def test_trivial_case(self):
trivial = np.zeros((25, 25))
peak_indices = peak.peak_local_max(trivial, min_distance=1, indices=True)
assert type(peak_indices) is np.ndarray
assert not peak_indices # inherent boolean-ness of empty list
peaks = peak.peak_local_max(trivial, min_distance=1, indices=False)
assert (peaks.astype(np.bool) == trivial).all()
def test_trivial_case(self):
trivial = np.zeros((25, 25))
peak_indices = peak.peak_local_max(trivial, min_distance=1, indices=True)
assert type(peak_indices) is np.ndarray
assert peak_indices.size == 0
peaks = peak.peak_local_max(trivial, min_distance=1, indices=False)
assert (peaks.astype(np.bool) == trivial).all()
def test_4D():
image = np.zeros((30, 30, 30, 30))
image[15, 15, 15, 15] = 1
image[5, 5, 5, 5] = 1
assert_equal(peak.peak_local_max(image), [[15, 15, 15, 15]])
assert_equal(peak.peak_local_max(image, min_distance=6), [[15, 15, 15, 15]])
assert_equal(peak.peak_local_max(image, exclude_border=False),
[[5, 5, 5, 5], [15, 15, 15, 15]])
assert_equal(peak.peak_local_max(image, min_distance=5),
[[5, 5, 5, 5], [15, 15, 15, 15]])
def test_num_peaks():
image = np.zeros((3, 7), dtype=np.uint8)
image[1, 1] = 10
image[1, 3] = 11
image[1, 5] = 12
assert len(peak.peak_local_max(image, min_distance=1)) == 3
peaks_limited = peak.peak_local_max(image, min_distance=1, num_peaks=2)
assert len(peaks_limited) == 2
assert (1, 3) in peaks_limited
assert (1, 5) in peaks_limited
def test_threshold_rel_default(self):
image = np.ones((5, 5))
image[2, 2] = 1
assert len(peak.peak_local_max(image)) == 0
image[2, 2] = 2
assert_equal(peak.peak_local_max(image), [[2, 2]])
image[2, 2] = 0
assert len(peak.peak_local_max(image, min_distance=0)) == image.size - 1
def test_sorted_peaks(self):
image = np.zeros((5, 5), dtype=np.uint8)
image[1, 1] = 20
image[3, 3] = 10
peaks = peak.peak_local_max(image, min_distance=1)
assert peaks.tolist() == [[3, 3], [1, 1]]
image = np.zeros((3, 10))
image[1, (1, 3, 5, 7)] = (1, 3, 2, 4)
peaks = peak.peak_local_max(image, min_distance=1)
assert peaks.tolist() == [[1, 7], [1, 5], [1, 3], [1, 1]]
def test_disk():
'''regression test of img-1194, footprint = [1]
Test peak.peak_local_max when every point is a local maximum
'''
image = np.random.uniform(size=(10, 20))
footprint = np.array([[1]])
result = peak.peak_local_max(image, labels=np.ones((10, 20)),
footprint=footprint,
min_distance=1, threshold_rel=0,
indices=False, exclude_border=False)
assert np.all(result)
result = peak.peak_local_max(image, footprint=footprint)
assert np.all(result)
def test_3D():
image = np.zeros((30, 30, 30))
image[15, 15, 15] = 1
image[5, 5, 5] = 1
assert_equal(peak.peak_local_max(image, min_distance=10, threshold_rel=0),
[[15, 15, 15]])
assert_equal(peak.peak_local_max(image, min_distance=6, threshold_rel=0),
[[15, 15, 15]])
assert_equal(peak.peak_local_max(image, min_distance=10, threshold_rel=0,
exclude_border=False),
[[5, 5, 5], [15, 15, 15]])
assert_equal(peak.peak_local_max(image, min_distance=5, threshold_rel=0),
[[5, 5, 5], [15, 15, 15]])
def test_num_peaks_and_labels(self):
image = np.zeros((7, 7), dtype=np.uint8)
labels = np.zeros((7, 7), dtype=np.uint8) + 20
image[1, 1] = 10
image[1, 3] = 11
image[1, 5] = 12
image[3, 5] = 8
image[5, 3] = 7
peaks_limited = peak.peak_local_max(
image, min_distance=1, threshold_abs=0, labels=labels)
assert len(peaks_limited) == 5
peaks_limited = peak.peak_local_max(
image, min_distance=1, threshold_abs=0, labels=labels, num_peaks=2)
assert len(peaks_limited) == 2
def test_4D(self):
image = np.zeros((30, 30, 30, 30))
image[15, 15, 15, 15] = 1
image[5, 5, 5, 5] = 1
assert_equal(peak.peak_local_max(image, min_distance=10, threshold_rel=0),
[[15, 15, 15, 15]])
assert_equal(peak.peak_local_max(image, min_distance=6, threshold_rel=0),
[[15, 15, 15, 15]])
assert sorted(peak.peak_local_max(image, min_distance=10, threshold_rel=0,
exclude_border=False).tolist()) == \
[[5, 5, 5, 5], [15, 15, 15, 15]]
assert sorted(peak.peak_local_max(image, min_distance=5,
threshold_rel=0).tolist()) == \
[[5, 5, 5, 5], [15, 15, 15, 15]]
def find_peaks(self, min_distance_mm=5):
"""
Find peaks in the image data.
