"""test_watershed.py - tests the watershed function""" import math import unittest import numpy as np import pytest from scipy import ndimage as ndi import skimage.measure from skimage._shared.filters import gaussian from skimage.feature import peak_local_max from skimage.measure import label from .._watershed import watershed eps = 1e-12 # fmt: off blob = np.array([[255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255], [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255], [255, 255, 255, 255, 255, 204, 204, 204, 204, 204, 204, 255, 255, 255, 255, 255], [255, 255, 255, 204, 204, 183, 153, 153, 153, 153, 183, 204, 204, 255, 255, 255], [255, 255, 204, 183, 153, 141, 111, 103, 103, 111, 141, 153, 183, 204, 255, 255], [255, 255, 204, 153, 111, 94, 72, 52, 52, 72, 94, 111, 153, 204, 255, 255], [255, 255, 204, 153, 111, 72, 39, 1, 1, 39, 72, 111, 153, 204, 255, 255], [255, 255, 204, 183, 141, 111, 72, 39, 39, 72, 111, 141, 183, 204, 255, 255], [255, 255, 255, 204, 183, 141, 111, 72, 72, 111, 141, 183, 204, 255, 255, 255], [255, 255, 255, 255, 204, 183, 141, 94, 94, 141, 183, 204, 255, 255, 255, 255], [255, 255, 255, 255, 255, 204, 153, 103, 103, 153, 204, 255, 255, 255, 255, 255], [255, 255, 255, 255, 204, 183, 141, 94, 94, 141, 183, 204, 255, 255, 255, 255], [255, 255, 255, 204, 183, 141, 111, 72, 72, 111, 141, 183, 204, 255, 255, 255], [255, 255, 204, 183, 141, 111, 72, 39, 39, 72, 111, 141, 183, 204, 255, 255], [255, 255, 204, 153, 111, 72, 39, 1, 1, 39, 72, 111, 153, 204, 255, 255], [255, 255, 204, 153, 111, 94, 72, 52, 52, 72, 94, 111, 153, 204, 255, 255], [255, 255, 204, 183, 153, 141, 111, 103, 103, 111, 141, 153, 183, 204, 255, 255], [255, 255, 255, 204, 204, 183, 153, 153, 153, 153, 183, 204, 204, 255, 255, 255], [255, 255, 255, 255, 255, 204, 204, 204, 204, 204, 204, 255, 255, 255, 255, 255], [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255], [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255]]) # fmt: on def diff(a, b): if not isinstance(a, np.ndarray): a = np.asarray(a) if not isinstance(b, np.ndarray): b = np.asarray(b) if (0 in a.shape) and (0 in b.shape): return 0.0 b[a == 0] = 0 if a.dtype in [np.complex64, np.complex128] or b.dtype in [ np.complex64, np.complex128, ]: a = np.asarray(a, np.complex128) b = np.asarray(b, np.complex128) t = ((a.real - b.real) ** 2).sum() + ((a.imag - b.imag) ** 2).sum() else: a = np.asarray(a) a = a.astype(np.float64) b = np.asarray(b) b = b.astype(np.float64) t = ((a - b) ** 2).sum() return math.sqrt(t) class TestWatershed(unittest.TestCase): eight = np.ones((3, 3), bool) def test_watershed01(self): "watershed 1" data = np.array( [ [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, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], ], np.uint8, ) markers = np.array( [ [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], ], np.int8, ) out = watershed(data, markers, self.eight) expected = np.array( [ [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], ] ) error = diff(expected, out) assert error < eps def test_watershed02(self): "watershed 2" data = np.array( [ [0, 0, 0, 0, 0, 0, 0], [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, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], ], np.uint8, ) markers = np.array( [ [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], ], np.int8, ) out = watershed(data, markers) error = diff( [ [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, 1, 1, 1, -1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, -1, 1, 1, 1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], ], out, ) self.assertTrue(error < eps) def test_watershed03(self): "watershed 3" data = np.array( [ [0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 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], [0, 0, 0, 0, 0, 0, 0], ], np.uint8, ) markers = np.array( [ [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1], ], np.int8, ) out = watershed(data, markers) error = diff( [ [-1, -1, -1, -1, -1, -1, -1], [-1, 0, 2, 0, 3, 0, -1], [-1, 2, 2, 0, 3, 