428 lines
15 KiB
Python
428 lines
15 KiB
Python
|
import numpy as np
|
||
|
|
from scipy.spatial import cKDTree
|
||
|
|
from ._hough_transform import (_hough_circle,
|
||
|
|
_hough_ellipse,
|
||
|
|
_hough_line,
|
||
|
|
_probabilistic_hough_line as _prob_hough_line)
|
||
|
|
|
||
|
|
|
||
|
|
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 ..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)
|
||
|
|
if a.any():
|
||
|
|
return (h, angles[a], dists[d])
|
||
|
|
else:
|
||
|
|
return (h, np.array([]), np.array([]))
|
||
|
|
|
||
|
|
|
||
|
|
def hough_circle(image, radius, normalize=True, full_output=False):
|
||
|
|
"""Perform a circular Hough transform.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : (M, N) ndarray
|
||
|
|
Input image with nonzero values representing edges.
|
||
|
|
radius : scalar or sequence of scalars
|
||
|
|
Radii at which to compute the Hough transform.
|
||
|
|
Floats are converted to integers.
|
||
|
|
normalize : boolean, optional (default True)
|
||
|
|
Normalize the accumulator with the number
|
||
|
|
of pixels used to draw the radius.
|
||
|
|
full_output : boolean, optional (default False)
|
||
|
|
Extend the output size by twice the largest
|
||
|
|
radius in order to detect centers outside the
|
||
|
|
input picture.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
H : 3D ndarray (radius index, (M + 2R, N + 2R) ndarray)
|
||
|
|
Hough transform accumulator for each radius.
|
||
|
|
R designates the larger radius if full_output is True.
|
||
|
|
Otherwise, R = 0.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from skimage.transform import hough_circle
|
||
|
|
>>> from skimage.draw import circle_perimeter
|
||
|
|
>>> img = np.zeros((100, 100), dtype=np.bool_)
|
||
|
|
>>> rr, cc = circle_perimeter(25, 35, 23)
|
||
|
|
>>> img[rr, cc] = 1
|
||
|
|
>>> try_radii = np.arange(5, 50)
|
||
|
|
>>> res = hough_circle(img, try_radii)
|
||
|
|
>>> ridx, r, c = np.unravel_index(np.argmax(res), res.shape)
|
||
|
|
>>> r, c, try_radii[ridx]
|
||
|
|
(25, 35, 23)
|
||
|
|
|
||
|
|
"""
|
||
|
|
radius = np.atleast_1d(np.asarray(radius))
|
||
|
|
return _hough_circle(image, radius.astype(np.intp),
|
||
|
|
normalize=normalize, full_output=full_output)
|
||
|
|
|
||
|
|
|
||
|
|
def hough_ellipse(image, threshold=4, accuracy=1, min_size=4, max_size=None):
|
||
|
|
"""Perform an elliptical Hough transform.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : (M, N) ndarray
|
||
|
|
Input image with nonzero values representing edges.
|
||
|
|
threshold : int, optional
|
||
|
|
Accumulator threshold value.
|
||
|
|
accuracy : double, optional
|
||
|
|
Bin size on the minor axis used in the accumulator.
|
||
|
|
min_size : int, optional
|
||
|
|
Minimal major axis length.
|
||
|
|
max_size : int, optional
|
||
|
|
Maximal minor axis length.
|
||
|
|
If None, the value is set to the half of the smaller
|
||
|
|
image dimension.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
result : ndarray with fields [(accumulator, yc, xc, a, b, orientation)].
|
||
|
|
Where ``(yc, xc)`` is the center, ``(a, b)`` the major and minor
|
||
|
|
axes, respectively. The `orientation` value follows
|
||
|
|
`skimage.draw.ellipse_perimeter` convention.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from skimage.transform import hough_ellipse
|
||
|
|
>>> from skimage.draw import ellipse_perimeter
|
||
|
|
>>> img = np.zeros((25, 25), dtype=np.uint8)
|
||
|
|
>>> rr, cc = ellipse_perimeter(10, 10, 6, 8)
|
||
|
|
>>> img[cc, rr] = 1
|
||
|
|
>>> result = hough_ellipse(img, threshold=8)
|
||
|
|
>>> result.tolist()
|
||
|
|
[(10, 10.0, 10.0, 8.0, 6.0, 0.0)]
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The accuracy must be chosen to produce a peak in the accumulator
|
||
|
|
distribution. In other words, a flat accumulator distribution with low
|
||
|
|
values may be caused by a too low bin size.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] Xie, Yonghong, and Qiang Ji. "A new efficient ellipse detection
|
||
|
|
method." Pattern Recognition, 2002. Proceedings. 16th International
|
||
|
|
Conference on. Vol. 2. IEEE, 2002
|
||
|
|
"""
|
||
|
|
return _hough_ellipse(image, threshold=threshold, accuracy=accuracy,
|
||
|
|
min_size=min_size, max_size=max_size)
|
||
|
|
|
||
|
|
|
||
|
|
def hough_line(image, theta=None):
|
||
|
|
"""Perform a straight line Hough transform.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : (M, N) ndarray
|
||
|
|
Input image with nonzero values representing edges.
