ndimage.measurements

Module Contents

Functions

label(input,structure=None,output=None) Label features in an array.
find_objects(input,max_label=0) Find objects in a labeled array.
labeled_comprehension(input,labels,index,func,out_dtype,default,pass_positions=False) Roughly equivalent to [func(input[labels == i]) for i in index].
_safely_castable_to_int(dt) Test whether the numpy data type dt can be safely cast to an int.
_stats(input,labels=None,index=None,centered=False) Count, sum, and optionally compute (sum - centre)^2 of input by label
sum(input,labels=None,index=None) Calculate the sum of the values of the array.
mean(input,labels=None,index=None) Calculate the mean of the values of an array at labels.
variance(input,labels=None,index=None) Calculate the variance of the values of an n-D image array, optionally at
standard_deviation(input,labels=None,index=None) Calculate the standard deviation of the values of an n-D image array,
_select(input,labels=None,index=None,find_min=False,find_max=False,find_min_positions=False,find_max_positions=False,find_median=False) Returns min, max, or both, plus their positions (if requested), and
minimum(input,labels=None,index=None) Calculate the minimum of the values of an array over labeled regions.
maximum(input,labels=None,index=None) Calculate the maximum of the values of an array over labeled regions.
median(input,labels=None,index=None) Calculate the median of the values of an array over labeled regions.
minimum_position(input,labels=None,index=None) Find the positions of the minimums of the values of an array at labels.
maximum_position(input,labels=None,index=None) Find the positions of the maximums of the values of an array at labels.
extrema(input,labels=None,index=None) Calculate the minimums and maximums of the values of an array
center_of_mass(input,labels=None,index=None) Calculate the center of mass of the values of an array at labels.
histogram(input,min,max,bins,labels=None,index=None) Calculate the histogram of the values of an array, optionally at labels.
watershed_ift(input,markers,structure=None,output=None) Apply watershed from markers using image foresting transform algorithm.
label(input, structure=None, output=None)

Label features in an array.

input : array_like
An array-like object to be labeled. Any non-zero values in input are counted as features and zero values are considered the background.
structure : array_like, optional

A structuring element that defines feature connections. structure must be symmetric. If no structuring element is provided, one is automatically generated with a squared connectivity equal to one. That is, for a 2-D input array, the default structuring element is:

[[0,1,0],
 [1,1,1],
 [0,1,0]]
output : (None, data-type, array_like), optional
If output is a data type, it specifies the type of the resulting labeled feature array If output is an array-like object, then output will be updated with the labeled features from this function. This function can operate in-place, by passing output=input. Note that the output must be able to store the largest label, or this function will raise an Exception.
label : ndarray or int
An integer ndarray where each unique feature in input has a unique label in the returned array.
num_features : int

How many objects were found.

If output is None, this function returns a tuple of (labeled_array, num_features).

If output is a ndarray, then it will be updated with values in labeled_array and only num_features will be returned by this function.

find_objects : generate a list of slices for the labeled features (or
objects); useful for finding features’ position or dimensions

Create an image with some features, then label it using the default (cross-shaped) structuring element:

>>> from scipy.ndimage import label, generate_binary_structure
>>> a = np.array([[0,0,1,1,0,0],
...               [0,0,0,1,0,0],
...               [1,1,0,0,1,0],
...               [0,0,0,1,0,0]])
>>> labeled_array, num_features = label(a)

Each of the 4 features are labeled with a different integer:

>>> num_features
4
>>> labeled_array
array([[0, 0, 1, 1, 0, 0],
       [0, 0, 0, 1, 0, 0],
       [2, 2, 0, 0, 3, 0],
       [0, 0, 0, 4, 0, 0]])

Generate a structuring element that will consider features connected even if they touch diagonally:

>>> s = generate_binary_structure(2,2)

or,

>>> s = [[1,1,1],
...      [1,1,1],
...      [1,1,1]]

Label the image using the new structuring element:

>>> labeled_array, num_features = label(a, structure=s)

Show the 2 labeled features (note that features 1, 3, and 4 from above are now considered a single feature):

>>> num_features
2
>>> labeled_array
array([[0, 0, 1, 1, 0, 0],
       [0, 0, 0, 1, 0, 0],
       [2, 2, 0, 0, 1, 0],
       [0, 0, 0, 1, 0, 0]])
find_objects(input, max_label=0)

Find objects in a labeled array.

input : ndarray of ints
Array containing objects defined by different labels. Labels with value 0 are ignored.
max_label : int, optional
Maximum label to be searched for in input. If max_label is not given, the positions of all objects are returned.
object_slices : list of tuples
A list of tuples, with each tuple containing N slices (with N the dimension of the input array). Slices correspond to the minimal parallelepiped that contains the object. If a number is missing, None is returned instead of a slice.

label, center_of_mass

This function is very useful for isolating a volume of interest inside a 3-D array, that cannot be “seen through”.