3, -1], [-1, 2, 2, 0, 3, 3, -1], [-1, 2, 2, 0, 3, 3, -1], [-1, 0, 2, 0, 3, 0, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], ], out, ) self.assertTrue(error < eps) def test_watershed04(self): "watershed 4" data = np.array( [ [0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 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], [0, 0, 0, 0, 0, 0, 0], ], np.uint8, ) markers = np.array( [ [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1], ], np.int8, ) out = watershed(data, markers, self.eight) error = diff( [ [-1, -1, -1, -1, -1, -1, -1], [-1, 2, 2, 0, 3, 3, -1], [-1, 2, 2, 0, 3, 3, -1], [-1, 2, 2, 0, 3, 3, -1], [-1, 2, 2, 0, 3, 3, -1], [-1, 2, 2, 0, 3, 3, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], ], out, ) self.assertTrue(error < eps) def test_watershed05(self): "watershed 5" data = np.array( [ [0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 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], [0, 0, 0, 0, 0, 0, 0], ], np.uint8, ) markers = np.array( [ [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1], ], np.int8, ) out = watershed(data, markers, self.eight) error = diff( [ [-1, -1, -1, -1, -1, -1, -1], [-1, 3, 3, 0, 2, 2, -1], [-1, 3, 3, 0, 2, 2, -1], [-1, 3, 3, 0, 2, 2, -1], [-1, 3, 3, 0, 2, 2, -1], [-1, 3, 3, 0, 2, 2, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], ], out, ) self.assertTrue(error < eps) def test_watershed06(self): "watershed 6" data = np.array( [ [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 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], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], ], np.uint8, ) markers = np.array( [ [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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], ], np.int8, ) out = watershed(data, markers, self.eight) error = diff( [ [-1, 1, 1, 1, 1, 1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, 1, 1, 1, 1, 1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], [-1, -1, -1, -1, -1, -1, -1], ], out, ) self.assertTrue(error < eps) def test_watershed07(self): "A regression test of a competitive case that failed" data = blob mask = data != 255 markers = np.zeros(data.shape, int) markers[6, 7] = 1 markers[14, 7] = 2 out = watershed(data, markers, self.eight, mask=mask) # # The two objects should be the same size, except possibly for the # border region # size1 = np.sum(out == 1) size2 = np.sum(out == 2) self.assertTrue(abs(size1 - size2) <= 6) def test_watershed08(self): "The border pixels + an edge are all the same value" data = blob.copy() data[10, 7:9] = 141 mask = data != 255 markers = np.zeros(data.shape, int) markers[6, 7] = 1 markers[14, 7] = 2 out = watershed(data, markers, self.eight, mask=mask) # # The two objects should be the same size, except possibly for the # border region # size1 = np.sum(out == 1) size2 = np.sum(out == 2) self.assertTrue(abs(size1 - size2) <= 6) def test_watershed09(self): """Test on an image of reasonable size This is here both for timing (does it take forever?) and to ensure that the memory constraints are reasonable """ image = np.zeros((1000, 1000)) coords = np.random.uniform(0, 1000, (100, 2)).astype(int) markers = np.zeros((1000, 1000), int) idx = 1 for x, y in coords: image[x, y] = 1 markers[x, y] = idx idx += 1 image = gaussian(image, sigma=4, mode='reflect') watershed(image, markers, self.eight) ndi.watershed_ift(image.astype(np.uint16), markers, self.eight) def test_watershed10(self): "watershed 10" data = np.array( [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], np.uint8 ) markers = np.array( [[1, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 4]], np.int8 ) out = watershed(data, markers, self.eight) error = diff([[1, 1, 2, 2], [1, 1, 2, 2], [3, 3, 4, 4], [3, 3, 4, 4]], out) self.assertTrue(error < eps) def test_watershed11(self): '''Make sure that all points on this plateau are assigned to closest seed''' # https://github.com/scikit-image/scikit-image/issues/803 # # Make sure that no point in a level image is farther away # from its