"""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 numpy as np import scipy.ndimage from skimage.morphology.watershed import watershed, _slow_watershed eps = 1e-12 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 out = _slow_watershed(data, markers, 8) 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 = 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]]) 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 = 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, 141, 141, 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]]) 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 = scipy.ndimage.gaussian_filter(image, 4) watershed(image, markers, self.eight) scipy.ndimage.watershed_ift(image.astype(np.uint16), markers, self.eight) if __name__ == "__main__": np.testing.run_module_suite()