def hough_line_peaks(hspace, angles, dists, min_distance=9, min_angle=10,
threshold=None, num_peaks=np.inf):
"""Return peaks in a straight line Hough transform.
Identifies most prominent lines separated by a certain angle and distance
in a Hough transform. Non-maximum suppression with different sizes is
applied separately in the first (distances) and second (angles) dimension
of the Hough space to identify peaks.
Parameters
----------
hspace : (N, M) array
Hough space returned by the `hough_line` function.
angles : (M,) array
Angles returned by the `hough_line` function. Assumed to be continuous.
(`angles[-1] - angles[0] == PI`).
dists : (N, ) array
Distances returned by the `hough_line` function.
min_distance : int, optional
Minimum distance separating lines (maximum filter size for first
dimension of hough space).
min_angle : int, optional
Minimum angle separating lines (maximum filter size for second
dimension of hough space).
threshold : float, optional
Minimum intensity of peaks. Default is `0.5 * max(hspace)`.
num_peaks : int, optional
Maximum number of peaks. When the number of peaks exceeds `num_peaks`,
return `num_peaks` coordinates based on peak intensity.
Returns
-------
accum, angles, dists : tuple of array
Peak values in Hough space, angles and distances.
Examples
--------
>>> from skimage.transform import hough_line, hough_line_peaks
>>> from skimage.draw import line
>>> img = np.zeros((15, 15), dtype=np.bool_)
>>> rr, cc = line(0, 0, 14, 14)
>>> img[rr, cc] = 1
>>> rr, cc = line(0, 14, 14, 0)
>>> img[cc, rr] = 1
>>> hspace, angles, dists = hough_line(img)
>>> hspace, angles, dists = hough_line_peaks(hspace, angles, dists)
>>> len(angles)
2
"""
from skimage.feature.peak import _prominent_peaks
h, a, d = _prominent_peaks(hspace, min_xdistance=min_angle,
min_ydistance=min_distance,
threshold=threshold,
num_peaks=num_peaks)
return (h, angles[a], dists[d])
def hough_line_peaks(hspace, angles, dists, min_distance=9, min_angle=10,
threshold=None, num_peaks=np.inf):
"""Return peaks in a straight line Hough transform.
Identifies most prominent lines separated by a certain angle and distance
in a Hough transform. Non-maximum suppression with different sizes is
applied separately in the first (distances) and second (angles) dimension
of the Hough space to identify peaks.
Parameters
----------
hspace : (N, M) array
Hough space returned by the `hough_line` function.
angles : (M,) array
Angles returned by the `hough_line` function. Assumed to be continuous.
(`angles[-1] - angles[0] == PI`).
dists : (N, ) array
Distances returned by the `hough_line` function.
min_distance : int, optional
Minimum distance separating lines (maximum filter size for first
dimension of hough space).
min_angle : int, optional
Minimum angle separating lines (maximum filter size for second
dimension of hough space).
threshold : float, optional
Minimum intensity of peaks. Default is `0.5 * max(hspace)`.
num_peaks : int, optional
Maximum number of peaks. When the number of peaks exceeds `num_peaks`,
return `num_peaks` coordinates based on peak intensity.
Returns
-------
accum, angles, dists : tuple of array
Peak values in Hough space, angles and distances.
