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227 lines
9.5 KiB
Python
227 lines
9.5 KiB
Python
import numpy as np
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from scipy.ndimage.filters import maximum_filter, minimum_filter, convolve
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from skimage.transform import integral_image
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from skimage.feature.corner import _compute_auto_correlation
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from skimage.util import img_as_float
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from skimage.morphology import convex_hull_image, octagon, star
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from skimage.feature.util import _mask_border_keypoints
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from skimage.feature.censure_cy import _censure_dob_loop
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OCTAGON_OUTER_SHAPE = [(5, 2), (5, 3), (7, 3), (9, 4), (9, 7), (13, 7),
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(15, 10), (15, 11), (15, 12), (17, 13), (17, 14)]
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OCTAGON_INNER_SHAPE = [(3, 0), (3, 1), (3, 2), (5, 2), (5, 3), (5, 4), (5, 5),
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(7, 5), (7, 6), (9, 6), (9, 7)]
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STAR_SHAPE = [1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 23, 32, 45, 46, 64, 90, 128]
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STAR_FILTER_SHAPE = [(1, 0), (3, 1), (4, 2), (5, 3), (7, 4), (8, 5),
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(9, 6), (11, 8), (13, 10), (14, 11), (15, 12), (16, 14)]
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def _get_filtered_image(image, min_scale, max_scale, mode):
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scales = np.zeros((image.shape[0], image.shape[1],
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max_scale - min_scale + 1), dtype=np.double)
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if mode == 'dob':
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# make scales[:, :, i] contiguous memory block
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item_size = scales.itemsize
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scales.strides = (item_size * scales.shape[0],
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item_size,
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item_size * scales.shape[0] * scales.shape[1])
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integral_img = integral_image(image)
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for i in range(max_scale - min_scale + 1):
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n = min_scale + i
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# Constant multipliers for the outer region and the inner region
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# of the bilevel filters with the constraint of keeping the
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# DC bias 0.
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inner_weight = (1.0 / (2 * n + 1)**2)
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outer_weight = (1.0 / (12 * n**2 + 4 * n))
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_censure_dob_loop(n, integral_img, scales[:, :, i],
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inner_weight, outer_weight)
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# NOTE : For the Octagon shaped filter, we implemented and evaluated the
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# slanted integral image based image filtering but the performance was
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# more or less equal to image filtering using
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# scipy.ndimage.filters.convolve(). Hence we have decided to use the
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# later for a much cleaner implementation.
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elif mode == 'octagon':
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# TODO : Decide the shapes of Octagon filters for scales > 7
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for i in range(max_scale - min_scale + 1):
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mo, no = OCTAGON_OUTER_SHAPE[min_scale + i - 1]
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mi, ni = OCTAGON_INNER_SHAPE[min_scale + i - 1]
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scales[:, :, i] = convolve(image,
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_octagon_filter_kernel(mo, no, mi, ni))
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elif mode == 'star':
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for i in range(max_scale - min_scale + 1):
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m = STAR_SHAPE[STAR_FILTER_SHAPE[min_scale + i - 1][0]]
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n = STAR_SHAPE[STAR_FILTER_SHAPE[min_scale + i - 1][1]]
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scales[:, :, i] = convolve(image,
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_star_filter_kernel(m, n))
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return scales
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def _octagon_filter_kernel(mo, no, mi, ni):
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outer = (mo + 2 * no)**2 - 2 * no * (no + 1)
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inner = (mi + 2 * ni)**2 - 2 * ni * (ni + 1)
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outer_weight = 1.0 / (outer - inner)
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inner_weight = 1.0 / inner
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c = ((mo + 2 * no) - (mi + 2 * ni)) // 2
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outer_oct = octagon(mo, no)
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inner_oct = np.zeros((mo + 2 * no, mo + 2 * no))
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inner_oct[c: -c, c: -c] = octagon(mi, ni)
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bfilter = (outer_weight * outer_oct -
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(outer_weight + inner_weight) * inner_oct)
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return bfilter
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def _star_filter_kernel(m, n):
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c = m + m // 2 - n - n // 2
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outer_star = star(m)
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inner_star = np.zeros_like(outer_star)
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inner_star[c: -c, c: -c] = star(n)
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outer_weight = 1.0 / (np.sum(outer_star - inner_star))
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inner_weight = 1.0 / np.sum(inner_star)
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bfilter = (outer_weight * outer_star -
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(outer_weight + inner_weight) * inner_star)
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return bfilter
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def _suppress_lines(feature_mask, image, sigma, line_threshold):
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Axx, Axy, Ayy = _compute_auto_correlation(image, sigma)
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feature_mask[(Axx + Ayy) * (Axx + Ayy)
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> line_threshold * (Axx * Ayy - Axy * Axy)] = False
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def keypoints_censure(image, min_scale=1, max_scale=7, mode='DoB',
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non_max_threshold=0.15, line_threshold=10):
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"""
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Extracts Censure keypoints along with the corresponding scale using
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either Difference of Boxes, Octagon or STAR bilevel filter.
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Parameters
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----------
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image : 2D ndarray
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Input image.