seed than any other # image = np.zeros((21, 21)) markers = np.zeros((21, 21), int) markers[5, 5] = 1 markers[5, 10] = 2 markers[10, 5] = 3 markers[10, 10] = 4 structure = np.array( [[False, True, False], [True, True, True], [False, True, False]] ) out = watershed(image, markers, structure) i, j = np.mgrid[0:21, 0:21] d = np.dstack( [ np.sqrt((i.astype(float) - i0) ** 2, (j.astype(float) - j0) ** 2) for i0, j0 in ((5, 5), (5, 10), (10, 5), (10, 10)) ] ) dmin = np.min(d, 2) self.assertTrue(np.all(d[i, j, out[i, j] - 1] == dmin)) def test_watershed12(self): "The watershed line" data = np.array( [ [ 203, 255, 203, 153, 153, 153, 153, 153, 153, 153, 153, 153, 153, 153, 153, 153, ], [ 203, 255, 203, 153, 153, 153, 102, 102, 102, 102, 102, 102, 153, 153, 153, 153, ], [ 203, 255, 203, 203, 153, 153, 102, 102, 77, 0, 102, 102, 153, 153, 203, 203, ], [ 203, 255, 255, 203, 153, 153, 153, 102, 102, 102, 102, 153, 153, 203, 203, 255, ], [ 203, 203, 255, 203, 203, 203, 153, 153, 153, 153, 153, 153, 203, 203, 255, 255, ], [ 153, 203, 255, 255, 255, 203, 203, 203, 203, 203, 203, 203, 203, 255, 255, 203, ], [ 153, 203, 203, 203, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 203, 203, ], [ 153, 153, 153, 203, 203, 203, 203, 203, 255, 203, 203, 203, 203, 203, 203, 153, ], [ 102, 102, 153, 153, 153, 153, 203, 203, 255, 203, 203, 255, 203, 153, 153, 153, ], [ 102, 102, 102, 102, 102, 153, 203, 255, 255, 203, 203, 203, 203, 153, 102, 153, ], [ 102, 51, 51, 102, 102, 153, 203, 255, 203, 203, 153, 153, 153, 153, 102, 153, ], [ 77, 51, 51, 102, 153, 153, 203, 255, 203, 203, 203, 153, 102, 102, 102, 153, ], [ 77, 0, 51, 102, 153, 203, 203, 255, 203, 255, 203, 153, 102, 51, 102, 153, ], [ 77, 0, 51, 102, 153, 203, 255, 255, 203, 203, 203, 153, 102, 0, 102, 153, ], [ 102, 0, 51, 102, 153, 203, 255, 203, 203, 153, 153, 153, 102, 102, 102, 153, ], [ 102, 102, 102, 102, 153, 203, 255, 203, 153, 153, 153, 153, 153, 153, 153, 153, ], ] ) markerbin = data == 0 marker = label(markerbin) ws = watershed(data, marker, connectivity=2, watershed_line=True) for lab, area in zip(range(4), [34, 74, 74, 74]): self.assertTrue(np.sum(ws == lab) == area) def test_watershed_input_not_modified(self): """Test to ensure input markers are not modified.""" image = np.random.default_rng().random(size=(21, 21)) markers = np.zeros((21, 21), dtype=np.uint8) markers[[5, 5, 15, 15], [5, 15, 5, 15]] = [1, 2, 3, 4] original_markers = np.copy(markers) result = watershed(image, markers) np.testing.assert_equal(original_markers, markers) assert not np.all(result == markers) def test_compact_watershed(): # in this test, when compactness is greater than zero the watershed line # is labeled with the closest marker (label=2) # when compactness is zero the watershed line is labeled with # the marker that reaches it first (label=1) # because it has a zero cost path to the line. image = np.zeros((5, 6)) image[:, 3] = 2 # watershed line image[:, 4:] = 1 seeds = np.zeros((5, 6), dtype=int) seeds[2, 0] = 1 seeds[2, 5] = 2 compact = watershed(image, seeds, compactness=0.01) expected = np.array( [ [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 2], ], dtype=int, ) np.testing.assert_equal(compact, expected) normal = watershed(image, seeds) expected = np.array( [ [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2], ], dtype=int, ) np.testing.assert_equal(normal, expected) # checks that compact watershed labels with watershed lines are # a subset of the labels from compact watershed for this specific example compact_wsl = watershed(image, seeds, compactness=0.01, watershed_line=True) difference = compact_wsl != compact difference[compact_wsl == 0] = False assert not np.any(difference) def test_watershed_with_markers_offset(): """ Regression test from https://github.com/scikit-image/scikit-image/issues/6632 Generate an initial image with two overlapping circles. """ # Generate an initial image with two overlapping circles x, y = np.indices((80, 80)) x1, y1, x2, y2 = 28, 28, 44, 52 r1, r2 = 16, 20 mask_circle1 = (x - x1) ** 2 + (y - y1) ** 2 < r1**2 mask_circle2 = (x - x2) ** 2 + (y - y2) ** 2 < r2**2 image = np.logical_or(mask_circle1, mask_circle2) # Now we want to separate the two objects in image # Generate the markers as local maxima of the distance to the background # and then apply an y-offset distance = ndi.distance_transform_edt(image) coords = peak_local_max(distance, footprint=np.ones((3, 3)), labels=image) coords[:, 0] += 6 mask = np.zeros(distance.shape, dtype=bool) mask[tuple(coords.T)] = True markers, _ = ndi.label(mask) labels = watershed(-distance, markers, mask=image) # Assert pixel count from reviewed reproducing example in bug report # Generally, assert both objects have covered their basin props = skimage.measure.regionprops(labels) assert props[0].eccentricity <= 0.5 assert props[1].eccentricity <= 0.5 assert props[0].num_pixels == 732 assert props[1].num_pixels == 1206 def test_watershed_simple_basin_overspill(): """ Test behavior when markers spill over into another basin / compete. Regression test for https://github.com/scikit-image/scikit-image/issues/6632. """ image = -np.array([1, 2, 2, 2, 2, 2, 3]) markers = np.array([1, 0, 0, 0, 0, 0, 2]) expected = np.array([1, 1, 1, 1, 2, 2, 2]) result = watershed(image, markers=markers, mask=image != 0) np.testing.assert_array_equal(result, expected) def test_numeric_seed_watershed(): """Test that passing just the number of seeds to watershed works.""" image = np.zeros((5, 6)) image[:, 3:] = 1 compact = watershed(image, 2, compactness=0.01) expected = np.array( [ [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2], ], dtype=np.int32, ) np.testing.assert_equal(compact, expected) @pytest.mark.parametrize( 'dtype', [np.uint8, np.int8, np.uint16, np.int16, np.uint32, np.int32, np.uint64, np.int64], ) def test_watershed_output_dtype(dtype): image = np.zeros((100, 100)) markers = np.zeros((100, 100), dtype) out = watershed(image, markers) assert out.dtype == markers.dtype def test_incorrect_markers_shape(): image = np.ones((5, 6)) markers = np.ones((5, 7)) with pytest.raises(ValueError): watershed(image, markers) def test_incorrect_mask_shape(): image = np.ones((5, 6)) mask = np.ones((5, 7)) with pytest.raises(ValueError): watershed(image, markers=4, mask=mask) def test_markers_in_mask(): data = blob mask = data != 255 out = watershed(data, 25, connectivity=2, mask=mask) # There should be no markers where the mask is false assert np.all(out[~mask] == 0) def test_no_markers(): data = blob mask = data != 255 out = watershed(data, mask=mask) assert np.max(out) == 2 def test_connectivity(): """ Watershed segmentation should output different result for different connectivity when markers are calculated where None is supplied. Issue = 5084 """ # Generate a dummy BrightnessTemperature image x, y = np.indices((406, 270)) x1, y1, x2, y2, x3, y3, x4, y4 = 200, 208, 300, 120, 100, 100, 340, 208 r1, r2, r3, r4 = 100, 50, 40, 80 mask_circle1 = (x - x1) ** 2 + (y - y1) ** 2 < r1**2 mask_circle2 = (x - x2) ** 2 + (y - y2) ** 2 < r2**2 mask_circle3 = (x - x3) ** 2 + (y - y3) ** 2 < r3**2 mask_circle4 = (x - x4) ** 2 + (y - y4) ** 2 < r4**2 image = np.logical_or(mask_circle1, mask_circle2) image = np.logical_or(image, mask_circle3) image = np.logical_or(image, mask_circle4) # calculate distance in discrete increase DummyBT = ndi.distance_transform_edt(image) DummyBT_dis = np.around(DummyBT / 12, decimals=0) * 12 # calculate the mask Img_mask = np.where(DummyBT_dis == 0, 0, 1) # segments for connectivity 1 and 2 labels_c1 = watershed( 200 - DummyBT_dis, mask=Img_mask, connectivity=1, compactness=0.01 ) labels_c2 = watershed( 200 - DummyBT_dis, mask=Img_mask, connectivity=2, compactness=0.01 ) # assertions assert np.unique(labels_c1).shape[0] == 6 assert np.unique(labels_c2).shape[0] == 5 # checking via area of each individual segment. for lab, area in zip(range(6), [61824, 3653, 20467, 11097, 1300, 11279]): assert np.sum(labels_c1 == lab) == area for lab, area in zip(range(5), [61824, 3653, 20466, 12385, 11292]): assert np.sum(labels_c2 == lab) == area