Arguments:
----------
min_distance_mm : float
Minimum distance between peaks in mm
Returns:
--------
peaks: PointSet
"""
from skimage.feature.peak import peak_local_max
from ..commons import affine_scaling
img = self.fetch()
dist = int(min_distance_mm / affine_scaling(img.affine) + 0.5)
voxels = peak_local_max(
img.get_fdata(),
exclude_border=False,
min_distance=dist,
)
return (
PointSet(
[np.dot(img.affine, [x, y, z, 1])[:3] for x, y, z in voxels],
space=self.space,
),
img,
)
def test_num_peaks3D(self):
# Issue 1354: the old code only hold for 2D arrays
# and this code would die with IndexError
image = np.zeros((10, 10, 100))
image[5,5,::5] = np.arange(20)
peaks_limited = peak.peak_local_max(image, min_distance=1, num_peaks=2)
assert len(peaks_limited) == 2
def test_absolute_threshold(self):
image = np.zeros((5, 5), dtype=np.uint8)
image[1, 1] = 10
image[3, 3] = 20
peaks = peak.peak_local_max(image, min_distance=1, threshold_abs=10)
assert len(peaks) == 1
assert_close(peaks, [(3, 3)])
def test_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 = peak.peak_local_max(image, labels=labels,
footprint=np.ones((3, 3), bool),
min_distance=1, threshold_rel=0,
indices=False, exclude_border=False)
assert np.all(result == expected)
result = peak.peak_local_max(image, labels=labels,
min_distance=1, threshold_rel=0,
indices=False, exclude_border=False)
assert np.all(result == expected)
def test_relative_threshold(self):
image = np.zeros((5, 5), dtype=np.uint8)
image[1, 1] = 10
image[3, 3] = 20
peaks = peak.peak_local_max(image, min_distance=1, threshold_rel=0.5)
assert len(peaks) == 1
assert_array_almost_equal(peaks, [(3, 3)])
def test_empty(self):
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
result = peak.peak_local_max(image, labels=labels,
footprint=np.ones((3, 3), bool),
min_distance=1, threshold_rel=0,
indices=False, exclude_border=False)
assert np.all(~ result)
def test_ndarray_exclude_border(self):
nd_image = np.zeros((5, 5, 5))
nd_image[[1, 0, 0], [0, 1, 0], [0, 0, 1]] = 1
nd_image[3, 0, 0] = 1
nd_image[2, 2, 2] = 1
expected = np.zeros_like(nd_image, dtype=np.bool)
expected[2, 2, 2] = True
expectedNoBorder = nd_image > 0
result = peak.peak_local_max(nd_image, min_distance=2,
exclude_border=2, indices=False)
assert_equal(result, expected)
# Check that bools work as expected
assert_equal(
peak.peak_local_max(nd_image, min_distance=2,
exclude_border=2, indices=False),
peak.peak_local_max(nd_image, min_distance=2,
exclude_border=True, indices=False)
)
assert_equal(
peak.peak_local_max(nd_image, min_distance=2,
exclude_border=0, indices=False),
peak.peak_local_max(nd_image, min_distance=2,
exclude_border=False, indices=False)
)
# Check both versions with no border
assert_equal(
peak.peak_local_max(nd_image, min_distance=2,
exclude_border=0, indices=False),
expectedNoBorder,
)
assert_equal(
peak.peak_local_max(nd_image,
exclude_border=False, indices=False),
expectedNoBorder,
)
def test_ndarray_exclude_border():
nd_image = np.zeros((5,5,5))
nd_image[[1,0,0],[0,1,0],[0,0,1]] = 1
nd_image[3,0,0] = 1
nd_image[2,2,2] = 1
expected = np.zeros_like(nd_image, dtype=np.bool)
expected[2,2,2] = True
result = peak.peak_local_max(nd_image, min_distance=2, indices=False)
assert (result == expected).all()
def test_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 = peak.peak_local_max(image, labels=labels,
footprint=np.ones((3, 3), bool),
min_distance=1, threshold_rel=0,
indices=False, exclude_border=False)
assert np.all(result == (labels == 1))
def test_input_labels_unmodified(self):
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
image[5, 5] = 1
labels[5, 5] = 1
labelsin = labels.copy()
result = peak.peak_local_max(image, labels=labels,
footprint=np.ones((3, 3), bool),
min_distance=1, threshold_rel=0,
indices=False, exclude_border=False)