>>> from scipy import ndimage
>>> a = np.zeros((6,6), dtype=int)
>>> a[2:4, 2:4] = 1
>>> a[4, 4] = 1
>>> a[:2, :3] = 2
>>> a[0, 5] = 3
>>> a
array([[2, 2, 2, 0, 0, 3],
       [2, 2, 2, 0, 0, 0],
       [0, 0, 1, 1, 0, 0],
       [0, 0, 1, 1, 0, 0],
       [0, 0, 0, 0, 1, 0],
       [0, 0, 0, 0, 0, 0]])
>>> ndimage.find_objects(a)
[(slice(2, 5, None), slice(2, 5, None)), (slice(0, 2, None), slice(0, 3, None)), (slice(0, 1, None), slice(5, 6, None))]
>>> ndimage.find_objects(a, max_label=2)
[(slice(2, 5, None), slice(2, 5, None)), (slice(0, 2, None), slice(0, 3, None))]
>>> ndimage.find_objects(a == 1, max_label=2)
[(slice(2, 5, None), slice(2, 5, None)), None]
>>> loc = ndimage.find_objects(a)[0]
>>> a[loc]
array([[1, 1, 0],
       [1, 1, 0],
       [0, 0, 1]])
labeled_comprehension(input, labels, index, func, out_dtype, default, pass_positions=False)

Roughly equivalent to [func(input[labels == i]) for i in index].

Sequentially applies an arbitrary function (that works on array_like input) to subsets of an n-D image array specified by labels and index. The option exists to provide the function with positional parameters as the second argument.

input : array_like
Data from which to select labels to process.
labels : array_like or None
Labels to objects in input. If not None, array must be same shape as input. If None, func is applied to raveled input.
index : int, sequence of ints or None
Subset of labels to which to apply func. If a scalar, a single value is returned. If None, func is applied to all non-zero values of labels.
func : callable
Python function to apply to labels from input.
out_dtype : dtype
Dtype to use for result.
default : int, float or None
Default return value when a element of index does not exist in labels.
pass_positions : bool, optional
If True, pass linear indices to func as a second argument. Default is False.
result : ndarray
Result of applying func to each of labels to input in index.
>>> a = np.array([[1, 2, 0, 0],
...               [5, 3, 0, 4],
...               [0, 0, 0, 7],
...               [9, 3, 0, 0]])
>>> from scipy import ndimage
>>> lbl, nlbl = ndimage.label(a)
>>> lbls = np.arange(1, nlbl+1)
>>> ndimage.labeled_comprehension(a, lbl, lbls, np.mean, float, 0)
array([ 2.75,  5.5 ,  6.  ])

Falling back to default:

>>> lbls = np.arange(1, nlbl+2)
>>> ndimage.labeled_comprehension(a, lbl, lbls, np.mean, float, -1)
array([ 2.75,  5.5 ,  6.  , -1.  ])

Passing positions:

>>> def fn(val, pos):
...     print("fn says: %s : %s" % (val, pos))
...     return (val.sum()) if (pos.sum() % 2 == 0) else (-val.sum())
...
>>> ndimage.labeled_comprehension(a, lbl, lbls, fn, float, 0, True)
fn says: [1 2 5 3] : [0 1 4 5]
fn says: [4 7] : [ 7 11]
fn says: [9 3] : [12 13]
array([ 11.,  11., -12.,   0.])
_safely_castable_to_int(dt)

Test whether the numpy data type dt can be safely cast to an int.

