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Add dense DAISY feature description.
This commit is contained in:
Anders Boesen Lindbo Larsen
@@ -1,3 +1,4 @@
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from ._daisy import daisy
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from ._hog import hog
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from .texture import greycomatrix, greycoprops, local_binary_pattern
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from .peak import peak_local_max
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import numpy as np
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import scipy as sp
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from numpy.linalg import norm
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from scipy import sqrt, pi, arctan2, cos, sin, exp
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from scipy.ndimage import gaussian_filter
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from scipy.special import iv
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def daisy(img, step=4, radius=15, rings=3, histograms=8, orientations=8,
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normalization='l1', sigmas=None, ring_radii=None):
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'''Extract DAISY feature descriptors densely for the given image.
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DAISY is a feature descriptor similar to SIFT formulated in a way
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that allows for fast dense extraction. Typically, this is practical
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for bag-of-features image representations.
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The implementation follows Tola et al. [1] but deviate on the
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following points:
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* Histogram bin contribution are smoothed with a circular
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Gaussian window over the tonal range (the angular range).
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* The sigma values of the spatial Gaussian smoothing in this code
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do not match the sigma values in the original code by Tola et
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al. [2]. In their code, spatial smoothing is applied to both the
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input image and the center histogram. However, this smoothing is
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not documented in [1] and, therefore, it is omitted.
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Parameters
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----------
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img : (M, N) array
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Input image (greyscale).
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step : int, optional
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Distance between descriptor sampling points.
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radius : int, optional
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Radius (in pixels) of the outermost ring.
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rings : int, optional
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Number of rings.
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histograms : int, optional
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Number of histograms sampled per ring.
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orientations : int, optional
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Number of orientations (bins) per histogram.
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normalization : {'l1', 'l2', 'daisy', 'off'}, optional
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How to normalize the descriptors:
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* 'l1': L1-normalization of each descriptor.
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* 'l2': L2-normalization of each descriptor.
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* 'daisy': L2-normalization of individual histograms.
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* 'off': Disable normalization.
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sigmas : 1D array of float, optional
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Standard deviation of spatial Gaussian smoothing for the center
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histogram and for each ring of histograms. The array of sigmas
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should be sorted from the center and out. I.e. the first sigma
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value specifies the spatial smoothing of the center histogram
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and the last sigma value specifies the spatial smoothing of the
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outermost ring.
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Specifying sigmas overrides the following parameter:
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rings = len(sigmas)-1
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ring_radii : 1D array of int, optional
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Radius (in pixels) for each ring.
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Specifying ring_radii overrides the following two parameters:
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rings = len(ring_radii)
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radius = ring_radii[-1]
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If both sigmas and ring_radii are given, they must satisfy
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len(ring_radii) == len(sigmas)+1
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since no radius is needed for the center histogram.
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Returns
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-------
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descs : array
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Grid of DAISY descriptors for the given image as an array
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dimensionality (P, Q, R) where
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P = ceil((M-radius*2)/step)
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Q = ceil((N-radius*2)/step)
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R = (rings*histograms + 1)*orientations
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References
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----------
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[1] Tola et al. "Daisy: An efficient dense descriptor applied to
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wide-baseline stereo." Pattern Analysis and Machine Intelligence,
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IEEE Transactions on 32.5 (2010): 815-830.
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[2] http://cvlab.epfl.ch/alumni/tola/daisy.html
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'''
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# Validate image format.
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if img.ndim > 2:
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raise ValueError('Only grey-level images are supported.')
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if img.dtype.kind == 'u':
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img = img.astype(float)
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img = img/255.
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# Validate parameters.
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if sigmas != None and ring_radii != None \
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and len(sigmas)-1 != len(ring_radii):
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raise ValueError('len(sigmas)-1 != len(ring_radii)')
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if ring_radii != None:
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rings = len(ring_radii)
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radius = ring_radii[-1]
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if sigmas != None:
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rings = len(sigmas)-1
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if sigmas == None:
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sigmas = [radius*(i+1)/float(2*rings) for i in range(rings)]
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if ring_radii == None:
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ring_radii = [radius*(i+1)/float(rings) for i in range(rings)]
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if normalization not in ['l1', 'l2', 'daisy', 'off']:
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raise ValueError('Invalid normalization method.')
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# Compute image derivatives.
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dx = np.zeros(img.shape)
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dy = np.zeros(img.shape)
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dx[:, :-1] = np.diff(img, n=1, axis=1)
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dy[:-1, :] = np.diff(img, n=1, axis=0)
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# Compute gradient orientation and magnitude and their contribution
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# to the histograms.
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grad_mag = sqrt(dx**2 + dy**2)
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grad_ori = arctan2(dy, dx)
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hist_sigma = pi/orientations
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kappa = 1./hist_sigma;
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bessel = iv(0, kappa)
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hist = np.empty((orientations,) + img.shape, dtype=float)
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for i in range(orientations):
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mu = 2*i*pi/orientations-pi
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# Weigh bin contribution by the circular normal distribution
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hist[i,:,:] = exp(kappa*cos(grad_ori-mu))/(2*pi*bessel)
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# Weigh bin contribution by the gradient magnitude
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hist[i,:,:] = np.multiply(hist[i,:,:], grad_mag)
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# Smooth orientation histograms for the center and all rings.
