_image = _get_bb_with_moving_centers(motion_frames, True, None, binary_img, y_bounds)
    >>> print("Top coordinates:", top)
    >>> print("Bottom coordinates:", bot)
    """
    print("Read and segment each sample image and rank shapes from top to bot and from left to right")
    k_size = 3
    if original_shape_hsize is not None:
        k_size = int((np.ceil(original_shape_hsize / 5) * 2) + 1)
    big_kernel = create_ellipse(k_size, k_size, min_size=3).astype(np.uint8)

    ordered_stats, ordered_centroids, ordered_image = rank_from_top_to_bottom_from_left_to_right(
        binary_image, y_boundaries, get_ordered_image=True)
    blob_number = ordered_stats.shape[0]

    ordered_image_i = ordered_image.copy()
    logging.info("For each frame, expand each previously confirmed shape to add area to its maximal bounding box")
    for step_i in np.arange(1, len(motion_list)):
        previously_ordered_centroids = ordered_centroids.copy()
        new_image_i = motion_list[step_i].copy()
        detected_shape_number = blob_number + 1
        c = 0
        while c < 5 and detected_shape_number == blob_number + 1:
            c += 1
            image_i = new_image_i
            new_image_i = cv2.dilate(image_i, cross_33, iterations=1)
            detected_shape_number, _ = cv2.connectedComponents(new_image_i, connectivity=8)
        if c == 0:
            break
        else:
            for shape_i in range(blob_number):
                shape_to_expand = ordered_image_i == (shape_i + 1)
                if not shape_to_expand.any():
                    continue
                shape_to_expand = shape_to_expand.astype(np.uint8)
                without_shape_i = ordered_image_i.copy()
                without_shape_i[ordered_image_i == (shape_i + 1)] = 0
                if k_size != 3:
                    test_shape = expand_until_neighbor_center_gets_nearer_than_own(shape_to_expand, without_shape_i,
                                                                                   ordered_centroids[shape_i, :],
                                                                                   np.delete(ordered_centroids, shape_i,
                                                                                             axis=0), big_kernel)
                else:
                    test_shape = shape_to_expand
                test_shape = expand_until_neighbor_center_gets_nearer_than_own(test_shape, without_shape_i,
                                                                               ordered_centroids[shape_i, :],
                                                                               np.delete(ordered_centroids, shape_i,
                                                                                         axis=0), cross_33)
                confirmed_shape = test_shape * image_i
                ordered_image_i[confirmed_shape > 0] = shape_i + 1


            mask_to_display = np.zeros(image_i.shape, dtype=np.uint8)
            mask_to_display[ordered_image_i > 0] = 1

            # If the blob moves enough to drastically change its gravity center,
            # update the ordered centroids at each frame.
            detected_shape_number, mask_to_display = cv2.connectedComponents(mask_to_display,
                                                                             connectivity=8)

            mask_to_display = mask_to_display.astype(np.uint8)
            while np.logical_and(detected_shape_number - 1 != blob_number,
                                 np.sum(mask_to_display > 0) < mask_to_display.size):
                mask_to_display = cv2.dilate(mask_to_display, cross_33, iterations=1)
                detected_shape_number, mask_to_display = cv2.connectedComponents(mask_to_display,
                                                                                 connectivity=8)
                mask_to_display[np.nonzero(mask_to_display)] = 1
                mask_to_display = mask_to_display.astype(np.uint8)
            ordered_stats, ordered_centroids = rank_from_top_to_bottom_from_left_to_right(mask_to_display, y_boundaries)

            if all_specimens_have_same_direction:
                # Adjust each centroid position according to the maximal centroid displacement.
                x_diffs = ordered_centroids[:, 0] - previously_ordered_centroids[:, 0]
                if np.mean(x_diffs) > 0: # They moved left, we add to x
                    add_to_x = np.max(x_diffs) - x_diffs
                else: #They moved right, we remove from x
                    add_to_x = np.min(x_diffs) - x_diffs
                ordered_centroids[:, 0] = ordered_centroids[:, 0] + add_to_x

                y_diffs = ordered_centroids[:, 1] - previously_ordered_centroids[:, 1]
                if np.mean(y_diffs) > 0:  # They moved down, we add to y
                    add_to_y = np.max(y_diffs) - y_diffs
                else:  # They moved up, we remove from y
                    add_to_y = np.min(y_diffs) - y_diffs
                ordered_centroids[:, 1] = ordered_centroids[:, 1] + add_to_y

            ordered_image_i = mask_to_display

    # Save each bounding box
    top = np.zeros(blob_number, dtype=np.int64)
    bot = np.repeat(binary_image.shape[0], blob_number)
    left = np.zeros(blob_number, dtype=np.int64)
    right = np.repeat(binary_image.shape[1], blob_number)
    for shape_i in range(blob_number):
        shape_i_indices = np.where(ordered_image_i == shape_i + 1)
        left[shape_i] = np.min(shape_i_indices[1])
        right[shape_i] = np.max(shape_i_indices[1])
        top[shape_i] = np.min(shape_i_indices[0])
        bot[shape_i] = np.max(shape_i_indices[0])
    return top, bot, left, right, ordered_image_i

get_contours(binary_image)

Find and return the contours of a binary image.

This function erodes the input binary image using a 3x3 cross-shaped structuring element and then subtracts the eroded image from the original to obtain the contours.

Parameters:

Name Type Description Default
binary_image ndarray of uint8

Input binary image from which to extract contours.

 required

Returns:

Name Type Description
out ndarray of uint8

Image containing only the contours extracted from binary_image.

Examples:

>>> binary_image = np.zeros((10, 10), dtype=np.uint8)
>>> binary_image[2:8, 2:8] = 1
>>> result = get_contours(binary_image)
>>> print(result)
[[0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0]
 [0 0 1 1 1 1 1 1 0 0]
 [0 0 1 0 0 0 0 1 0 0]
 [0 0 1 0 0 0 0 1 0 0]
 [0 0 1 0 0 0 0 1 0 0]
 [0 0 1 0 0 0 0 1 0 0]
 [0 0 1 1 1 1 1 1 0 0]
 [0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def get_contours(binary_image: NDArray[np.uint8]) -> NDArray[np.uint8]:
    """
    Find and return the contours of a binary image.

    This function erodes the input binary image using a 3x3 cross-shaped
    structuring element and then subtracts the eroded image from the original to obtain the contours.

    Parameters
    ----------
    binary_image : ndarray of uint8
        Input binary image from which to extract contours.

    Returns
    -------
    out : ndarray of uint8
        Image containing only the contours extracted from `binary_image`.

    Examples
    --------
    >>> binary_image = np.zeros((10, 10), dtype=np.uint8)
    >>> binary_image[2:8, 2:8] = 1
    >>> result = get_contours(binary_image)
    >>> print(result)
    [[0 0 0 0 0 0 0 0 0 0]
     [0 0 0 0 0 0 0 0 0 0]
     [0 0 1 1 1 1 1 1 0 0]
     [0 0 1 0 0 0 0 1 0 0]
     [0 0 1 0 0 0 0 1 0 0]
     [0 0 1 0 0 0 0 1 0 0]
     [0 0 1 0 0 0 0 1 0 0]
     [0 0 1 1 1 1 1 1 0 0]
     [0 0 0 0 0 0 0 0 0 0]
     [0 0 0 0 0 0 0 0 0 0]]
    """
    if not isinstance(binary_image.dtype, np.uint8):
        binary_image = binary_image.astype(np.uint8)
    if np.all(binary_image):
        contours = 1 - image_borders(binary_image.shape)
    elif np.any(binary_image):
        eroded_binary = cv2.erode(binary_image, cross_33, borderType=cv2.BORDER_CONSTANT, borderValue=0)
        contours = binary_image - eroded_binary
    else:
        contours = binary_image
    return contours

get_largest_connected_component(segmentation)

Find the largest connected component in a segmentation image.

This function labels all connected components in a binary segmentation image, determines the size of each component, and returns information about the largest connected component.