_stats(input, labels=None, index=None, centered=False)

Count, sum, and optionally compute (sum - centre)^2 of input by label

input : array_like, n-dimensional
The input data to be analyzed.
labels : array_like (n-dimensional), optional
The labels of the data in input. This array must be broadcast compatible with input; typically it is the same shape as input. If labels is None, all nonzero values in input are treated as the single labeled group.
index : label or sequence of labels, optional
These are the labels of the groups for which the stats are computed. If index is None, the stats are computed for the single group where labels is greater than 0.
centered : bool, optional
If True, the centered sum of squares for each labeled group is also returned. Default is False.
counts : int or ndarray of ints
The number of elements in each labeled group.
sums : scalar or ndarray of scalars
The sums of the values in each labeled group.
sums_c : scalar or ndarray of scalars, optional
The sums of mean-centered squares of the values in each labeled group. This is only returned if centered is True.
sum(input, labels=None, index=None)

Calculate the sum of the values of the array.

input : array_like
Values of input inside the regions defined by labels are summed together.
labels : array_like of ints, optional
Assign labels to the values of the array. Has to have the same shape as input.
index : array_like, optional
A single label number or a sequence of label numbers of the objects to be measured.
sum : ndarray or scalar
An array of the sums of values of input inside the regions defined by labels with the same shape as index. If ‘index’ is None or scalar, a scalar is returned.

mean, median

>>> from scipy import ndimage
>>> input =  [0,1,2,3]
>>> labels = [1,1,2,2]
>>> ndimage.sum(input, labels, index=[1,2])
[1.0, 5.0]
>>> ndimage.sum(input, labels, index=1)
1
>>> ndimage.sum(input, labels)
6
mean(input, labels=None, index=None)

Calculate the mean of the values of an array at labels.

input : array_like
Array on which to compute the mean of elements over distinct regions.
labels : array_like, optional
Array of labels of same shape, or broadcastable to the same shape as input. All elements sharing the same label form one region over which the mean of the elements is computed.
index : int or sequence of ints, optional
Labels of the objects over which the mean is to be computed. Default is None, in which case the mean for all values where label is greater than 0 is calculated.
out : list
Sequence of same length as index, with the mean of the different regions labeled by the labels in index.

ndimage.variance, ndimage.standard_deviation, ndimage.minimum, ndimage.maximum, ndimage.sum ndimage.label

>>> from scipy import ndimage
>>> a = np.arange(25).reshape((5,5))
>>> labels = np.zeros_like(a)
>>> labels[3:5,3:5] = 1
>>> index = np.unique(labels)
>>> labels
array([[0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 1, 1],
       [0, 0, 0, 1, 1]])
>>> index
array([0, 1])
>>> ndimage.mean(a, labels=labels, index=index)
[10.285714285714286, 21.0]
variance(input, labels=None, index=None)

Calculate the variance of the values of an n-D image array, optionally at specified sub-regions.

input : array_like
Nd-image data to process.
labels : array_like, optional
Labels defining sub-regions in input. If not None, must be same shape as input.
index : int or sequence of ints, optional
labels to include in output. If None (default), all values where labels is non-zero are used.
variance : float or ndarray
Values of variance, for each sub-region if labels and index are specified.

label, standard_deviation, maximum, minimum, extrema

>>> a = np.array([[1, 2, 0, 0],
...               [5, 3, 0, 4],
...               [0, 0, 0, 7],
...               [9, 3, 0, 0]])
>>> from scipy import ndimage
>>> ndimage.variance(a)
7.609375

Features to process can be specified using labels and index:

>>> lbl, nlbl = ndimage.label(a)
>>> ndimage.variance(a, lbl, index=np.arange(1, nlbl+1))
array([ 2.1875,  2.25  ,  9.    ])

If no index is given, all non-zero labels are processed:

>>> ndimage.variance(a, lbl)
6.1875
standard_deviation(input, labels=None, index=None)

Calculate the standard deviation of the values of an n-D image array, optionally at specified sub-regions.

input : array_like
Nd-image data to process.
labels : array_like, optional
Labels to identify sub-regions in input. If not None, must be same shape as input.
index : int or sequence of ints, optional
labels to include in output. If None (default), all values where labels is non-zero are used.
standard_deviation : float or ndarray
Values of standard deviation, for each sub-region if labels and index are specified.

label, variance, maximum, minimum, extrema

>>> a = np.array([[1, 2, 0, 0],
...               [5, 3, 0, 4],
...               [0, 0, 0, 7],
...               [9, 3, 0, 0]])
>>> from scipy import ndimage
>>> ndimage.standard_deviation(a)
2.7585095613392387