Examples
--------
>>> from skimage.transform import hough_line, hough_line_peaks
>>> from skimage.draw import line
>>> img = np.zeros((15, 15), dtype=np.bool_)
>>> rr, cc = line(0, 0, 14, 14)
>>> img[rr, cc] = 1
>>> rr, cc = line(0, 14, 14, 0)
>>> img[cc, rr] = 1
>>> hspace, angles, dists = hough_line(img)
>>> hspace, angles, dists = hough_line_peaks(hspace, angles, dists)
>>> len(angles)
2
"""
from skimage.feature.peak import _prominent_peaks
h, a, d = _prominent_peaks(hspace, min_xdistance=min_angle,
min_ydistance=min_distance,
threshold=threshold,
num_peaks=num_peaks)
return (h, angles[a], dists[d])
def test_threshold(self):
image = np.zeros((15, 15))
x0, y0, i0 = (12, 8, 10)
x1, y1, i1 = (2, 2, 8)
x2, y2, i2 = (5, 13, 10)
image[y0, x0] = i0
image[y1, x1] = i1
image[y2, x2] = i2
out = peak._prominent_peaks(image, threshold=None)
assert len(out[0]) == 3
for i, x, y in zip(out[0], out[1], out[2]):
self.assertTrue(i in (i0, i1, i2))
self.assertTrue(x in (x0, x1, x2))
out = peak._prominent_peaks(image, threshold=9)
assert len(out[0]) == 2
for i, x, y in zip(out[0], out[1], out[2]):
self.assertTrue(i in (i0, i2))
self.assertTrue(x in (x0, x2))
self.assertTrue(y in (y0, y2))
def test_threshold(self):
image = np.zeros((15, 15))
x0, y0, i0 = (12, 8, 10)
x1, y1, i1 = (2, 2, 8)
x2, y2, i2 = (5, 13, 10)
image[y0, x0] = i0
image[y1, x1] = i1
image[y2, x2] = i2
out = peak._prominent_peaks(image, threshold=None)
assert len(out[0]) == 3
for i, x, y in zip (out[0], out[1], out[2]):
self.assertTrue(i in (i0, i1, i2))
self.assertTrue(x in (x0, x1, x2))
out = peak._prominent_peaks(image, threshold=9)
assert len(out[0]) == 2
for i, x, y in zip (out[0], out[1], out[2]):
self.assertTrue(i in (i0, i2))
self.assertTrue(x in (x0, x2))
self.assertTrue(y in (y0, y2))
def test_peaks_in_contact(self):
image = np.zeros((15, 15))
x0, y0, i0 = (8, 8, 1)
x1, y1, i1 = (7, 7, 1) # prominent peak
x2, y2, i2 = (6, 6, 1)
image[y0, x0] = i0
image[y1, x1] = i1
image[y2, x2] = i2
out = peak._prominent_peaks(image, min_xdistance=3,
min_ydistance=3,)
assert_equal(out[0], np.array((i1,)))
assert_equal(out[1], np.array((x1,)))
assert_equal(out[2], np.array((y1,)))
def test_peaks_in_contact(self):
image = np.zeros((15, 15))
x0, y0, i0 = (8, 8, 1)
x1, y1, i1 = (7, 7, 1) # prominent peak
x2, y2, i2 = (6, 6, 1)
image[y0, x0] = i0
image[y1, x1] = i1
image[y2, x2] = i2
out = peak._prominent_peaks(image, min_xdistance=3,
min_ydistance=3,)
assert_equal(out[0], np.array((i1,)))
assert_equal(out[1], np.array((x1,)))
assert_equal(out[2], np.array((y1,)))
def test_isolated_peaks(self):
image = np.zeros((15, 15))
x0, y0, i0 = (12, 8, 1)
x1, y1, i1 = (2, 2, 1)
x2, y2, i2 = (5, 13, 1)
image[y0, x0] = i0
image[y1, x1] = i1
image[y2, x2] = i2
out = peak._prominent_peaks(image)
assert len(out[0]) == 3
for i, x, y in zip(out[0], out[1], out[2]):
assert i in (i0, i1, i2)
assert x in (x0, x1, x2)
assert y in (y0, y1, y2)
def hough_circle_peaks(hspaces,
radii,
min_xdistance=1,
min_ydistance=1,
threshold=None,
num_peaks=np.inf,
total_num_peaks=np.inf,
normalize=False):
"""Return peaks in a circle Hough transform.
Identifies most prominent circles separated by certain distances in a
Hough space. Non-maximum suppression with different sizes is applied
separately in the first and second dimension of the Hough space to
identify peaks.
Parameters
----------
hspaces : (N, M) array
Hough spaces returned by the `hough_circle` function.
radii : (M,) array
Radii corresponding to Hough spaces.
min_xdistance : int, optional
Minimum distance separating centers in the x dimension.
min_ydistance : int, optional
Minimum distance separating centers in the y dimension.
threshold : float, optional
Minimum intensity of peaks in each Hough space.
Default is `0.5 * max(hspace)`.
num_peaks : int, optional
Maximum number of peaks in each Hough space. When the
number of peaks exceeds `num_peaks`, only `num_peaks`
coordinates based on peak intensity are considered for the
corresponding radius.
total_num_peaks : int, optional
Maximum number of peaks. When the number of peaks exceeds `num_peaks`,
return `num_peaks` coordinates based on peak intensity.
normalize : bool, optional
If True, normalize the accumulator by the radius to sort the prominent
peaks.