Parameters:

Name Type Description Default
segmentation ndarray of uint8

Binary segmentation image where different integer values represent different connected components.

 required

Returns:

Type Description
Tuple[int, ndarray of bool]

A tuple containing: - The size of the largest connected component. - A boolean mask representing the largest connected component in the input segmentation image.

Examples:

>>> segmentation = np.zeros((10, 10), dtype=np.uint8)
>>> segmentation[2:6, 2:5] = 1
>>> segmentation[6:9, 6:9] = 1
>>> size, mask = get_largest_connected_component(segmentation)
>>> print(size)
12
Source code in src/cellects/image_analysis/morphological_operations.py 
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def get_largest_connected_component(segmentation: NDArray[np.uint8]) -> Tuple[np.int64, NDArray[bool]]:
    """
    Find the largest connected component in a segmentation image.

    This function labels all connected components in a binary
    segmentation image, determines the size of each component,
    and returns information about the largest connected component.

    Parameters
    ----------
    segmentation : ndarray of uint8
        Binary segmentation image where different integer values represent
        different connected components.

    Returns
    -------
    Tuple[int, ndarray of bool]
        A tuple containing:
        - The size of the largest connected component.
        - A boolean mask representing the largest connected
          component in the input segmentation image.

    Examples
    --------
    >>> segmentation = np.zeros((10, 10), dtype=np.uint8)
    >>> segmentation[2:6, 2:5] = 1
    >>> segmentation[6:9, 6:9] = 1
    >>> size, mask = get_largest_connected_component(segmentation)
    >>> print(size)
    12
    """
    labels = label(segmentation)
    assert(labels.max() != 0) # assume at least 1 CC
    con_comp_sizes = np.bincount(labels.flat)[1:]
    largest_idx = np.argmax(con_comp_sizes)
    largest_connected_component = labels == largest_idx + 1
    return con_comp_sizes[largest_idx], largest_connected_component

get_line_points(start, end)

Get line points between two endpoints using Bresenham's line algorithm.

This function calculates all the integer coordinate points that form a line between two endpoints using Bresenham's line algorithm. It is optimized for performance using Numba's just-in-time compilation.

Parameters:

Name Type Description Default
start tuple of int

The starting point coordinates (y0, x0).

 required
end tuple of int

The ending point coordinates (y1, x1).

 required

Returns:

Name Type Description
out ndarray of int

Array of points representing the line, with shape (N, 2), where N is the number of points on the line.

Examples:

>>> start = (0, 0)
>>> end = (1, 2)
>>> points = get_line_points(start, end)
>>> print(points)
[[0 0]
[0 1]
[1 2]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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@njit()
def get_line_points(start, end) -> NDArray[int]:
    """
    Get line points between two endpoints using Bresenham's line algorithm.

    This function calculates all the integer coordinate points that form a
    line between two endpoints using Bresenham's line algorithm. It is
    optimized for performance using Numba's just-in-time compilation.

    Parameters
    ----------
    start : tuple of int
        The starting point coordinates (y0, x0).
    end : tuple of int
        The ending point coordinates (y1, x1).

    Returns
    -------
    out : ndarray of int
        Array of points representing the line, with shape (N, 2), where N is
        the number of points on the line.

    Examples
    --------
    >>> start = (0, 0)
    >>> end = (1, 2)
    >>> points = get_line_points(start, end)
    >>> print(points)
    [[0 0]
    [0 1]
    [1 2]]
    """
    y0, x0 = start
    y1, x1 = end

    # Calculate differences
    dx = np.abs(x1 - x0)
    dy = np.abs(y1 - y0)

    # Determine step direction
    sx = 1 if x0 < x1 else -1
    sy = 1 if y0 < y1 else -1

    # Initialize
    err = dx - dy
    points = []
    x, y = x0, y0

    while True:
        points.append([y, x])

        # Check if we've reached the end
        if x == x1 and y == y1:
            break

        # Calculate error for next step
        e2 = 2 * err

        if e2 > -dy:
            err -= dy
            x += sx

        if e2 < dx:
            err += dx
            y += sy

    return np.array(points)

get_min_or_max_euclidean_pair(coords, min_or_max='max')

Find the pair of points in a given set with the minimum or maximum Euclidean distance.

Parameters:

Name Type Description Default
coords Union[ndarray, Tuple]

An Nx2 numpy array or a tuple of two arrays, each containing the x and y coordinates of points.

 required
min_or_max str

Whether to find the 'min' or 'max' distance pair. Default is 'max'.

 'max'

Returns:

Type Description
Tuple[ndarray, ndarray]

A tuple containing the coordinates of the two points that form the minimum or maximum distance pair.

Raises:

Type Description
ValueError

If min_or_max is not 'min' or 'max'.
Notes
  • The function first computes all pairwise distances in condensed form using pdist.
  • Then, it finds the index of the minimum or maximum distance.
  • Finally, it maps this index to the actual point indices using a binary search method.

Examples:

>>> coords = np.array([[0, 1], [2, 3], [4, 5]])
>>> point1, point2 = get_min_or_max_euclidean_pair(coords, min_or_max="max")
>>> print(point1)
[0 1]
>>> print(point2)
[4 5]
>>> coords = (np.array([0, 2, 4, 8, 1, 5]), np.array([0, 2, 4, 8, 0, 5]))
>>> point1, point2 = get_min_or_max_euclidean_pair(coords, min_or_max="min")
>>> print(point1)
[0 0]
>>> print(point2)
[1 0]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def get_min_or_max_euclidean_pair(coords, min_or_max: str="max") -> Tuple[np.ndarray, np.ndarray]:
    """
    Find the pair of points in a given set with the minimum or maximum Euclidean distance.

    Parameters
    ----------
    coords : Union[np.ndarray, Tuple]
        An Nx2 numpy array or a tuple of two arrays, each containing the x and y coordinates of points.
    min_or_max : str, optional
        Whether to find the 'min' or 'max' distance pair. Default is 'max'.

    Returns
    -------
    Tuple[np.ndarray, np.ndarray]
        A tuple containing the coordinates of the two points that form the minimum or maximum distance pair.

    Raises
    ------
    ValueError
        If `min_or_max` is not 'min' or 'max'.

    Notes
    -----
    - The function first computes all pairwise distances in condensed form using `pdist`.
    - Then, it finds the index of the minimum or maximum distance.
    - Finally, it maps this index to the actual point indices using a binary search method.

    Examples
    --------
    >>> coords = np.array([[0, 1], [2, 3], [4, 5]])
    >>> point1, point2 = get_min_or_max_euclidean_pair(coords, min_or_max="max")
    >>> print(point1)
    [0 1]
    >>> print(point2)
    [4 5]
    >>> coords = (np.array([0, 2, 4, 8, 1, 5]), np.array([0, 2, 4, 8, 0, 5]))
    >>> point1, point2 = get_min_or_max_euclidean_pair(coords, min_or_max="min")
    >>> print(point1)
    [0 0]
    >>> print(point2)
    [1 0]

    """
    if isinstance(coords, Tuple):
        coords = np.column_stack(coords)
    N = coords.shape[0]
    if N <= 1:
        return (coords[0], coords[0]) if N == 1 else None

    # Step 1: Compute all pairwise distances in condensed form
    distances = pdist(coords)

    # Step 2: Find the index of the maximum distance
    if min_or_max == "max":
        idx = np.argmax(distances)
    elif min_or_max == "min":
        idx = np.argmin(distances)
    else:
        raise ValueError

    # Step 3: Map this index to (i, j) using a binary search method

    def get_pair_index(k):
        low, high = 0, N
        while low < high:
            mid = (low + high) // 2
            total = mid * (2 * N - mid - 1) // 2
            if total <= k:
                low = mid + 1
            else:
                high = mid

        i = low - 1
        prev_sum = i * (2 * N - i - 1) // 2
        j_index_in_row = k - prev_sum
        return i, i + j_index_in_row + 1  # Ensure j > i

    i, j = get_pair_index(idx)
    return coords[i], coords[j]

get_minimal_distance_between_2_shapes(image_of_2_shapes, increase_speed=True)

Get the minimal distance between two shapes in an image.