Features to process can be specified using labels and index:

>>> lbl, nlbl = ndimage.label(a)
>>> ndimage.standard_deviation(a, lbl, index=np.arange(1, nlbl+1))
array([ 1.479,  1.5  ,  3.   ])

If no index is given, non-zero labels are processed:

>>> ndimage.standard_deviation(a, lbl)
2.4874685927665499
_select(input, labels=None, index=None, find_min=False, find_max=False, find_min_positions=False, find_max_positions=False, find_median=False)

Returns min, max, or both, plus their positions (if requested), and median.

minimum(input, labels=None, index=None)

Calculate the minimum of the values of an array over labeled regions.

input : array_like
Array_like of values. For each region specified by labels, the minimal values of input over the region is computed.
labels : array_like, optional
An array_like of integers marking different regions over which the minimum value of input is to be computed. labels must have the same shape as input. If labels is not specified, the minimum over the whole array is returned.
index : array_like, optional
A list of region labels that are taken into account for computing the minima. If index is None, the minimum over all elements where labels is non-zero is returned.
minimum : float or list of floats
List of minima of input over the regions determined by labels and whose index is in index. If index or labels are not specified, a float is returned: the minimal value of input if labels is None, and the minimal value of elements where labels is greater than zero if index is None.

label, maximum, median, minimum_position, extrema, sum, mean, variance, standard_deviation

The function returns a Python list and not a Numpy array, use np.array to convert the list to an array.

>>> from scipy import ndimage
>>> a = np.array([[1, 2, 0, 0],
...               [5, 3, 0, 4],
...               [0, 0, 0, 7],
...               [9, 3, 0, 0]])
>>> labels, labels_nb = ndimage.label(a)
>>> labels
array([[1, 1, 0, 0],
       [1, 1, 0, 2],
       [0, 0, 0, 2],
       [3, 3, 0, 0]])
>>> ndimage.minimum(a, labels=labels, index=np.arange(1, labels_nb + 1))
[1.0, 4.0, 3.0]
>>> ndimage.minimum(a)
0.0
>>> ndimage.minimum(a, labels=labels)
1.0
maximum(input, labels=None, index=None)

Calculate the maximum of the values of an array over labeled regions.

input : array_like
Array_like of values. For each region specified by labels, the maximal values of input over the region is computed.
labels : array_like, optional
An array of integers marking different regions over which the maximum value of input is to be computed. labels must have the same shape as input. If labels is not specified, the maximum over the whole array is returned.
index : array_like, optional
A list of region labels that are taken into account for computing the maxima. If index is None, the maximum over all elements where labels is non-zero is returned.
output : float or list of floats
List of maxima of input over the regions determined by labels and whose index is in index. If index or labels are not specified, a float is returned: the maximal value of input if labels is None, and the maximal value of elements where labels is greater than zero if index is None.

label, minimum, median, maximum_position, extrema, sum, mean, variance, standard_deviation

The function returns a Python list and not a Numpy array, use np.array to convert the list to an array.

>>> a = np.arange(16).reshape((4,4))
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15]])
>>> labels = np.zeros_like(a)
>>> labels[:2,:2] = 1
>>> labels[2:, 1:3] = 2
>>> labels
array([[1, 1, 0, 0],
       [1, 1, 0, 0],
       [0, 2, 2, 0],
       [0, 2, 2, 0]])
>>> from scipy import ndimage
>>> ndimage.maximum(a)
15.0
>>> ndimage.maximum(a, labels=labels, index=[1,2])
[5.0, 14.0]
>>> ndimage.maximum(a, labels=labels)
14.0
>>> b = np.array([[1, 2, 0, 0],
...               [5, 3, 0, 4],
...               [0, 0, 0, 7],
...               [9, 3, 0, 0]])
>>> labels, labels_nb = ndimage.label(b)
>>> labels
array([[1, 1, 0, 0],
       [1, 1, 0, 2],
       [0, 0, 0, 2],
       [3, 3, 0, 0]])
>>> ndimage.maximum(b, labels=labels, index=np.arange(1, labels_nb + 1))
[5.0, 7.0, 9.0]
median(input, labels=None, index=None)

Calculate the median of the values of an array over labeled regions.

input : array_like
Array_like of values. For each region specified by labels, the median value of input over the region is computed.
labels : array_like, optional
An array_like of integers marking different regions over which the median value of input is to be computed. labels must have the same shape as input. If labels is not specified, the median over the whole array is returned.
index : array_like, optional
A list of region labels that are taken into account for computing the medians. If index is None, the median over all elements where labels is non-zero is returned.
median : float or list of floats
List of medians of input over the regions determined by labels and whose index is in index. If index or labels are not specified, a float is returned: the median value of input if labels is None, and the median value of elements where labels is greater than zero if index is None.

label, minimum, maximum, extrema, sum, mean, variance, standard_deviation

The function returns a Python list and not a Numpy array, use np.array to convert the list to an array.