assert np.all(labels == labelsin)
def test_num_peaks(self):
image = np.zeros((7, 7), dtype=np.uint8)
image[1, 1] = 10
image[1, 3] = 11
image[1, 5] = 12
image[3, 5] = 8
image[5, 3] = 7
assert len(peak.peak_local_max(image, min_distance=1, threshold_abs=0)) == 5
peaks_limited = peak.peak_local_max(
image, min_distance=1, threshold_abs=0, num_peaks=2)
assert len(peaks_limited) == 2
assert (1, 3) in peaks_limited
assert (1, 5) in peaks_limited
peaks_limited = peak.peak_local_max(
image, min_distance=1, threshold_abs=0, num_peaks=4)
assert len(peaks_limited) == 4
assert (1, 3) in peaks_limited
assert (1, 5) in peaks_limited
assert (1, 1) in peaks_limited
assert (3, 5) in peaks_limited
def test_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 = peak.peak_local_max(image, labels=labels,
footprint=np.ones((3, 3), bool),
min_distance=1, threshold_rel=0,
indices=False, exclude_border=False)
assert np.all(result == expected)
def test_noisy_peaks(self):
peak_locations = [(7, 7), (7, 13), (13, 7), (13, 13)]
# image with noise of amplitude 0.8 and peaks of amplitude 1
image = 0.8 * np.random.rand(20, 20)
for r, c in peak_locations:
image[r, c] = 1
peaks_detected = peak.peak_local_max(image, min_distance=5)
assert len(peaks_detected) == len(peak_locations)
for loc in peaks_detected:
assert tuple(loc) in peak_locations
def test_num_peaks_tot_vs_labels_4quadrants(self):
np.random.seed(21)
image = np.random.uniform(size=(20, 30))
i, j = np.mgrid[0:20, 0:30]
labels = 1 + (i >= 10) + (j >= 15) * 2
result = peak.peak_local_max(image, labels=labels,
min_distance=1, threshold_rel=0,
indices=True,
num_peaks=np.inf,
num_peaks_per_label=2)
assert len(result) == 8
result = peak.peak_local_max(image, labels=labels,
min_distance=1, threshold_rel=0,
indices=True,
num_peaks=np.inf,
num_peaks_per_label=1)
assert len(result) == 4
result = peak.peak_local_max(image, labels=labels,
min_distance=1, threshold_rel=0,
indices=True,
num_peaks=2,
num_peaks_per_label=2)
assert len(result) == 2
def test_indices_with_labels():
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 = peak.peak_local_max(image, labels=labels, min_distance=1,
threshold_rel=0, footprint=footprint,
indices=True, exclude_border=False)
assert (result == np.transpose(expected.nonzero())).all()
def test_four_quadrants(self):
image = np.random.uniform(size=(20, 30))
i, j = np.mgrid[0:20, 0:30]
labels = 1 + (i >= 10) + (j >= 15) * 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, 10), (10, 20)):
for jmin, jmax in ((0, 15), (15, 30)):
expected[imin:imax, jmin:jmax] = ndi.maximum_filter(
image[imin:imax, jmin:jmax], footprint=footprint)
expected = (expected == image)
result = peak.peak_local_max(image, labels=labels, footprint=footprint,
min_distance=1, threshold_rel=0,
indices=False, exclude_border=False)
assert np.all(result == expected)
def test_reorder_labels():
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
labels[labels == 4] = 5
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] = ndi.maximum_filter(
image[imin:imax, jmin:jmax], footprint=footprint)
expected = (expected == image)
result = peak.peak_local_max(image, labels=labels, min_distance=1,
threshold_rel=0, footprint=footprint,
indices=False, exclude_border=False)
assert (result == expected).all()
def test_adjacent_different_objects():
image = np.zeros((10, 20))
labels = np.zeros((10, 20), int)
image[5, 5] = 1
image[5, 6] = 0.5
labels[5, 5] = 1
labels[5, 6] = 2
expected = labels > 0
result = peak.peak_local_max(
image,
labels=labels,
footprint=np.ones((3, 3), bool),
min_distance=1,
threshold_rel=0,
indices=False,
exclude_border=False,
)
assert np.all(result == expected)
def blob_log(image, min_sigma=1, max_sigma=50, num_sigma=10, threshold=.2,
overlap=.5, log_scale=False):
"""Finds blobs in the given grayscale image.