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sigmas = [sigmas[0]] + sigmas
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hist_smooth = np.empty((rings+1,)+hist.shape, dtype=float)
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for i in range(rings+1):
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for j in range(orientations):
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hist_smooth[i,j,:,:] = \
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gaussian_filter(hist[j,:,:], sigma=sigmas[i])
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# Assemble descriptor grid.
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theta = [2*pi*j/histograms for j in range(histograms)]
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desc_dims = (rings*histograms + 1)*orientations
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descs = np.empty((desc_dims, img.shape[0]-2*radius,
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img.shape[1]-2*radius))
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descs[:orientations,:,:] = \
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hist_smooth[0,:,radius:-radius,radius:-radius]
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idx = orientations
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for i in range(rings):
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for j in range(histograms):
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y_min = radius + int(round(ring_radii[i]*sin(theta[j])))
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y_max = descs.shape[1] + y_min
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x_min = radius + int(round(ring_radii[i]*cos(theta[j])))
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x_max = descs.shape[2] + x_min
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descs[idx:idx+orientations,:,:] = \
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hist_smooth[i+1,:,y_min:y_max,x_min:x_max]
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idx += orientations
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descs = descs[:,::step,::step]
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descs = descs.swapaxes(0,1).swapaxes(1,2)
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# Normalize descriptors.
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if normalization != 'off':
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descs += 1e-10
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if normalization == 'l1':
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descs /= np.sum(descs, axis=2)[:,:,np.newaxis]
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elif normalization == 'l2':
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descs /= sqrt(np.sum(descs**2, axis=2))[:,:,np.newaxis]
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elif normalization == 'daisy':
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for i in range(0, desc_dims, orientations):
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norms = sqrt(np.sum(descs[:,:,i:i+orientations]**2,
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axis=2))
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descs[:,:,i:i+orientations] /= norms[:,:,np.newaxis]
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return descs
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@@ -0,0 +1,88 @@
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import numpy as np
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from numpy.testing import assert_raises, assert_almost_equal
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from numpy import sqrt, ceil
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from skimage import data
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from skimage import img_as_float
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from skimage.feature import daisy
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def test_daisy_color_image_unsupported_error():
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img = np.zeros((20, 20, 3))
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assert_raises(ValueError, daisy, img)
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def test_daisy_desc_dims():
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img = img_as_float(data.lena()[:128, :128].mean(axis=2))
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rings = 2
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histograms = 4
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orientations = 3
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descs = daisy(img, rings=rings, histograms=histograms, orientations=orientations)
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assert(descs.shape[2] == (rings*histograms + 1)*orientations)
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rings = 4
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histograms = 5
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orientations = 13
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descs = daisy(img, rings=rings, histograms=histograms, orientations=orientations)
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assert(descs.shape[2] == (rings*histograms + 1)*orientations)
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def test_descs_shape():
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img = img_as_float(data.lena()[:256, :256].mean(axis=2))
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radius = 20
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step = 8
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descs = daisy(img, radius=radius, step=step)
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assert(descs.shape[0] == ceil((img.shape[0]-radius*2)/float(step)))
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assert(descs.shape[1] == ceil((img.shape[1]-radius*2)/float(step)))
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img = img[:-1,:-2]
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radius = 5
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step = 3
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descs = daisy(img, radius=radius, step=step)
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assert(descs.shape[0] == ceil((img.shape[0]-radius*2)/float(step)))
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assert(descs.shape[1] == ceil((img.shape[1]-radius*2)/float(step)))
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def test_daisy_incompatible_sigmas_and_radii():
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img = img_as_float(data.lena()[:128, :128].mean(axis=2))
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sigmas = [1, 2]
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radii = [1, 2]
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assert_raises(ValueError, daisy, img, sigmas=sigmas, ring_radii=radii)
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def test_daisy_normalization():
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img = img_as_float(data.lena()[:64, :64].mean(axis=2))
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descs = daisy(img, normalization='l1')
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for i in range(descs.shape[0]):
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for j in range(descs.shape[1]):
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assert_almost_equal(np.sum(descs[i,j,:]), 1)
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descs_ = daisy(img)
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assert_almost_equal(descs, descs_)
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descs = daisy(img, normalization='l2')
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for i in range(descs.shape[0]):
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for j in range(descs.shape[1]):
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assert_almost_equal(sqrt(np.sum(descs[i,j,:]**2)), 1)
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orientations = 8
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descs = daisy(img, orientations=orientations, normalization='daisy')
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desc_dims = descs.shape[2]
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for i in range(descs.shape[0]):
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for j in range(descs.shape[1]):
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for k in range(0, desc_dims, orientations):
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assert_almost_equal(sqrt(np.sum(
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descs[i,j,k:k+orientations]**2)), 1)
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img = np.zeros((50, 50))
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descs = daisy(img, normalization='off')
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for i in range(descs.shape[0]):
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for j in range(descs.shape[1]):
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assert_almost_equal(np.sum(descs[i,j,:]), 0)
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assert_raises(ValueError, daisy, img, normalization='does_not_exist')
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if __name__ == '__main__':
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from numpy import testing
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testing.run_module_suite()
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