>>> from scipy import ndimage
>>> a = np.array([[1, 2, 0, 1],
...               [5, 3, 0, 4],
...               [0, 0, 0, 7],
...               [9, 3, 0, 0]])
>>> labels, labels_nb = ndimage.label(a)
>>> labels
array([[1, 1, 0, 2],
       [1, 1, 0, 2],
       [0, 0, 0, 2],
       [3, 3, 0, 0]])
>>> ndimage.median(a, labels=labels, index=np.arange(1, labels_nb + 1))
[2.5, 4.0, 6.0]
>>> ndimage.median(a)
1.0
>>> ndimage.median(a, labels=labels)
3.0
minimum_position(input, labels=None, index=None)

Find the positions of the minimums of the values of an array at labels.

input : array_like
Array_like of values.
labels : array_like, optional

An array of integers marking different regions over which the position of the minimum value of input is to be computed. labels must have the same shape as input. If labels is not specified, the location of the first minimum over the whole array is returned.

The labels argument only works when index is specified.

index : array_like, optional

A list of region labels that are taken into account for finding the location of the minima. If index is None, the first minimum over all elements where labels is non-zero is returned.

The index argument only works when labels is specified.

output : list of tuples of ints

Tuple of ints or list of tuples of ints that specify the location of minima of input over the regions determined by labels and whose index is in index.

If index or labels are not specified, a tuple of ints is returned specifying the location of the first minimal value of input.

label, minimum, median, maximum_position, extrema, sum, mean, variance, standard_deviation

maximum_position(input, labels=None, index=None)

Find the positions of the maximums of the values of an array at labels.

For each region specified by labels, the position of the maximum value of input within the region is returned.

input : array_like
Array_like of values.
labels : array_like, optional

An array of integers marking different regions over which the position of the maximum value of input is to be computed. labels must have the same shape as input. If labels is not specified, the location of the first maximum over the whole array is returned.

The labels argument only works when index is specified.

index : array_like, optional

A list of region labels that are taken into account for finding the location of the maxima. If index is None, the first maximum over all elements where labels is non-zero is returned.

The index argument only works when labels is specified.

output : list of tuples of ints

List of tuples of ints that specify the location of maxima of input over the regions determined by labels and whose index is in index.

If index or labels are not specified, a tuple of ints is returned specifying the location of the first maximal value of input.

label, minimum, median, maximum_position, extrema, sum, mean, variance, standard_deviation

extrema(input, labels=None, index=None)

Calculate the minimums and maximums of the values of an array at labels, along with their positions.

input : ndarray
Nd-image data to process.
labels : ndarray, optional
Labels of features in input. If not None, must be same shape as input.
index : int or sequence of ints, optional
Labels to include in output. If None (default), all values where non-zero labels are used.
minimums, maximums : int or ndarray
Values of minimums and maximums in each feature.
min_positions, max_positions : tuple or list of tuples
Each tuple gives the n-D coordinates of the corresponding minimum or maximum.

maximum, minimum, maximum_position, minimum_position, center_of_mass

>>> a = np.array([[1, 2, 0, 0],
...               [5, 3, 0, 4],
...               [0, 0, 0, 7],
...               [9, 3, 0, 0]])
>>> from scipy import ndimage
>>> ndimage.extrema(a)
(0, 9, (0, 2), (3, 0))

Features to process can be specified using labels and index:

>>> lbl, nlbl = ndimage.label(a)
>>> ndimage.extrema(a, lbl, index=np.arange(1, nlbl+1))
(array([1, 4, 3]),
 array([5, 7, 9]),
 [(0, 0), (1, 3), (3, 1)],
 [(1, 0), (2, 3), (3, 0)])