This function calculates the minimal Euclidean distance between two different shapes represented by binary values 1 and 2 in a given image. It can optionally reduce the image size for faster processing.

Parameters:

Name Type Description Default
image_of_2_shapes ndarray of int8

Binary image containing two shapes to measure distance between.

 required
increase_speed bool

Flag to reduce image size for faster computation. Default is True.

 True

Returns:

Name Type Description
min_distance float64

The minimal Euclidean distance between the two shapes.

Examples:

>>> import numpy as np
>>> image = np.array([[1, 0], [0, 2]])
>>> distance = get_minimal_distance_between_2_shapes(image)
>>> print(distance)
expected output
Source code in src/cellects/image_analysis/morphological_operations.py 
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def get_minimal_distance_between_2_shapes(image_of_2_shapes: NDArray[np.uint8], increase_speed: bool=True) -> float:
    """
    Get the minimal distance between two shapes in an image.

    This function calculates the minimal Euclidean distance between
    two different shapes represented by binary values 1 and 2 in a given image.
    It can optionally reduce the image size for faster processing.

    Parameters
    ----------
    image_of_2_shapes : ndarray of int8
        Binary image containing two shapes to measure distance between.
    increase_speed : bool, optional
        Flag to reduce image size for faster computation. Default is True.

    Returns
    -------
    min_distance : float64
        The minimal Euclidean distance between the two shapes.

    Examples
    --------
    >>> import numpy as np
    >>> image = np.array([[1, 0], [0, 2]])
    >>> distance = get_minimal_distance_between_2_shapes(image)
    >>> print(distance)
    expected output
    """
    if increase_speed:
        shape1_idx, shape2_idx = reduce_image_size_for_speed(image_of_2_shapes)
    else:
        shape1_idx, shape2_idx = np.nonzero(image_of_2_shapes == 1), np.nonzero(image_of_2_shapes == 2)
    t = KDTree(np.transpose(shape1_idx))
    dists, nns = t.query(np.transpose(shape2_idx), 1)
    return np.min(dists)

get_quick_bounding_boxes(binary_image, ordered_image, ordered_stats)

Compute bounding boxes for shapes in a binary image.

Parameters:

Name Type Description Default
binary_image NDArray[uint8]

A 2D array representing the binary image.

 required
ordered_image NDArray

An array containing the ordered image data.

 required
ordered_stats NDArray

A 2D array with statistics about the shapes in the image.

 required

Returns:

Type Description
Tuple[NDArray, NDArray, NDArray, NDArray]

A tuple containing four arrays: - top: Array of y-coordinates for the top edge of bounding boxes. - bot: Array of y-coordinates for the bottom edge of bounding boxes. - left: Array of x-coordinates for the left edge of bounding boxes. - right: Array of x-coordinates for the right edge of bounding boxes.

Examples:

>>> binary_image = np.array([[0, 1], [0, 0], [1, 0]], dtype=np.uint8)
>>> ordered_image = np.array([[0, 1], [0, 0], [2, 0]], dtype=np.uint8)
>>> ordered_stats = np.array([[1, 0, 1, 1, 1], [0, 2, 1, 1, 1]], dtype=np.int32)
>>> top, bot, left, right = get_quick_bounding_boxes(binary_image, ordered_image, ordered_stats)
>>> print(top)
[-1  1]
>>> print(bot)
[2 4]
>>> print(left)
[0 -1]
>>> print(right)
[3 2]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def get_quick_bounding_boxes(binary_image: NDArray[np.uint8], ordered_image: NDArray, ordered_stats: NDArray) -> Tuple[NDArray, NDArray, NDArray, NDArray]:
    """
    Compute bounding boxes for shapes in a binary image.

    Parameters
    ----------
    binary_image : NDArray[np.uint8]
        A 2D array representing the binary image.
    ordered_image : NDArray
        An array containing the ordered image data.
    ordered_stats : NDArray
        A 2D array with statistics about the shapes in the image.

    Returns
    -------
    Tuple[NDArray, NDArray, NDArray, NDArray]
        A tuple containing four arrays:
        - top: Array of y-coordinates for the top edge of bounding boxes.
        - bot: Array of y-coordinates for the bottom edge of bounding boxes.
        - left: Array of x-coordinates for the left edge of bounding boxes.
        - right: Array of x-coordinates for the right edge of bounding boxes.

    Examples
    --------
    >>> binary_image = np.array([[0, 1], [0, 0], [1, 0]], dtype=np.uint8)
    >>> ordered_image = np.array([[0, 1], [0, 0], [2, 0]], dtype=np.uint8)
    >>> ordered_stats = np.array([[1, 0, 1, 1, 1], [0, 2, 1, 1, 1]], dtype=np.int32)
    >>> top, bot, left, right = get_quick_bounding_boxes(binary_image, ordered_image, ordered_stats)
    >>> print(top)
    [-1  1]
    >>> print(bot)
    [2 4]
    >>> print(left)
    [0 -1]
    >>> print(right)
    [3 2]
    """
    shapes = get_contours(binary_image)
    x_min = ordered_stats[:, 0]
    y_min = ordered_stats[:, 1]
    x_max = ordered_stats[:, 0] + ordered_stats[:, 2]
    y_max = ordered_stats[:, 1] + ordered_stats[:, 3]
    x_min_dist = shapes.shape[1]
    y_min_dist = shapes.shape[0]

    shapes *= ordered_image
    shape_nb = (len(np.unique(shapes)) - 1)
    i = 0
    a_indices, b_indices = np.triu_indices(shape_nb, 1)
    a_indices, b_indices = a_indices + 1, b_indices + 1
    all_distances = np.zeros((len(a_indices), 3), dtype=float)
    # For every pair of components, find the minimal distance
    for (a, b) in zip(a_indices, b_indices):
        x_dist = np.absolute(x_max[a - 1] - x_min[b - 1])
        y_dist = np.absolute(y_max[a - 1] - y_min[b - 1])
        if x_dist < 2 * x_min_dist and y_dist < 2 * y_min_dist:
            sub_shapes = np.logical_or(shapes == a, shapes == b) * shapes
            sub_shapes = sub_shapes[np.min((y_min[a - 1], y_min[b - 1])):np.max((y_max[a - 1], y_max[b - 1])),
                         np.min((x_min[a - 1], x_min[b - 1])):np.max((x_max[a - 1], x_max[b - 1]))]
            sub_shapes[sub_shapes == a] = 1
            sub_shapes[sub_shapes == b] = 2
            if np.any(sub_shapes == 1) and np.any(sub_shapes == 2):
                all_distances[i, :] = a, b, get_minimal_distance_between_2_shapes(sub_shapes, False)

                if x_dist > y_dist:
                    x_min_dist = np.min((x_min_dist, x_dist))
                else:
                    y_min_dist = np.min((y_min_dist, y_dist))
                i += 1
    shape_number = ordered_stats.shape[0]
    top = np.zeros(shape_number, dtype=np.int64)
    bot = np.repeat(binary_image.shape[0], shape_number)
    left = np.zeros(shape_number, dtype=np.int64)
    right = np.repeat(binary_image.shape[1], shape_number)
    for shape_i in np.arange(1, shape_nb + 1):
        # Get where the shape i appear in pairwise comparisons
        idx = np.nonzero(np.logical_or(all_distances[:, 0] == shape_i, all_distances[:, 1] == shape_i))
        # Compute the minimal distance related to shape i and divide by 2
        if len(all_distances[idx, 2]) > 0:
            dist = all_distances[idx, 2].min() // 2
        else:
            dist = 1
            # Save the coordinates of the arena around shape i
        top[shape_i - 1] = y_min[shape_i - 1] - dist.astype(np.int64)
        bot[shape_i - 1] = y_max[shape_i - 1] + dist.astype(np.int64)
        left[shape_i - 1] = x_min[shape_i - 1] - dist.astype(np.int64)
        right[shape_i - 1] = x_max[shape_i - 1] + dist.astype(np.int64)
    return top, bot, left, right

get_radius_distance_against_time(binary_video, field)

Calculate the radius distance against time from a binary video and field.