|
||
|
|
theta : 1D ndarray of double, optional
|
||
|
|
Angles at which to compute the transform, in radians.
|
||
|
|
Defaults to a vector of 180 angles evenly spaced from -pi/2 to pi/2.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
hspace : 2-D ndarray of uint64
|
||
|
|
Hough transform accumulator.
|
||
|
|
angles : ndarray
|
||
|
|
Angles at which the transform is computed, in radians.
|
||
|
|
distances : ndarray
|
||
|
|
Distance values.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The origin is the top left corner of the original image.
|
||
|
|
X and Y axis are horizontal and vertical edges respectively.
|
||
|
|
The distance is the minimal algebraic distance from the origin
|
||
|
|
to the detected line.
|
||
|
|
The angle accuracy can be improved by decreasing the step size in
|
||
|
|
the `theta` array.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
Generate a test image:
|
||
|
|
|
||
|
|
>>> img = np.zeros((100, 150), dtype=bool)
|
||
|
|
>>> img[30, :] = 1
|
||
|
|
>>> img[:, 65] = 1
|
||
|
|
>>> img[35:45, 35:50] = 1
|
||
|
|
>>> for i in range(90):
|
||
|
|
... img[i, i] = 1
|
||
|
|
>>> img += np.random.random(img.shape) > 0.95
|
||
|
|
|
||
|
|
Apply the Hough transform:
|
||
|
|
|
||
|
|
>>> out, angles, d = hough_line(img)
|
||
|
|
|
||
|
|
.. plot:: hough_tf.py
|
||
|
|
|
||
|
|
"""
|
||
|
|
if image.ndim != 2:
|
||
|
|
raise ValueError('The input image `image` must be 2D.')
|
||
|
|
|
||
|
|
if theta is None:
|
||
|
|
# These values are approximations of pi/2
|
||
|
|
theta = np.linspace(-np.pi / 2, np.pi / 2, 180)
|
||
|
|
|
||
|
|
return _hough_line(image, theta=theta)
|
||
|
|
|
||
|
|
|
||
|
|
def probabilistic_hough_line(image, threshold=10, line_length=50, line_gap=10,
|
||
|
|
theta=None, seed=None):
|
||
|
|
"""Return lines from a progressive probabilistic line Hough transform.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : (M, N) ndarray
|
||
|
|
Input image with nonzero values representing edges.
|
||
|
|
threshold : int, optional
|
||
|
|
Threshold
|
||
|
|
line_length : int, optional
|
||
|
|
Minimum accepted length of detected lines.
|
||
|
|
Increase the parameter to extract longer lines.
|
||
|
|
line_gap : int, optional
|
||
|
|
Maximum gap between pixels to still form a line.
|
||
|
|
Increase the parameter to merge broken lines more aggressively.
|
||
|
|
theta : 1D ndarray, dtype=double, optional
|
||
|
|
Angles at which to compute the transform, in radians.
|
||
|
|
If None, use a range from -pi/2 to pi/2.
|
||
|
|
seed : int, optional
|
||
|
|
Seed to initialize the random number generator.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
lines : list
|
||
|
|
List of lines identified, lines in format ((x0, y0), (x1, y1)),
|
||
|
|
indicating line start and end.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] C. Galamhos, J. Matas and J. Kittler, "Progressive probabilistic
|
||
|
|
Hough transform for line detection", in IEEE Computer Society
|
||
|
|
Conference on Computer Vision and Pattern Recognition, 1999.
|
||
|
|
"""
|
||
|
|
|
||
|
|
if image.ndim != 2:
|
||
|
|
raise ValueError('The input image `image` must be 2D.')
|
||
|
|
|
||
|
|
if theta is None:
|
||
|
|
theta = np.pi / 2 - np.arange(180) / 180.0 * np.pi
|
||
|
|
|
||
|
|
return _prob_hough_line(image, threshold=threshold, line_length=line_length,
|
||
|
|
line_gap=line_gap, theta=theta, seed=seed)
|
||
|
|
|
||
|
|
|
||
|
|
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 given
|
||
|
|
Hough spaces. Non-maximum suppression with different sizes is applied
|
||
|
|
separately in the first and second dimension of the Hough space to
|
||
|
|
identify peaks. For circles with different radius but close in distance,
|
||
|
|
only the one with highest peak is kept.