If no index is given, non-zero labels are processed:

>>> ndimage.extrema(a, lbl)
(1, 9, (0, 0), (3, 0))
center_of_mass(input, labels=None, index=None)

Calculate the center of mass of the values of an array at labels.

input : ndarray
Data from which to calculate center-of-mass. The masses can either be positive or negative.
labels : ndarray, optional
Labels for objects in input, as generated by ndimage.label. Only used with index. Dimensions must be the same as input.
index : int or sequence of ints, optional
Labels for which to calculate centers-of-mass. If not specified, all labels greater than zero are used. Only used with labels.
center_of_mass : tuple, or list of tuples
Coordinates of centers-of-mass.
>>> a = np.array(([0,0,0,0],
...               [0,1,1,0],
...               [0,1,1,0],
...               [0,1,1,0]))
>>> from scipy import ndimage
>>> ndimage.measurements.center_of_mass(a)
(2.0, 1.5)

Calculation of multiple objects in an image

>>> b = np.array(([0,1,1,0],
...               [0,1,0,0],
...               [0,0,0,0],
...               [0,0,1,1],
...               [0,0,1,1]))
>>> lbl = ndimage.label(b)[0]
>>> ndimage.measurements.center_of_mass(b, lbl, [1,2])
[(0.33333333333333331, 1.3333333333333333), (3.5, 2.5)]

Negative masses are also accepted, which can occur for example when bias is removed from measured data due to random noise.

>>> c = np.array(([-1,0,0,0],
...               [0,-1,-1,0],
...               [0,1,-1,0],
...               [0,1,1,0]))
>>> ndimage.measurements.center_of_mass(c)
(-4.0, 1.0)

If there are division by zero issues, the function does not raise an error but rather issues a RuntimeWarning before returning inf and/or NaN.

>>> d = np.array([-1, 1])
>>> ndimage.measurements.center_of_mass(d)
(inf,)
histogram(input, min, max, bins, labels=None, index=None)

Calculate the histogram of the values of an array, optionally at labels.

Histogram calculates the frequency of values in an array within bins determined by min, max, and bins. The labels and index keywords can limit the scope of the histogram to specified sub-regions within the array.

input : array_like
Data for which to calculate histogram.
min, max : int
Minimum and maximum values of range of histogram bins.
bins : int
Number of bins.
labels : array_like, optional
Labels for objects in input. If not None, must be same shape as input.
index : int or sequence of ints, optional
Label or labels for which to calculate histogram. If None, all values where label is greater than zero are used
hist : ndarray
Histogram counts.
>>> a = np.array([[ 0.    ,  0.2146,  0.5962,  0.    ],
...               [ 0.    ,  0.7778,  0.    ,  0.    ],
...               [ 0.    ,  0.    ,  0.    ,  0.    ],
...               [ 0.    ,  0.    ,  0.7181,  0.2787],
...               [ 0.    ,  0.    ,  0.6573,  0.3094]])
>>> from scipy import ndimage
>>> ndimage.measurements.histogram(a, 0, 1, 10)
array([13,  0,  2,  1,  0,  1,  1,  2,  0,  0])

With labels and no indices, non-zero elements are counted:

>>> lbl, nlbl = ndimage.label(a)
>>> ndimage.measurements.histogram(a, 0, 1, 10, lbl)
array([0, 0, 2, 1, 0, 1, 1, 2, 0, 0])

Indices can be used to count only certain objects:

>>> ndimage.measurements.histogram(a, 0, 1, 10, lbl, 2)
array([0, 0, 1, 1, 0, 0, 1, 1, 0, 0])
watershed_ift(input, markers, structure=None, output=None)

Apply watershed from markers using image foresting transform algorithm.

input : array_like
Input.
markers : array_like
Markers are points within each watershed that form the beginning of the process. Negative markers are considered background markers which are processed after the other markers.
structure : structure element, optional
A structuring element defining the connectivity of the object can be provided. If None, an element is generated with a squared connectivity equal to one.
output : ndarray, optional
An output array can optionally be provided. The same shape as input.
watershed_ift : ndarray
Output. Same shape as input.
[1]A.X. Falcao, J. Stolfi and R. de Alencar Lotufo, “The image foresting transform: theory, algorithms, and applications”, Pattern Analysis and Machine Intelligence, vol. 26, pp. 19-29, 2004.