This function computes the change in radius distances over time by analyzing a binary video and mapping it to corresponding field values.

Parameters:

Name Type Description Default
binary_video ndarray of uint8

Binary video data.

 required
field ndarray

Field values to analyze the radius distances against.

 required

Returns:

Name Type Description
distance_against_time ndarray of float32

Radius distances over time.
time_start int

Starting time index where the radius distance measurement begins.
time_end int

Ending time index where the radius distance measurement ends.

Examples:

>>> binary_video = np.ones((10, 5, 5), dtype=np.uint8)

>>> distance_against_time, time_start, time_end = get_radius_distance_against_time(binary_video, field)
Source code in src/cellects/image_analysis/morphological_operations.py 
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def get_radius_distance_against_time(binary_video: NDArray[np.uint8], field) -> Tuple[NDArray[np.float32], int, int]:
    """
    Calculate the radius distance against time from a binary video and field.

    This function computes the change in radius distances over time
    by analyzing a binary video and mapping it to corresponding field values.

    Parameters
    ----------
    binary_video : ndarray of uint8
        Binary video data.
    field : ndarray
        Field values to analyze the radius distances against.

    Returns
    -------
    distance_against_time : ndarray of float32
        Radius distances over time.
    time_start : int
        Starting time index where the radius distance measurement begins.
    time_end : int
        Ending time index where the radius distance measurement ends.

    Examples
    --------
    >>> binary_video = np.ones((10, 5, 5), dtype=np.uint8)

    >>> distance_against_time, time_start, time_end = get_radius_distance_against_time(binary_video, field)
    """
    pixel_start = np.max(field[field > 0])
    pixel_end = np.min(field[field > 0])
    time_span = np.arange(binary_video.shape[0])
    time_start = 0
    time_end = time_span[-1]
    start_not_found: bool = True
    for t in time_span:
        if start_not_found:
            if np.any((field == pixel_start) * binary_video[t, :, :]):
                start_not_found = False
                time_start = t
        if np.any((field == pixel_end) * binary_video[t, :, :]):
            time_end = t
            break
    distance_against_time = np.linspace(pixel_start, pixel_end, (time_end - time_start + 1))
    distance_against_time = np.round(distance_against_time).astype(np.float32)
    return distance_against_time, time_start, time_end

image_borders(dimensions, shape='rectangular')

Create an image with borders, either rectangular or circular.

Parameters:

Name Type Description Default
dimensions tuple

The dimensions of the image (height, width).

 required
shape str

The shape of the borders. Options are "rectangular" or "circular". Defaults to "rectangular".

 'rectangular'

Returns:

Name Type Description
out ndarray of uint8

The image with borders. If the shape is "circular", an ellipse border; if "rectangular", a rectangular border.

Examples:

>>> borders = image_borders((3, 3), "rectangle")
>>> print(borders)
[[0 0 0]
 [0 1 0]
 [0 0 0]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def image_borders(dimensions: tuple, shape: str="rectangular") -> NDArray[np.uint8]:
    """
    Create an image with borders, either rectangular or circular.

    Parameters
    ----------
    dimensions : tuple
        The dimensions of the image (height, width).
    shape : str, optional
        The shape of the borders. Options are "rectangular" or "circular".
        Defaults to "rectangular".

    Returns
    -------
    out : ndarray of uint8
        The image with borders. If the shape is "circular", an ellipse border;
        if "rectangular", a rectangular border.

    Examples
    --------
    >>> borders = image_borders((3, 3), "rectangle")
    >>> print(borders)
    [[0 0 0]
     [0 1 0]
     [0 0 0]]
    """
    if shape == "circle":
        borders = create_ellipse(dimensions[0], dimensions[1])
        img_contours = image_borders(dimensions)
        borders = borders * img_contours
    else:
        borders = np.ones(dimensions, dtype=np.uint8)
        borders[0, :] = 0
        borders[:, 0] = 0
        borders[- 1, :] = 0
        borders[:, - 1] = 0
    return borders

inverted_distance_transform(original_shape, max_distance=None, with_erosion=0)

Calculate the distance transform around ones in a binary image, with optional erosion.

This function computes the Euclidean distance transform where zero values represent the background and ones represent the foreground. Optionally, it erodes the input image before computing the distance transform, and limits distances based on a maximum value.

Parameters:

Name Type Description Default
original_shape ndarray of uint8

Input binary image where ones represent the foreground.

 required
max_distance int

Maximum distance value to threshold. If None (default), no thresholding is applied.

 None
with_erosion int

Number of iterations for erosion. If 0 (default), no erosion is applied.

 0

Returns:

Name Type Description
out ndarray of uint32

Distance transform array where each element represents the distance to the nearest zero value in the input image.
See also

rounded_distance_transform : less precise (outputs int) and faster for small max_distance values.

Examples:

>>> segmentation = np.zeros((4, 4), dtype=np.uint8)
>>> segmentation[1:3, 1:3] = 1
>>> gravity = inverted_distance_transform(segmentation, max_distance=2)
>>> print(gravity)
[[1.         1.41421356 1.41421356 1.        ]
 [1.41421356 0.         0.         1.41421356]
 [1.41421356 0.         0.         1.41421356]
 [1.         1.41421356 1.41421356 1.        ]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def inverted_distance_transform(original_shape: NDArray[np.uint8], max_distance: int=None, with_erosion: int=0) -> NDArray[np.uint32]:
    """
    Calculate the distance transform around ones in a binary image, with optional erosion.

    This function computes the Euclidean distance transform where zero values
    represent the background and ones represent the foreground. Optionally,
    it erodes the input image before computing the distance transform, and
    limits distances based on a maximum value.

    Parameters
    ----------
    original_shape : ndarray of uint8
        Input binary image where ones represent the foreground.
    max_distance : int, optional
        Maximum distance value to threshold. If None (default), no thresholding is applied.
    with_erosion : int, optional
        Number of iterations for erosion. If 0 (default), no erosion is applied.

    Returns
    -------
    out : ndarray of uint32
        Distance transform array where each element represents the distance
        to the nearest zero value in the input image.

    See also
    --------
    rounded_distance_transform : less precise (outputs int) and faster for small max_distance values.

    Examples
    --------
    >>> segmentation = np.zeros((4, 4), dtype=np.uint8)
    >>> segmentation[1:3, 1:3] = 1
    >>> gravity = inverted_distance_transform(segmentation, max_distance=2)
    >>> print(gravity)
    [[1.         1.41421356 1.41421356 1.        ]
     [1.41421356 0.         0.         1.41421356]
     [1.41421356 0.         0.         1.41421356]
     [1.         1.41421356 1.41421356 1.        ]]
    """
    if with_erosion:
        original_shape = cv2.erode(original_shape, cross_33, iterations=with_erosion, borderType=cv2.BORDER_CONSTANT, borderValue=0)
    gravity_field = distance_transform_edt(1 - original_shape)
    if max_distance is not None:
        if max_distance > np.min(original_shape.shape) / 2:
            max_distance = (np.min(original_shape.shape) // 2).astype(np.uint32)
        gravity_field[gravity_field >= max_distance] = 0
    gravity_field[gravity_field > 0] = 1 + gravity_field.max() - gravity_field[gravity_field > 0]
    return gravity_field

keep_largest_shape(indexed_shapes)

Keep the largest shape from an array of indexed shapes.

This function identifies the most frequent non-zero shape in the input array and returns a binary mask where elements matching this shape are set to 1, and others are set to 0. The function uses NumPy's bincount to count occurrences of each shape and assumes that the first element (index 0) is not part of any shape classification.

Parameters:

Name Type Description Default
indexed_shapes ndarray of int32

Input array containing indexed shapes.

 required

Returns:

Name Type Description
out ndarray of uint8

Binary mask where the largest shape is marked as 1.

