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2024-10-07 10:13:40 +07:00

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Python

"""test_watershed.py - tests the watershed function
"""
import math
import unittest
import numpy as np
import pytest
from scipy import ndimage as ndi
from skimage._shared.filters import gaussian
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():
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)
@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, 1301, 11278]):
assert np.sum(labels_c1 == lab) == area
for lab, area in zip(range(5), [61824, 3653, 20466, 12386, 11291]):
assert np.sum(labels_c2 == lab) == area