Blobs are found using the Laplacian of Gaussian (LoG) method [1]_.
For each blob found, the method returns its coordinates and the standard
deviation of the Gaussian kernel that detected the blob.
Parameters
----------
image : 2D or 3D ndarray
Input grayscale image, blobs are assumed to be light on dark
background (white on black).
min_sigma : float, optional
The minimum standard deviation for Gaussian Kernel. Keep this low to
detect smaller blobs.
max_sigma : float, optional
The maximum standard deviation for Gaussian Kernel. Keep this high to
detect larger blobs.
num_sigma : int, optional
The number of intermediate values of standard deviations to consider
between `min_sigma` and `max_sigma`.
threshold : float, optional.
The absolute lower bound for scale space maxima. Local maxima smaller
than thresh are ignored. Reduce this to detect blobs with less
intensities.
overlap : float, optional
A value between 0 and 1. If the area of two blobs overlaps by a
fraction greater than `threshold`, the smaller blob is eliminated.
log_scale : bool, optional
If set intermediate values of standard deviations are interpolated
using a logarithmic scale to the base `10`. If not, linear
interpolation is used.
Returns
-------
A : (n, image.ndim + 1) ndarray
A 2d array with each row representing 3 values for a 2D image,
and 4 values for a 3D image: ``(r, c, sigma)`` or ``(f, r, c, sigma)``
where ``(r, c)`` or ``(f, r, c)`` are coordinates of the blob and
``sigma`` is the standard deviation of the Gaussian kernel which
detected the blob.
References
----------
.. [1] http://en.wikipedia.org/wiki/Blob_detection#The_Laplacian_of_Gaussian
Examples
--------
>>> from skimage import data, feature, exposure
>>> img = data.coins()
>>> img = exposure.equalize_hist(img) # improves detection
>>> feature.blob_log(img, threshold = .3)
array([[ 113. , 323. , 1. ],
[ 121. , 272. , 17.33333333],
[ 124. , 336. , 11.88888889],
[ 126. , 46. , 11.88888889],
[ 126. , 208. , 11.88888889],
[ 127. , 102. , 11.88888889],
[ 128. , 154. , 11.88888889],
[ 185. , 344. , 17.33333333],
[ 194. , 213. , 17.33333333],
[ 194. , 276. , 17.33333333],
[ 197. , 44. , 11.88888889],
[ 198. , 103. , 11.88888889],
[ 198. , 155. , 11.88888889],
[ 260. , 174. , 17.33333333],
[ 263. , 244. , 17.33333333],
[ 263. , 302. , 17.33333333],
[ 266. , 115. , 11.88888889]])
Notes
-----
The radius of each blob is approximately :math:`\sqrt{2}sigma` for
a 2-D image and :math:`\sqrt{3}sigma` for a 3-D image.
"""
image = img_as_float(image)
if log_scale:
start, stop = log(min_sigma, 10), log(max_sigma, 10)
sigma_list = np.logspace(start, stop, num_sigma)
else:
sigma_list = np.linspace(min_sigma, max_sigma, num_sigma)
# computing gaussian laplace
# s**2 provides scale invariance
gl_images = [-gaussian_laplace(image, s) * s ** 2 for s in sigma_list]
# Replace by image_cube = np.stack(hessian_images, axis=-1)
# When we upgrade minimal requirements to NumPy 1.10
sl = (slice(None),) * image.ndim + (np.newaxis,)
arrays = [np.asanyarray(arr) for arr in gl_images]
extended_arrays = [arr[sl] for arr in arrays]
image_cube = np.concatenate(extended_arrays, axis=-1)
local_maxima = peak_local_max(image_cube, threshold_abs=threshold,
footprint=np.ones((3,) * (image.ndim + 1)),
threshold_rel=0.0,
exclude_border=False)
# Convert local_maxima to float64
lm = local_maxima.astype(np.float64)
# Convert the last index to its corresponding scale value
lm[:, -1] = sigma_list[local_maxima[:, -1]]
return _prune_blobs(lm, overlap)
def blob_dog(image, min_sigma=1, max_sigma=50, sigma_ratio=1.6, threshold=2.0,
overlap=.5, ):
"""Finds blobs in the given grayscale image.