Returns
-------
accum, cx, cy, rad : tuple of array
Peak values in Hough space, x and y center coordinates and radii.
Examples
--------
>>> from skimage import transform as tf
>>> from skimage import draw
>>> img = np.zeros((120, 100), dtype=int)
>>> radius, x_0, y_0 = (20, 99, 50)
>>> y, x = draw.circle_perimeter(y_0, x_0, radius)
>>> img[x, y] = 1
>>> hspaces = tf.hough_circle(img, radius)
>>> accum, cx, cy, rad = hough_circle_peaks(hspaces, [radius,])
"""
from skimage.feature.peak import _prominent_peaks
r = []
cx = []
cy = []
accum = []
for rad, hp in zip(radii, hspaces):
h_p, x_p, y_p = _prominent_peaks(hp,
min_xdistance=min_xdistance,
min_ydistance=min_ydistance,
threshold=threshold,
num_peaks=num_peaks)
r.extend((rad, ) * len(h_p))
cx.extend(x_p)
cy.extend(y_p)
accum.extend(h_p)
r = np.array(r)
cx = np.array(cx)
cy = np.array(cy)
accum = np.array(accum)
if normalize:
s = np.argsort(accum / r)
else:
s = np.argsort(accum)
if total_num_peaks != np.inf:
tnp = total_num_peaks
return (accum[s][::-1][:tnp], cx[s][::-1][:tnp], cy[s][::-1][:tnp],
r[s][::-1][:tnp])
return (accum[s][::-1], cx[s][::-1], cy[s][::-1], r[s][::-1])
def hough_circle_peaks(hspaces, radii, min_xdistance=1, min_ydistance=1,
threshold=None, num_peaks=np.inf,
total_num_peaks=np.inf, normalize=False):
"""Return peaks in a circle Hough transform.
Identifies most prominent circles separated by certain distances in a
Hough space. Non-maximum suppression with different sizes is applied
separately in the first and second dimension of the Hough space to
identify peaks.
Parameters
----------
hspaces : (N, M) array
Hough spaces returned by the `hough_circle` function.
radii : (M,) array
Radii corresponding to Hough spaces.
min_xdistance : int, optional
Minimum distance separating centers in the x dimension.
min_ydistance : int, optional
Minimum distance separating centers in the y dimension.
threshold : float, optional
Minimum intensity of peaks in each Hough space.
Default is `0.5 * max(hspace)`.
num_peaks : int, optional
Maximum number of peaks in each Hough space. When the
number of peaks exceeds `num_peaks`, only `num_peaks`
coordinates based on peak intensity are considered for the
corresponding radius.
total_num_peaks : int, optional
Maximum number of peaks. When the number of peaks exceeds `num_peaks`,
return `num_peaks` coordinates based on peak intensity.
normalize : bool, optional
If True, normalize the accumulator by the radius to sort the prominent
peaks.
Returns
-------
accum, cx, cy, rad : tuple of array
Peak values in Hough space, x and y center coordinates and radii.
Examples
--------
>>> from skimage import transform as tf
>>> from skimage import draw
>>> img = np.zeros((120, 100), dtype=int)
>>> radius, x_0, y_0 = (20, 99, 50)
>>> y, x = draw.circle_perimeter(y_0, x_0, radius)
>>> img[x, y] = 1
>>> hspaces = tf.hough_circle(img, radius)
>>> accum, cx, cy, rad = hough_circle_peaks(hspaces, [radius,])
"""
from skimage.feature.peak import _prominent_peaks
r = []
cx = []
cy = []
accum = []
for rad, hp in zip(radii, hspaces):
h_p, x_p, y_p = _prominent_peaks(hp,
min_xdistance=min_xdistance,
min_ydistance=min_ydistance,
threshold=threshold,
num_peaks=num_peaks)
r.extend((rad,)*len(h_p))
cx.extend(x_p)
cy.extend(y_p)
accum.extend(h_p)
r = np.array(r)
cx = np.array(cx)
cy = np.array(cy)
accum = np.array(accum)
if normalize:
s = np.argsort(accum / r)
else:
s = np.argsort(accum)
if total_num_peaks != np.inf:
tnp = total_num_peaks
return (accum[s][::-1][:tnp], cx[s][::-1][:tnp], cy[s][::-1][:tnp],
r[s][::-1][:tnp])
return (accum[s][::-1], cx[s][::-1], cy[s][::-1], r[s][::-1])
