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scikit-image/skimage/morphology/tests/test_watershed.py
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"""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, is_local_maximum
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.failUnless(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.failUnless(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.failUnless(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.failUnless(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.failUnless(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)
class TestIsLocalMaximum(unittest.TestCase):
def test_00_00_empty(self):
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
result = is_local_maximum(image, labels, np.ones((3, 3), bool))
self.assertTrue(np.all(~ result))
def test_01_01_one_point(self):
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
image[5, 5] = 1
labels[5, 5] = 1
result = is_local_maximum(image, labels, np.ones((3, 3), bool))
self.assertTrue(np.all(result == (labels == 1)))
def test_01_02_adjacent_and_same(self):
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
image[5, 5:6] = 1
labels[5, 5:6] = 1
result = is_local_maximum(image, labels, np.ones((3, 3), bool))
self.assertTrue(np.all(result == (labels == 1)))
def test_01_03_adjacent_and_different(self):
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
image[5, 5] = 1
image[5, 6] = .5
labels[5, 5:6] = 1
expected = (image == 1)
result = is_local_maximum(image, labels, np.ones((3, 3), bool))
self.assertTrue(np.all(result == expected))
result = is_local_maximum(image, labels)
self.assertTrue(np.all(result == expected))
def test_01_04_not_adjacent_and_different(self):
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
image[5, 5] = 1
image[5, 8] = .5
labels[image > 0] = 1
expected = (labels == 1)
result = is_local_maximum(image, labels, np.ones((3, 3), bool))
self.assertTrue(np.all(result == expected))
def test_01_05_two_objects(self):
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
image[5, 5] = 1
image[5, 15] = .5
labels[5, 5] = 1
labels[5, 15] = 2
expected = (labels > 0)
result = is_local_maximum(image, labels, np.ones((3, 3), bool))
self.assertTrue(np.all(result == expected))
def test_01_06_adjacent_different_objects(self):
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
image[5, 5] = 1
image[5, 6] = .5
labels[5, 5] = 1
labels[5, 6] = 2
expected = (labels > 0)
result = is_local_maximum(image, labels, np.ones((3, 3), bool))
self.assertTrue(np.all(result == expected))
def test_02_01_four_quadrants(self):
np.random.seed(21)
image = np.random.uniform(size=(40, 60))
i, j = np.mgrid[0:40, 0:60]
labels = 1 + (i >= 20) + (j >= 30) * 2
i, j = np.mgrid[-3:4, -3:4]
footprint = (i * i + j * j <= 9)
expected = np.zeros(image.shape, float)
for imin, imax in ((0, 20), (20, 40)):
for jmin, jmax in ((0, 30), (30, 60)):
expected[imin:imax, jmin:jmax] = scipy.ndimage.maximum_filter(
image[imin:imax, jmin:jmax], footprint=footprint)
expected = (expected == image)
result = is_local_maximum(image, labels, footprint)
self.assertTrue(np.all(result == expected))
def test_03_01_disk_1(self):
'''regression test of img-1194, footprint = [1]
Test is_local_maximum when every point is a local maximum
'''
np.random.seed(31)
image = np.random.uniform(size=(10, 20))
footprint = np.array([[1]])
result = is_local_maximum(image, np.ones((10, 20)), footprint)
self.assertTrue(np.all(result))
result = is_local_maximum(image, footprint=footprint)
self.assertTrue(np.all(result))
if __name__ == "__main__":
np.testing.run_module_suite()
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