Blobs are found using the Difference of Gaussian (DoG) method [1]_.
For each blob found, the method returns its coordinates and the standard
deviation of the Gaussian kernel that detected the blob.
Parameters
----------
image : 2D or 3D ndarray
Input grayscale image, blobs are assumed to be light on dark
background (white on black).
min_sigma : float, optional
The minimum standard deviation for Gaussian Kernel. Keep this low to
detect smaller blobs.
max_sigma : float, optional
The maximum standard deviation for Gaussian Kernel. Keep this high to
detect larger blobs.
sigma_ratio : float, optional
The ratio between the standard deviation of Gaussian Kernels used for
computing the Difference of Gaussians
threshold : float, optional.
The absolute lower bound for scale space maxima. Local maxima smaller
than thresh are ignored. Reduce this to detect blobs with less
intensities.
overlap : float, optional
A value between 0 and 1. If the area of two blobs overlaps by a
fraction greater than `threshold`, the smaller blob is eliminated.
Returns
-------
A : (n, image.ndim + 1) ndarray
A 2d array with each row representing 3 values for a 2D image,
and 4 values for a 3D image: ``(r, c, sigma)`` or ``(p, r, c, sigma)``
where ``(r, c)`` or ``(p, r, c)`` are coordinates of the blob and
``sigma`` is the standard deviation of the Gaussian kernel which
detected the blob.
References
----------
.. [1] http://en.wikipedia.org/wiki/Blob_detection#The_difference_of_Gaussians_approach
Examples
--------
>>> from skimage import data, feature
>>> feature.blob_dog(data.coins(), threshold=.5, max_sigma=40)
array([[ 45. , 336. , 16.777216],
[ 52. , 155. , 16.777216],
[ 52. , 216. , 16.777216],
[ 54. , 42. , 16.777216],
[ 54. , 276. , 10.48576 ],
[ 58. , 100. , 10.48576 ],
[ 120. , 272. , 16.777216],
[ 124. , 337. , 10.48576 ],
[ 125. , 45. , 16.777216],
[ 125. , 208. , 10.48576 ],
[ 127. , 102. , 10.48576 ],
[ 128. , 154. , 10.48576 ],
[ 185. , 347. , 16.777216],
[ 193. , 213. , 16.777216],
[ 194. , 277. , 16.777216],
[ 195. , 102. , 16.777216],
[ 196. , 43. , 10.48576 ],
[ 198. , 155. , 10.48576 ],
[ 260. , 46. , 16.777216],
[ 261. , 173. , 16.777216],
[ 263. , 245. , 16.777216],
[ 263. , 302. , 16.777216],
[ 267. , 115. , 10.48576 ],
[ 267. , 359. , 16.777216]])
Notes
-----
The radius of each blob is approximately :math:`\sqrt{2}sigma` for
a 2-D image and :math:`\sqrt{3}sigma` for a 3-D image.
"""
image = img_as_float(image)
# k such that min_sigma*(sigma_ratio**k) > max_sigma
k = int(log(float(max_sigma) / min_sigma, sigma_ratio)) + 1
# a geometric progression of standard deviations for gaussian kernels
sigma_list = np.array([min_sigma * (sigma_ratio ** i)
for i in range(k + 1)])
gaussian_images = [gaussian_filter(image, s) for s in sigma_list]
# computing difference between two successive Gaussian blurred images
# multiplying with standard deviation provides scale invariance
dog_images = [(gaussian_images[i] - gaussian_images[i + 1])
* sigma_list[i] for i in range(k)]
# Replace by image_cube = np.stack(hessian_images, axis=-1)
# When we upgrade minimal requirements to NumPy 1.10
sl = (slice(None),) * image.ndim + (np.newaxis,)
arrays = [np.asanyarray(arr) for arr in dog_images]
extended_arrays = [arr[sl] for arr in arrays]
image_cube = np.concatenate(extended_arrays, axis=-1)
# local_maxima = get_local_maxima(image_cube, threshold)
local_maxima = peak_local_max(image_cube, threshold_abs=threshold,
footprint=np.ones((3,) * (image.ndim + 1)),
threshold_rel=0.0,
exclude_border=False)
# Convert local_maxima to float64
lm = local_maxima.astype(np.float64)
# Convert the last index to its corresponding scale value
lm[:, -1] = sigma_list[local_maxima[:, -1]]
return _prune_blobs(lm, overlap)
def test_flat_peak(self):
image = np.zeros((5, 5), dtype=np.uint8)
image[1:3, 1:3] = 10
peaks = peak.peak_local_max(image, min_distance=1)
assert len(peaks) == 4