Examples:

>>> indexed_shapes = np.array([0, 2, 2, 3, 1], dtype=np.int32)
>>> keep_largest_shape(indexed_shapes)
array([0, 1, 1, 0, 0], dtype=uint8)
Source code in src/cellects/image_analysis/morphological_operations.py 
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@njit()
def keep_largest_shape(indexed_shapes: NDArray[np.int32]) -> NDArray[np.uint8]:
    """
    Keep the largest shape from an array of indexed shapes.

    This function identifies the most frequent non-zero shape in the input
    array and returns a binary mask where elements matching this shape are set to 1,
    and others are set to 0. The function uses NumPy's bincount to count occurrences
    of each shape and assumes that the first element (index 0) is not part of any
    shape classification.

    Parameters
    ----------
    indexed_shapes : ndarray of int32
        Input array containing indexed shapes.

    Returns
    -------
    out : ndarray of uint8
        Binary mask where the largest shape is marked as 1.

    Examples
    --------
    >>> indexed_shapes = np.array([0, 2, 2, 3, 1], dtype=np.int32)
    >>> keep_largest_shape(indexed_shapes)
    array([0, 1, 1, 0, 0], dtype=uint8)
    """
    label_counts = np.bincount(indexed_shapes.flatten())
    largest_label = 1 + np.argmax(label_counts[1:])
    return (indexed_shapes == largest_label).astype(np.uint8)

keep_one_connected_component(binary_image)

Keep only one connected component in a binary image.

This function filters out all but the largest connected component in a binary image, effectively isolating it from other noise or objects. The function ensures the input is in uint8 format before processing.

Parameters:

Name Type Description Default
binary_image ndarray of uint8

Binary image containing one or more connected components.

 required

Returns:

Type Description
ndarray of uint8

Image with only the largest connected component retained.

Examples:

>>> all_shapes = np.zeros((5, 5), dtype=np.uint8)
>>> all_shapes[0:2, 0:2] = 1
>>> all_shapes[3:4, 3:4] = 1
>>> res = keep_one_connected_component(all_shapes)
>>> print(res)
[[1 1 0 0 0]
 [1 1 0 0 0]
 [0 0 0 0 0]
 [0 0 0 0 0]
 [0 0 0 0 0]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def keep_one_connected_component(binary_image: NDArray[np.uint8])-> NDArray[np.uint8]:
    """
    Keep only one connected component in a binary image.

    This function filters out all but the largest connected component in
    a binary image, effectively isolating it from other noise or objects.
    The function ensures the input is in uint8 format before processing.

    Parameters
    ----------
    binary_image : ndarray of uint8
        Binary image containing one or more connected components.

    Returns
    -------
    ndarray of uint8
        Image with only the largest connected component retained.

    Examples
    -------
    >>> all_shapes = np.zeros((5, 5), dtype=np.uint8)
    >>> all_shapes[0:2, 0:2] = 1
    >>> all_shapes[3:4, 3:4] = 1
    >>> res = keep_one_connected_component(all_shapes)
    >>> print(res)
    [[1 1 0 0 0]
     [1 1 0 0 0]
     [0 0 0 0 0]
     [0 0 0 0 0]
     [0 0 0 0 0]]
    """
    if binary_image.dtype != np.uint8:
        binary_image = binary_image.astype(np.uint8)
    num_labels, sh = cv2.connectedComponents(binary_image)
    if num_labels <= 1:
        return binary_image.astype(np.uint8)
    else:
        return keep_largest_shape(sh)

keep_shape_connected_with_ref(all_shapes, reference_shape)

Keep shape connected with reference.

This function analyzes the connected components of a binary image represented by all_shapes and returns the first component that intersects with the reference_shape. If no such component is found, it returns None.

Parameters:

Name Type Description Default
all_shapes ndarray of uint8

Binary image containing all shapes to analyze.

 required
reference_shape ndarray of uint8

Binary reference shape used for intersection check.

 required

Returns:

Name Type Description
out ndarray of uint8 or None

The first connected component that intersects with the reference shape, or None if no such component is found.

Examples:

>>> all_shapes = np.zeros((5, 5), dtype=np.uint8)
>>> reference_shape = np.zeros((5, 5), dtype=np.uint8)
>>> reference_shape[3, 3] = 1
>>> all_shapes[0:2, 0:2] = 1
>>> all_shapes[3:4, 3:4] = 1
>>> res = keep_shape_connected_with_ref(all_shapes, reference_shape)
>>> print(res)
[[0 0 0 0 0]
 [0 0 0 0 0]
 [0 0 0 0 0]
 [0 0 0 1 0]
 [0 0 0 0 0]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def keep_shape_connected_with_ref(all_shapes: NDArray[np.uint8], reference_shape: NDArray[np.uint8]) -> NDArray[np.uint8]:
    """
    Keep shape connected with reference.

    This function analyzes the connected components of a binary image represented by `all_shapes`
    and returns the first component that intersects with the `reference_shape`.
    If no such component is found, it returns None.

    Parameters
    ----------
    all_shapes : ndarray of uint8
        Binary image containing all shapes to analyze.
    reference_shape : ndarray of uint8
        Binary reference shape used for intersection check.

    Returns
    -------
    out : ndarray of uint8 or None
        The first connected component that intersects with the reference shape,
        or None if no such component is found.

    Examples
    -------
    >>> all_shapes = np.zeros((5, 5), dtype=np.uint8)
    >>> reference_shape = np.zeros((5, 5), dtype=np.uint8)
    >>> reference_shape[3, 3] = 1
    >>> all_shapes[0:2, 0:2] = 1
    >>> all_shapes[3:4, 3:4] = 1
    >>> res = keep_shape_connected_with_ref(all_shapes, reference_shape)
    >>> print(res)
    [[0 0 0 0 0]
     [0 0 0 0 0]
     [0 0 0 0 0]
     [0 0 0 1 0]
     [0 0 0 0 0]]
    """
    number, order = cv2.connectedComponents(all_shapes, ltype=cv2.CV_16U)
    expanded_shape = None
    if number > 1:
        for i in np.arange(1, number):
            expanded_shape_test = np.zeros(order.shape, np.uint8)
            expanded_shape_test[order == i] = 1
            if np.any(expanded_shape_test * reference_shape):
                break
        if np.any(expanded_shape_test * reference_shape):
            expanded_shape = expanded_shape_test
        else:
            expanded_shape = reference_shape
    return expanded_shape

prepare_box_counting(binary_image, min_im_side=128, min_mesh_side=8, zoom_step=0, contours=True)

Prepare box counting parameters for image analysis.

Prepares parameters for box counting method based on binary image input. Adjusts image size, computes side lengths, and applies contour extraction if specified.

Parameters:

Name Type Description Default
binary_image ndarray of uint8

Binary image for analysis.

 required
min_im_side int

Minimum side length threshold. Default is 128.

 128
min_mesh_side int

Minimum mesh side length. Default is 8.

 8
zoom_step int

Zoom step for side lengths computation. Default is 0.

 0
contours bool

Whether to apply contour extraction. Default is True.

 True

Returns:

Name Type Description
out tuple of ndarray of uint8, ndarray (or None)

Cropped binary image and computed side lengths.

Examples:

>>> binary_image = np.zeros((10, 10), dtype=np.uint8)
>>> binary_image[2:4, 2:6] = 1
>>> binary_image[7:9, 4:7] = 1
>>> binary_image[4:7, 5] = 1
>>> cropped_img, side_lengths = prepare_box_counting(binary_image, min_im_side=2, min_mesh_side=2)
>>> print(cropped_img), print(side_lengths)
[[0 0 0 0 0 0 0]
 [0 1 1 1 1 0 0]
 [0 1 1 1 1 0 0]
 [0 0 0 0 1 0 0]
 [0 0 0 0 1 0 0]
 [0 0 0 0 1 0 0]
 [0 0 0 1 0 1 0]
 [0 0 0 1 1 1 0]
 [0 0 0 0 0 0 0]]
[4 2]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def prepare_box_counting(binary_image: NDArray[np.uint8], min_im_side: int=128, min_mesh_side: int=8, zoom_step: int=0, contours: bool=True)-> Tuple[NDArray[np.uint8], NDArray[np.uint8]]:
    """Prepare box counting parameters for image analysis.

