"""test_watershed.py - tests the watershed function Originally part of CellProfiler, code licensed under both GPL and BSD licenses. Website: http://www.cellprofiler.org Copyright (c) 2003-2009 Massachusetts Institute of Technology Copyright (c) 2009-2011 Broad Institute All rights reserved. Original author: Lee Kamentsky """ #Portions of this test were taken from scipy's watershed test in test_ndimage.py # # Copyright (C) 2003-2005 Peter J. Verveer # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # # 2. Redistributions in binary form must reproduce the above # copyright notice, this list of conditions and the following # disclaimer in the documentation and/or other materials provided # with the distribution. # # 3. The name of the author may not be used to endorse or promote # products derived from this software without specific prior # written permission. # # THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS # OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED # WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE # ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY # DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL # DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE # GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS # INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, # WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING # NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS # SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. import math import unittest import pytest import numpy as np from scipy import ndimage as ndi from .._watershed import watershed from skimage.measure import label eps = 1e-12 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]]) 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 = ndi.gaussian_filter(image, 4) 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_compact_watershed(): image = np.zeros((5, 6)) image[:, 3:] = 1 seeds = np.zeros((5, 6), dtype=int) seeds[2, 0] = 1 seeds[2, 3] = 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.ones(image.shape, dtype=int) expected[2, 3:] = 2 np.testing.assert_equal(normal, 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) def test_incorrect_markers_shape(): with pytest.raises(ValueError): image = np.ones((5, 6)) markers = np.ones((5, 7)) output = watershed(image, markers) def test_incorrect_mask_shape(): with pytest.raises(ValueError): image = np.ones((5, 6)) mask = np.ones((5, 7)) output = 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 if __name__ == "__main__": np.testing.run_module_suite()