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min_scale : positive integer
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Minimum scale to extract keypoints from.
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max_scale : positive integer
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Maximum scale to extract keypoints from. The keypoints will be
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extracted from all the scales except the first and the last i.e.
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from the scales in the range [min_scale + 1, max_scale - 1].
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mode : ('DoB', 'Octagon', 'STAR')
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Type of bilevel filter used to get the scales of the input image.
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Possible values are 'DoB', 'Octagon' and 'STAR'. The three modes
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represent the shape of the bilevel filters i.e. box(square), octagon
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and star respectively. For instance, a bilevel octagon filter consists
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of a smaller inner octagon and a larger outer octagon with the filter
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weights being uniformly negative in both the inner octagon while
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uniformly positive in the difference region. Use STAR and Octagon for
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better features and DoB for better performance.
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non_max_threshold : float
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Threshold value used to suppress maximas and minimas with a weak
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magnitude response obtained after Non-Maximal Suppression.
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line_threshold : float
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Threshold for rejecting interest points which have ratio of principal
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curvatures greater than this value.
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Returns
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-------
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keypoints : (N, 2) array
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Location of the extracted keypoints in the (row, col) format.
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scales : (N, 1) array
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The corresponding scale of the N extracted keypoints.
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References
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----------
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.. [1] Motilal Agrawal, Kurt Konolige and Morten Rufus Blas
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"CenSurE: Center Surround Extremas for Realtime Feature
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Detection and Matching",
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http://link.springer.com/content/pdf/10.1007%2F978-3-540-88693-8_8.pdf
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.. [2] Adam Schmidt, Marek Kraft, Michal Fularz and Zuzanna Domagala
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"Comparative Assessment of Point Feature Detectors and
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Descriptors in the Context of Robot Navigation"
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http://www.jamris.org/01_2013/saveas.php?QUEST=JAMRIS_No01_2013_P_11-20.pdf
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"""
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# (1) First we generate the required scales on the input grayscale image
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# using a bilevel filter and stack them up in `filter_response`.
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# (2) We then perform Non-Maximal suppression in 3 x 3 x 3 window on the
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# filter_response to suppress points that are neither minima or maxima in
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# 3 x 3 x 3 neighbourhood. We obtain a boolean ndarray `feature_mask`
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# containing all the minimas and maximas in `filter_response` as True.
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# (3) Then we suppress all the points in the `feature_mask` for which the
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# corresponding point in the image at a particular scale has the ratio of
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# principal curvatures greater than `line_threshold`.
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# (4) Finally, we remove the border keypoints and return the keypoints
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# along with its corresponding scale.
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image = np.squeeze(image)
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if image.ndim != 2:
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raise ValueError("Only 2-D gray-scale images supported.")
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mode = mode.lower()
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if mode not in ('dob', 'octagon', 'star'):
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raise ValueError('Mode must be one of "DoB", "Octagon", "STAR".')
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if max_scale - min_scale < 2:
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raise ValueError('The number of scales should be greater than or'
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'equal to 3.')
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image = img_as_float(image)
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image = np.ascontiguousarray(image)
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# Generating all the scales
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filter_response = _get_filtered_image(image, min_scale, max_scale, mode)
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# Suppressing points that are neither minima or maxima in their 3 x 3 x 3
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# neighbourhood to zero
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minimas = minimum_filter(filter_response, (3, 3, 3)) == filter_response
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maximas = maximum_filter(filter_response, (3, 3, 3)) == filter_response
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feature_mask = minimas | maximas
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feature_mask[filter_response < non_max_threshold] = False
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for i in range(1, max_scale - min_scale):
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# sigma = (window_size - 1) / 6.0, so the window covers > 99% of the
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# kernel's distribution
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# window_size = 7 + 2 * (min_scale - 1 + i)
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# Hence sigma = 1 + (min_scale - 1 + i)/ 3.0
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_suppress_lines(feature_mask[:, :, i], image,
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(1 + (min_scale + i - 1) / 3.0), line_threshold)
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rows, cols, scales = np.nonzero(feature_mask[..., 1:max_scale - min_scale])
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keypoints = np.column_stack([rows, cols])
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scales = scales + min_scale + 1
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if mode == 'dob':
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return keypoints, scales
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cumulative_mask = np.zeros(keypoints.shape[0], dtype=np.bool)
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if mode == 'octagon':
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for i in range(min_scale + 1, max_scale):
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c = (OCTAGON_OUTER_SHAPE[i - 1][0] - 1) // 2 \
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+ OCTAGON_OUTER_SHAPE[i - 1][1]
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cumulative_mask |= _mask_border_keypoints(image, keypoints, c) \
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& (scales == i)
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elif mode == 'star':
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for i in range(min_scale + 1, max_scale):
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c = STAR_SHAPE[STAR_FILTER_SHAPE[i - 1][0]] \
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+ STAR_SHAPE[STAR_FILTER_SHAPE[i - 1][0]] // 2
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cumulative_mask |= _mask_border_keypoints(image, keypoints, c) \
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& (scales == i)
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return keypoints[cumulative_mask], scales[cumulative_mask]
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