    Prepares parameters for box counting method based on binary
    image input. Adjusts image size, computes side lengths, and applies
    contour extraction if specified.

    Parameters
    ----------
    binary_image : ndarray of uint8
        Binary image for analysis.
    min_im_side : int, optional
        Minimum side length threshold. Default is 128.
    min_mesh_side : int, optional
        Minimum mesh side length. Default is 8.
    zoom_step : int, optional
        Zoom step for side lengths computation. Default is 0.
    contours : bool, optional
        Whether to apply contour extraction. Default is True.

    Returns
    -------
    out : tuple of ndarray of uint8, ndarray (or None)
        Cropped binary image and computed side lengths.

    Examples
    --------
    >>> binary_image = np.zeros((10, 10), dtype=np.uint8)
    >>> binary_image[2:4, 2:6] = 1
    >>> binary_image[7:9, 4:7] = 1
    >>> binary_image[4:7, 5] = 1
    >>> cropped_img, side_lengths = prepare_box_counting(binary_image, min_im_side=2, min_mesh_side=2)
    >>> print(cropped_img), print(side_lengths)
    [[0 0 0 0 0 0 0]
     [0 1 1 1 1 0 0]
     [0 1 1 1 1 0 0]
     [0 0 0 0 1 0 0]
     [0 0 0 0 1 0 0]
     [0 0 0 0 1 0 0]
     [0 0 0 1 0 1 0]
     [0 0 0 1 1 1 0]
     [0 0 0 0 0 0 0]]
    [4 2]
    """
    side_lengths = None
    zoomed_binary = binary_image
    binary_idx = np.nonzero(binary_image)
    if binary_idx[0].size:
        min_y = np.min(binary_idx[0])
        min_y = np.max((min_y - 1, 0))

        min_x = np.min(binary_idx[1])
        min_x = np.max((min_x - 1, 0))

        max_y = np.max(binary_idx[0])
        max_y = np.min((max_y + 1, binary_image.shape[0] - 1))

        max_x = np.max(binary_idx[1])
        max_x = np.min((max_x + 1, binary_image.shape[1] - 1))

        zoomed_binary = binary_image[min_y:(max_y + 1), min_x: (max_x + 1)].copy()
        min_side = np.min(zoomed_binary.shape)
        if min_side >= min_im_side:
            if contours:
                zoomed_binary = get_contours(zoomed_binary)
            if zoom_step == 0:
                max_power = int(np.floor(np.log2(min_side)))  # Largest integer power of 2
                side_lengths = 2 ** np.arange(max_power, int(np.log2(min_mesh_side // 2)), -1)
            else:
                side_lengths = np.arange(min_mesh_side, min_side, zoom_step)
    return zoomed_binary, side_lengths

rank_from_top_to_bottom_from_left_to_right(binary_image, y_boundaries, get_ordered_image=False)

Rank components in a binary image from top to bottom and from left to right.

This function processes a binary image to rank its components based on their centroids. It first sorts the components row by row and then orders them within each row from left to right. If the ordering fails, it attempts an alternative algorithm and returns the ordered statistics and centroids.

Parameters:

Name Type Description Default
binary_image ndarray of uint8

The input binary image to process.

 required
y_boundaries ndarray of int

Boundary information for the y-coordinates.

 required
get_ordered_image bool

If True, returns an ordered image in addition to the statistics and centroids. Default is False.

 False

Returns:

Type Description
tuple

If get_ordered_image is True, returns a tuple containing: - ordered_stats : ndarray of int Statistics for the ordered components. - ordered_centroids : ndarray of float64 Centroids for the ordered components. - ordered_image : ndarray of uint8 The binary image with ordered component labels.

If get_ordered_image is False, returns a tuple containing: - ordered_stats : ndarray of int Statistics for the ordered components. - ordered_centroids : ndarray of float64 Centroids for the ordered components.
Source code in src/cellects/image_analysis/morphological_operations.py 
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def rank_from_top_to_bottom_from_left_to_right(binary_image: NDArray[np.uint8], y_boundaries: NDArray[int], get_ordered_image: bool=False) -> Tuple:
    """
    Rank components in a binary image from top to bottom and from left to right.

    This function processes a binary image to rank its components based on
    their centroids. It first sorts the components row by row and then orders them
    within each row from left to right. If the ordering fails, it attempts an alternative
    algorithm and returns the ordered statistics and centroids.

    Parameters
    ----------
    binary_image : ndarray of uint8
        The input binary image to process.
    y_boundaries : ndarray of int
        Boundary information for the y-coordinates.
    get_ordered_image : bool, optional
        If True, returns an ordered image in addition to the statistics and centroids.
        Default is False.

    Returns
    -------
    tuple
        If `get_ordered_image` is True, returns a tuple containing:
        - ordered_stats : ndarray of int
            Statistics for the ordered components.
        - ordered_centroids : ndarray of float64
            Centroids for the ordered components.
        - ordered_image : ndarray of uint8
            The binary image with ordered component labels.

        If `get_ordered_image` is False, returns a tuple containing:
        - ordered_stats : ndarray of int
            Statistics for the ordered components.
        - ordered_centroids : ndarray of float64
            Centroids for the ordered components.
    """
    nb_components, output, stats, centroids = cv2.connectedComponentsWithStats(binary_image.astype(np.uint8),
                                                                               connectivity=8)

    centroids = centroids[1:, :]
    final_order = np.zeros(centroids.shape[0], dtype=np.uint8)
    sorted_against_y = np.argsort(centroids[:, 1])
    # row_nb = (y_boundaries == 1).sum()
    row_nb = np.max(((y_boundaries == 1).sum(), (y_boundaries == - 1).sum()))
    if row_nb > 0:
        component_per_row = int(np.ceil((nb_components - 1) / row_nb))
        for row_i in range(row_nb):
            row_i_start = row_i * component_per_row
            if row_i == (row_nb - 1):
                sorted_against_x = np.argsort(centroids[sorted_against_y[row_i_start:], 0])
                final_order[row_i_start:] = sorted_against_y[row_i_start:][sorted_against_x]
            else:
                row_i_end = (row_i + 1) * component_per_row
                sorted_against_x = np.argsort(centroids[sorted_against_y[row_i_start:row_i_end], 0])
                final_order[row_i_start:row_i_end] = sorted_against_y[row_i_start:row_i_end][sorted_against_x]
    else:
        final_order = np.argsort(centroids[:, 0])
    ordered_centroids = centroids[final_order, :]
    ordered_stats = stats[1:, :]
    ordered_stats = ordered_stats[final_order, :]

    if get_ordered_image:
        old_to_new = np.zeros_like(final_order)
        old_to_new[final_order] = np.arange(len(final_order))
        mapping_array = np.zeros(binary_image.shape, dtype=np.uint8)
        mapping_array[output != 0] = old_to_new[output[output != 0] - 1] + 1
        ordered_image = mapping_array.copy()
        return ordered_stats, ordered_centroids, ordered_image
    else:
        return ordered_stats, ordered_centroids

reduce_image_size_for_speed(image_of_2_shapes)

Reduces the size of an image containing two shapes for faster processing.

The function iteratively divides the image into quadrants and keeps only those that contain both shapes until a minimal size is reached.

Parameters:

Name Type Description Default
image_of_2_shapes ndarray of uint8

The input image containing two shapes.

 required

Returns:

Name Type Description
out tuple of tuples

The indices of the first and second shape in the reduced image.

