diff --git a/skimage/transform/hough_transform.py b/skimage/transform/hough_transform.py index 4e3acd6e..05d5cfbe 100644 --- a/skimage/transform/hough_transform.py +++ b/skimage/transform/hough_transform.py @@ -1,9 +1,11 @@ -__all__ = ['hough', 'probabilistic_hough'] +__all__ = ['hough', 'hough_peaks', 'probabilistic_hough'] from itertools import izip as zip import numpy as np +from scipy import ndimage from ._hough_transform import _probabilistic_hough +from skimage import measure, morphology def _hough(img, theta=None): @@ -110,10 +112,10 @@ def hough(img, theta=None): ------- H : 2-D ndarray of uint64 Hough transform accumulator. - distances : ndarray - Distance values. theta : ndarray Angles at which the transform was computed. + distances : ndarray + Distance values. Examples -------- @@ -135,3 +137,127 @@ def hough(img, theta=None): """ return _hough(img, theta) + + +def hough_peaks(hspace, angles, dists, min_distance=10, min_angle=10, + threshold=None, num_peaks=np.inf): + """Return peaks in 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` function. + angles : (M,) array + Angles returned by the `hough` function. Assumed to be continuous + (`angles[-1] - angles[0] == PI`). + dists : (N, ) array + Distances returned by the `hough` function. + min_distance : int + Minimum distance separating lines (maximum filter size for first + dimension of hough space). + min_angle : int + Minimum angle separating lines (maximum filter size for second + dimension of hough space). + threshold : float + Minimum intensity of peaks. Default is `0.5 * max(hspace)`. + num_peaks : int + Maximum number of peaks. When the number of peaks exceeds `num_peaks`, + return `num_peaks` coordinates based on peak intensity. + + Returns + ------- + hspace, angles, dists : tuple of array + Peak values in hough space, angles and distances. + + Examples + -------- + >>> import numpy as np + >>> from skimage.transform import hough, hough_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(img) + >>> hspace, angles, dists = hough_peaks(hspace, angles, dists) + >>> angles + array([ 0.74590887, -0.79856126]) + >>> dists + array([ 10.74418605, 0.51162791]) + + """ + + hspace = hspace.copy() + rows, cols = hspace.shape + + if threshold is None: + threshold = 0.5 * np.max(hspace) + + distance_size = 2 * min_distance + 1 + angle_size = 2 * min_angle + 1 + hspace_max = ndimage.maximum_filter1d(hspace, size=distance_size, axis=0, + mode='constant', cval=0) + hspace_max = ndimage.maximum_filter1d(hspace_max, size=angle_size, axis=1, + mode='constant', cval=0) + mask = (hspace == hspace_max) + hspace *= mask + hspace_t = hspace > threshold + + label_hspace = morphology.label(hspace_t) + props = measure.regionprops(label_hspace, ['Centroid']) + coords = np.array([np.round(p['Centroid']) for p in props], dtype=int) + + hspace_peaks = [] + dist_peaks = [] + angle_peaks = [] + + # relative coordinate grid for local neighbourhood suppression + dist_ext, angle_ext = np.mgrid[-min_distance:min_distance + 1, + -min_angle:min_angle + 1] + + for dist_idx, angle_idx in coords: + accum = hspace[dist_idx, angle_idx] + if accum > threshold: + # absolute coordinate grid for local neighbourhood suppression + dist_nh = dist_idx + dist_ext + angle_nh = angle_idx + angle_ext + + # no reflection for distance neighbourhood + dist_in = np.logical_and(dist_nh > 0, dist_nh < rows) + dist_nh = dist_nh[dist_in] + angle_nh = angle_nh[dist_in] + + # reflect angles and assume angles are continuous, e.g. + # (..., 88, 89, -90, -89, ..., 89, -90, -89, ...) + angle_low = angle_nh < 0 + dist_nh[angle_low] = rows - dist_nh[angle_low] + angle_nh[angle_low] += cols + angle_high = angle_nh >= cols + dist_nh[angle_high] = rows - dist_nh[angle_high] + angle_nh[angle_high] -= cols + + # suppress neighbourhood + hspace[dist_nh, angle_nh] = 0 + + # add current line to peaks + hspace_peaks.append(accum) + dist_peaks.append(dists[dist_idx]) + angle_peaks.append(angles[angle_idx]) + + hspace_peaks = np.array(hspace_peaks) + dist_peaks = np.array(dist_peaks) + angle_peaks = np.array(angle_peaks) + + if num_peaks < len(hspace_peaks): + idx_maxsort = np.argsort(hspace_peaks)[::-1][:num_peaks] + hspace_peaks = hspace_peaks[idx_maxsort] + dist_peaks = dist_peaks[idx_maxsort] + angle_peaks = angle_peaks[idx_maxsort] + + return hspace_peaks, angle_peaks, dist_peaks diff --git a/skimage/transform/tests/test_hough_transform.py b/skimage/transform/tests/test_hough_transform.py index 03b63d07..a38e6e76 100644 --- a/skimage/transform/tests/test_hough_transform.py +++ b/skimage/transform/tests/test_hough_transform.py @@ -72,5 +72,43 @@ def test_probabilistic_hough(): assert([(25, 25), (74, 74)] in sorted_lines) +def test_hough_peaks_dist(): + img = np.zeros((100, 100), dtype=np.bool_) + img[:, 30] = True + img[:, 40] = True + hspace, angles, dists = tf.hough(img) + assert len(tf.hough_peaks(hspace, angles, dists, min_distance=5)[0]) == 2 + assert len(tf.hough_peaks(hspace, angles, dists, min_distance=15)[0]) == 1 + + +def test_hough_peaks_angle(): + img = np.zeros((100, 100), dtype=np.bool_) + img[:, 0] = True + img[0, :] = True + + hspace, angles, dists = tf.hough(img) + assert len(tf.hough_peaks(hspace, angles, dists, min_angle=45)[0]) == 2 + assert len(tf.hough_peaks(hspace, angles, dists, min_angle=90)[0]) == 1 + + theta = np.linspace(0, np.pi, 100) + hspace, angles, dists = tf.hough(img, theta) + assert len(tf.hough_peaks(hspace, angles, dists, min_angle=45)[0]) == 2 + assert len(tf.hough_peaks(hspace, angles, dists, min_angle=90)[0]) == 1 + + theta = np.linspace(np.pi / 3, 4. / 3 * np.pi, 100) + hspace, angles, dists = tf.hough(img, theta) + assert len(tf.hough_peaks(hspace, angles, dists, min_angle=45)[0]) == 2 + assert len(tf.hough_peaks(hspace, angles, dists, min_angle=90)[0]) == 1 + + +def test_hough_peaks_num(): + img = np.zeros((100, 100), dtype=np.bool_) + img[:, 30] = True + img[:, 40] = True + hspace, angles, dists = tf.hough(img) + assert len(tf.hough_peaks(hspace, angles, dists, min_distance=0, + min_angle=0, num_peaks=1)[0]) == 1 + + if __name__ == "__main__": run_module_suite()