|
||
|
|
|
||
|
|
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, 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 = transform.hough_circle(img, radius)
|
||
|
|
>>> accum, cx, cy, rad = hough_circle_peaks(hspaces, [radius,])
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Circles with bigger radius have higher peaks in Hough space. If larger
|
||
|
|
circles are preferred over smaller ones, `normalize` should be False.
|
||
|
|
Otherwise, circles will be returned in the order of decreasing voting
|
||
|
|
number.
|
||
|
|
"""
|
||
|
|
from ..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)
|
||
|
|
accum_sorted, cx_sorted, cy_sorted, r_sorted = \
|
||
|
|
accum[s][::-1], cx[s][::-1], cy[s][::-1], r[s][::-1]
|
||
|
|
|
||
|
|
tnp = len(accum_sorted) if total_num_peaks == np.inf else total_num_peaks
|
||
|
|
|
||
|
|
# Skip searching for neighboring circles
|
||
|
|
# if default min_xdistance and min_ydistance are used
|
||
|
|
# or if no peak was detected
|
||
|
|
if (min_xdistance == 1 and min_ydistance == 1) or len(accum_sorted) == 0:
|
||
|
|
return (accum_sorted[:tnp],
|
||
|
|
cx_sorted[:tnp],
|
||
|
|
cy_sorted[:tnp],
|
||
|
|
r_sorted[:tnp])
|
||
|
|
|
||
|
|
# For circles with centers too close, only keep the one with
|
||
|
|
# the highest peak
|
||
|
|
should_keep = label_distant_points(
|
||
|
|
cx_sorted, cy_sorted, min_xdistance, min_ydistance, tnp
|
||
|
|
)
|
||
|
|
return (accum_sorted[should_keep],
|
||
|
|
cx_sorted[should_keep],
|
||
|
|
cy_sorted[should_keep],
|
||
|
|
r_sorted[should_keep])
|
||
|
|
|
||
|
|
|
||
|
|
def label_distant_points(xs, ys, min_xdistance, min_ydistance, max_points):
|
||
|
|
"""Keep points that are separated by certain distance in each dimension.
|
||
|
|
|
||
|
|
The first point is always accpeted and all subsequent points are selected
|
||
|
|
so that they are distant from all their preceding ones.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
xs : array
|
||
|
|
X coordinates of points.
|
||
|
|
ys : array
|
||
|
|
Y coordinates of points.
|
||
|
|
min_xdistance : int
|
||
|
|
Minimum distance separating points in the x dimension.
|
||
|
|
min_ydistance : int
|
||
|
|
Minimum distance separating points in the y dimension.
|
||
|
|
max_points : int
|
||
|
|
Max number of distant points to keep.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
should_keep : array of bool
|
||
|
|
A mask array for distant points to keep.
|
||
|
|
"""
|
||
|
|
is_neighbor = np.zeros(len(xs), dtype=bool)
|
||
|
|
coordinates = np.stack([xs, ys], axis=1)
|
||
|
|
# Use a KDTree to search for neighboring points effectively
|
||
|
|
kd_tree = cKDTree(coordinates)
|
||
|
|
n_pts = 0
|
||
|
|
for i in range(len(xs)):
|
||
|
|
if n_pts >= max_points:
|
||
|
|
# Ignore the point if points to keep reaches maximum
|
||
|
|
is_neighbor[i] = True
|
||
|
|
elif not is_neighbor[i]:
|
||
|
|
# Find a short list of candidates to remove
|
||
|
|
# by searching within a circle
|
||
|
|
neighbors_i = kd_tree.query_ball_point(
|
||
|
|
(xs[i], ys[i]),
|
||
|
|
np.hypot(min_xdistance, min_ydistance)
|
||
|
|
)
|
||
|
|
# Check distance in both dimensions and mark if close
|
||
|
|
for ni in neighbors_i:
|
||
|
|
x_close = abs(xs[ni] - xs[i]) <= min_xdistance
|
||
|
|
y_close = abs(ys[ni] - ys[i]) <= min_ydistance
|
||
|
|
if x_close and y_close and ni > i:
|
||
|
|
is_neighbor[ni] = True
|
||
|
|
n_pts += 1
|
||
|
|
should_keep = ~is_neighbor
|
||
|
|
return should_keep
|