Examples:

>>> image_of_2_shapes = np.zeros((10, 10), dtype=np.uint8)
>>> image_of_2_shapes[1:3, 1:3] = 1
>>> image_of_2_shapes[1:3, 4:6] = 2
>>> shape1_idx, shape2_idx = reduce_image_size_for_speed(image_of_2_shapes)
>>> print(shape1_idx)
(array([1, 1, 2, 2]), array([1, 2, 1, 2]))
Source code in src/cellects/image_analysis/morphological_operations.py 
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@njit()
def reduce_image_size_for_speed(image_of_2_shapes: NDArray[np.uint8]) -> Tuple[Tuple, Tuple]:
    """
    Reduces the size of an image containing two shapes for faster processing.

    The function iteratively divides the image into quadrants and keeps only
    those that contain both shapes until a minimal size is reached.

    Parameters
    ----------
    image_of_2_shapes : ndarray of uint8
        The input image containing two shapes.

    Returns
    -------
    out : tuple of tuples
        The indices of the first and second shape in the reduced image.

    Examples
    --------
    >>> image_of_2_shapes = np.zeros((10, 10), dtype=np.uint8)
    >>> image_of_2_shapes[1:3, 1:3] = 1
    >>> image_of_2_shapes[1:3, 4:6] = 2
    >>> shape1_idx, shape2_idx = reduce_image_size_for_speed(image_of_2_shapes)
    >>> print(shape1_idx)
    (array([1, 1, 2, 2]), array([1, 2, 1, 2]))
    """
    sub_image = image_of_2_shapes.copy()
    y_size, x_size = sub_image.shape
    images_list = [sub_image]
    good_images = [0]
    sub_image = images_list[good_images[0]]
    while (len(good_images) == 1 or len(good_images) == 2) and y_size > 3 and x_size > 3:
        y_size, x_size = sub_image.shape
        images_list = []
        images_list.append(sub_image[:((y_size // 2) + 1), :((x_size // 2) + 1)])
        images_list.append(sub_image[:((y_size // 2) + 1), (x_size // 2):])
        images_list.append(sub_image[(y_size // 2):, :((x_size // 2) + 1)])
        images_list.append(sub_image[(y_size // 2):, (x_size // 2):])
        good_images = []
        for idx, image in enumerate(images_list):
            if np.any(image == 2):
                if np.any(image == 1):
                    good_images.append(idx)
        if len(good_images) == 0:
            break
        elif len(good_images) == 2:
            if good_images == [0, 1]:
                sub_image = np.concatenate((images_list[good_images[0]], images_list[good_images[1]]), axis=1)
            elif good_images == [0, 2]:
                sub_image = np.concatenate((images_list[good_images[0]], images_list[good_images[1]]), axis=0)
            elif good_images == [1, 3]:
                sub_image = np.concatenate((images_list[good_images[0]], images_list[good_images[1]]), axis=0)
            elif good_images == [2, 3]:
                sub_image = np.concatenate((images_list[good_images[0]], images_list[good_images[1]]), axis=1)
            else:
                pass
        else:
            sub_image = images_list[good_images[0]]

    shape1_idx = np.nonzero(sub_image == 1)
    shape2_idx = np.nonzero(sub_image == 2)
    return shape1_idx, shape2_idx

rounded_inverted_distance_transform(original_shape, max_distance=None, with_erosion=0)

Perform rounded inverted distance transform on a binary image.

This function computes the inverse of the Euclidean distance transform, where each pixel value represents its distance to the nearest zero pixel. The operation can include erosion and will stop either at a given max distance or until no further expansion is needed.

Parameters:

Name Type Description Default
original_shape ndarray of uint8

Input binary image to be processed.

 required
max_distance int

Maximum distance for the expansion. If None, no limit is applied.

 None
with_erosion int

Number of erosion iterations to apply before the transform. Default is 0.

 0

Returns:

Name Type Description
out ndarray of uint32

Output image containing the rounded inverted distance transform.

Examples:

>>> segmentation = np.zeros((4, 4), dtype=np.uint8)
>>> segmentation[1:3, 1:3] = 1
>>> gravity = rounded_inverted_distance_transform(segmentation, max_distance=2)
>>> print(gravity)
[[1 2 2 1]
 [2 0 0 2]
 [2 0 0 2]
 [1 2 2 1]]
Source code in src/cellects/image_analysis/morphological_operations.py 
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def rounded_inverted_distance_transform(original_shape: NDArray[np.uint8], max_distance: int=None, with_erosion: int=0) -> NDArray[np.uint32]:
    """
    Perform rounded inverted distance transform on a binary image.

    This function computes the inverse of the Euclidean distance transform,
    where each pixel value represents its distance to the nearest zero
    pixel. The operation can include erosion and will stop either at a given
    max distance or until no further expansion is needed.

    Parameters
    ----------
    original_shape : ndarray of uint8
        Input binary image to be processed.
    max_distance : int, optional
        Maximum distance for the expansion. If None, no limit is applied.
    with_erosion : int, optional
        Number of erosion iterations to apply before the transform. Default is 0.

    Returns
    -------
    out : ndarray of uint32
        Output image containing the rounded inverted distance transform.

    Examples
    --------
    >>> segmentation = np.zeros((4, 4), dtype=np.uint8)
    >>> segmentation[1:3, 1:3] = 1
    >>> gravity = rounded_inverted_distance_transform(segmentation, max_distance=2)
    >>> print(gravity)
    [[1 2 2 1]
     [2 0 0 2]
     [2 0 0 2]
     [1 2 2 1]]
    """
    if with_erosion > 0:
        original_shape = cv2.erode(original_shape, cross_33, iterations=with_erosion, borderType=cv2.BORDER_CONSTANT, borderValue=0)
    expand = original_shape.copy()
    if max_distance is not None:
        if max_distance > np.max(original_shape.shape):
            max_distance = np.max(original_shape.shape).astype(np.uint32)
        gravity_field = np.zeros(original_shape.shape , np.uint32)
        for gravi in np.arange(max_distance):
            expand = cv2.dilate(expand, cross_33, iterations=1, borderType=cv2.BORDER_CONSTANT, borderValue=0)
            gravity_field[np.logical_xor(expand, original_shape)] += 1
    else:
        gravity_field = np.zeros(original_shape.shape , np.uint32)
        while np.any(np.equal(original_shape + expand, 0)):
            expand = cv2.dilate(expand, cross_33, iterations=1, borderType=cv2.BORDER_CONSTANT, borderValue=0)
            gravity_field[np.logical_xor(expand, original_shape)] += 1
    return gravity_field

shape_selection(binary_image, several_blob_per_arena, true_shape_number=None, horizontal_size=None, spot_shape=None, bio_mask=None, back_mask=None)

Process the binary image to identify and validate shapes.

This method processes a binary image to detect connected components, validate their sizes, and handle bio and back masks if specified. It ensures that the number of validated shapes matches the expected sample number or applies additional filtering if necessary.

Args: use_bio_and_back_masks (bool): Whether to use bio and back masks during the processing. Default is False.

Selects and validates the shapes of stains based on their size and shape.

This method performs two main tasks: 1. Removes stains whose horizontal size varies too much from a reference value. 2. Determines the shape of each remaining stain and only keeps those that correspond to a reference shape.

The method first removes stains whose horizontal size is outside the specified confidence interval. Then, it identifies shapes that do not correspond to a predefined reference shape and removes them as well.

Args: horizontal_size (int): The expected horizontal size of the stains to use as a reference. shape (str): The shape type ('circle' or 'rectangle') that the stains should match. Other shapes are not currently supported. confint (float): The confidence interval as a decimal representing the percentage within which the size of the stains should fall. do_not_delete (NDArray, optional): An array of stain indices that should not be deleted. Default is None.

Source code in src/cellects/image_analysis/morphological_operations.py 
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def shape_selection(binary_image:NDArray, several_blob_per_arena: bool, true_shape_number: int=None,
                    horizontal_size: int=None, spot_shape: str=None, bio_mask:NDArray=None, back_mask:NDArray=None):
    """
    Process the binary image to identify and validate shapes.

    This method processes a binary image to detect connected components,
    validate their sizes, and handle bio and back masks if specified.
    It ensures that the number of validated shapes matches the expected
    sample number or applies additional filtering if necessary.

    Args:
        use_bio_and_back_masks (bool): Whether to use bio and back masks
            during the processing. Default is False.

    Selects and validates the shapes of stains based on their size and shape.

    This method performs two main tasks:
    1. Removes stains whose horizontal size varies too much from a reference value.
    2. Determines the shape of each remaining stain and only keeps those that correspond to a reference shape.

    The method first removes stains whose horizontal size is outside the specified confidence interval. Then, it identifies shapes that do not correspond to a predefined reference shape and removes them as well.

    Args:
        horizontal_size (int): The expected horizontal size of the stains to use as a reference.
        shape (str): The shape type ('circle' or 'rectangle')
            that the stains should match. Other shapes are not currently supported.
        confint (float): The confidence interval as a decimal
            representing the percentage within which the size of the stains should fall.
        do_not_delete (NDArray, optional): An array of stain indices that should not be deleted.
            Default is None.

    """

    shape_number, shapes, stats, centroids = cv2.connectedComponentsWithStats(binary_image, connectivity=8)
    do_not_delete = None
    if bio_mask is not None or back_mask is not None:
        if back_mask is not None:
            if np.any(shapes[back_mask]):
                shapes[np.isin(shapes, np.unique(shapes[back_mask]))] = 0
                shape_number, shapes, stats, centroids = cv2.connectedComponentsWithStats(
                    (shapes > 0).astype(np.uint8), connectivity=8)
        if bio_mask is not None:
            if np.any(shapes[bio_mask]):
                do_not_delete = np.unique(shapes[bio_mask])
                do_not_delete = do_not_delete[do_not_delete != 0]
    shape_number -= 1

    if not several_blob_per_arena and horizontal_size is not None:
        ordered_shapes = shapes.copy()
        if spot_shape is None:
            c_spot_shapes = spot_shapes
            c_spot_sizes = spot_sizes
        else:
            if spot_shape == 'circle':
                c_spot_shapes = spot_shapes[::2]
            else:
                c_spot_shapes = spot_shapes[::-2]
            c_spot_sizes = spot_sizes[::2]

        # shape_number = stats.shape[0]
        counter = 0
        while shape_number != true_shape_number and counter < len(spot_size_coefficients):
            shape = c_spot_shapes[counter]
            confint = c_spot_sizes[counter]
            # counter+=1;horizontal_size = self.spot_size; shape = self.parent.spot_shapes[counter];confint = self.parent.spot_size_confints[::-1][counter]
            # stats columns contain in that order:
            # - x leftmost coordinate of boundingbox
            # - y topmost coordinate of boundingbox
            # - The horizontal size of the bounding box.
            # - The vertical size of the bounding box.
            # - The total area (in pixels) of the connected component.

            # First, remove each stain which horizontal size varies too much from reference
            size_interval = [horizontal_size * (1 - confint), horizontal_size * (1 + confint)]
            cc_to_remove = np.argwhere(np.logical_or(stats[:, 2] < size_interval[0], stats[:, 2] > size_interval[1]))

            if do_not_delete is None:
                ordered_shapes[np.isin(ordered_shapes, cc_to_remove)] = 0
            else:
                ordered_shapes[np.logical_and(np.isin(ordered_shapes, cc_to_remove),
                                              np.logical_not(np.isin(ordered_shapes, do_not_delete)))] = 0

            # Second, determine the shape of each stain to only keep the ones corresponding to the reference shape
            validated_shapes = np.zeros(ordered_shapes.shape, dtype=np.uint8)
            validated_shapes[ordered_shapes > 0] = 1
            nb_components, ordered_shapes, stats, centroids = cv2.connectedComponentsWithStats(validated_shapes,
                                                                                               connectivity=8)
            if nb_components > 1:
                if shape == 'circle':
                    surf_interval = [np.pi * np.square(horizontal_size // 2) * (1 - confint),
                                     np.pi * np.square(horizontal_size // 2) * (1 + confint)]
                    cc_to_remove = np.argwhere(
                        np.logical_or(stats[:, 4] < surf_interval[0], stats[:, 4] > surf_interval[1]))
                elif shape == 'rectangle':
                    # If the smaller side is the horizontal one, use the user provided horizontal side
                    if np.argmin((np.mean(stats[1:, 2]), np.mean(stats[1:, 3]))) == 0:
                        surf_interval = [np.square(horizontal_size) * (1 - confint),
                                         np.square(horizontal_size) * (1 + confint)]
                        cc_to_remove = np.argwhere(
                            np.logical_or(stats[:, 4] < surf_interval[0], stats[:, 4] > surf_interval[1]))
                    # If the smaller side is the vertical one, use the median vertical length shape
                    else:
                        surf_interval = [np.square(np.median(stats[1:, 3])) * (1 - confint),
                                         np.square(np.median(stats[1:, 3])) * (1 + confint)]
                        cc_to_remove = np.argwhere(
                            np.logical_or(stats[:, 4] < surf_interval[0], stats[:, 4] > surf_interval[1]))
                else:
                    logging.info("Original blob shape not well written")

                if do_not_delete is None:
                    ordered_shapes[np.isin(ordered_shapes, cc_to_remove)] = 0
                else:
                    ordered_shapes[np.logical_and(np.isin(ordered_shapes, cc_to_remove),
                                                  np.logical_not(np.isin(ordered_shapes, do_not_delete)))] = 0
                # There was only that before:
                validated_shapes = np.zeros(ordered_shapes.shape, dtype=np.uint8)
                validated_shapes[np.nonzero(ordered_shapes)] = 1
                nb_components, ordered_shapes, stats, centroids = cv2.connectedComponentsWithStats(validated_shapes,
                                                                                                   connectivity=8)

            shape_number = nb_components - 1
            counter += 1

        if shape_number == true_shape_number:
            shapes = ordered_shapes
    if true_shape_number is None or shape_number == true_shape_number:
        validated_shapes = np.zeros(shapes.shape, dtype=np.uint8)
        validated_shapes[shapes > 0] = 1
    else:
        max_size = binary_image.size * 0.75
        min_size = 10
        cc_to_remove = np.argwhere(np.logical_or(stats[1:, 4] < min_size, stats[1:, 4] > max_size)) + 1
        shapes[np.isin(shapes, cc_to_remove)] = 0
        validated_shapes = np.zeros(shapes.shape, dtype=np.uint8)
        validated_shapes[shapes > 0] = 1
        shape_number, shapes, stats, centroids = cv2.connectedComponentsWithStats(validated_shapes, connectivity=8)
        if not several_blob_per_arena and true_shape_number is not None and shape_number > true_shape_number:
            # Sort shapes by size and compare the largest with the second largest
            # If the difference is too large, remove that largest shape.
            cc_to_remove = np.array([], dtype=np.uint8)
            to_remove = np.array([], dtype=np.uint8)
            stats = stats[1:, :]
            while stats.shape[0] > true_shape_number and to_remove is not None:
                # 1) rank by height
                sorted_height = np.argsort(stats[:, 2])
                # and only consider the number of shapes we want to detect
                standard_error = np.std(stats[sorted_height, 2][-true_shape_number:])
                differences = np.diff(stats[sorted_height, 2])
                # Look for very big changes from one height to the next
                if differences.any() and np.max(differences) > 2 * standard_error:
                    # Within these, remove shapes that are too large
                    to_remove = sorted_height[np.argmax(differences)]
                    cc_to_remove = np.append(cc_to_remove, to_remove + 1)
                    stats = np.delete(stats, to_remove, 0)

                else:
                    to_remove = None
            shapes[np.isin(shapes, cc_to_remove)] = 0
            validated_shapes = np.zeros(shapes.shape, dtype=np.uint8)
            validated_shapes[shapes > 0] = 1
            shape_number, shapes, stats, centroids = cv2.connectedComponentsWithStats(validated_shapes, connectivity=8)

        shape_number -= 1
    return validated_shapes, shape_number, stats, centroids