import numpy as np
from numpy import sqrt, pi, arctan2, cos, sin, exp
from scipy.ndimage import gaussian_filter
from .. import img_as_float, draw
from ..color import gray2rgb
from .._shared.utils import check_nD
def daisy(image, step=4, radius=15, rings=3, histograms=8, orientations=8,
normalization='l1', sigmas=None, ring_radii=None, visualize=False):
'''Extract DAISY feature descriptors densely for the given image.
DAISY is a feature descriptor similar to SIFT formulated in a way that
allows for fast dense extraction. Typically, this is practical for
bag-of-features image representations.
The implementation follows Tola et al. [1]_ but deviate on the following
points:
* Histogram bin contribution are smoothed with a circular Gaussian
window over the tonal range (the angular range).
* The sigma values of the spatial Gaussian smoothing in this code do not
match the sigma values in the original code by Tola et al. [2]_. In
their code, spatial smoothing is applied to both the input image and
the center histogram. However, this smoothing is not documented in [1]_
and, therefore, it is omitted.
Parameters
----------
image : (M, N) array
Input image (grayscale).
step : int, optional
Distance between descriptor sampling points.
radius : int, optional
Radius (in pixels) of the outermost ring.
rings : int, optional
Number of rings.
histograms : int, optional
Number of histograms sampled per ring.
orientations : int, optional
Number of orientations (bins) per histogram.
normalization : [ 'l1' | 'l2' | 'daisy' | 'off' ], optional
How to normalize the descriptors
* 'l1': L1-normalization of each descriptor.
* 'l2': L2-normalization of each descriptor.
* 'daisy': L2-normalization of individual histograms.
* 'off': Disable normalization.
sigmas : 1D array of float, optional
Standard deviation of spatial Gaussian smoothing for the center
histogram and for each ring of histograms. The array of sigmas should
be sorted from the center and out. I.e. the first sigma value defines
the spatial smoothing of the center histogram and the last sigma value
defines the spatial smoothing of the outermost ring. Specifying sigmas
overrides the following parameter.
``rings = len(sigmas) - 1``
ring_radii : 1D array of int, optional
Radius (in pixels) for each ring. Specifying ring_radii overrides the
following two parameters.
``rings = len(ring_radii)``
``radius = ring_radii[-1]``
If both sigmas and ring_radii are given, they must satisfy the
following predicate since no radius is needed for the center
histogram.
``len(ring_radii) == len(sigmas) + 1``
visualize : bool, optional
Generate a visualization of the DAISY descriptors
Returns
-------
descs : array
Grid of DAISY descriptors for the given image as an array
dimensionality (P, Q, R) where
``P = ceil((M - radius*2) / step)``
``Q = ceil((N - radius*2) / step)``
``R = (rings * histograms + 1) * orientations``
descs_img : (M, N, 3) array (only if visualize==True)
Visualization of the DAISY descriptors.
References
----------
.. [1] Tola et al. "Daisy: An efficient dense descriptor applied to wide-
baseline stereo." Pattern Analysis and Machine Intelligence, IEEE
Transactions on 32.5 (2010): 815-830.
.. [2] http://cvlab.epfl.ch/software/daisy
'''
check_nD(image, 2, 'img')
image = img_as_float(image)
# Validate parameters.
if sigmas is not None and ring_radii is not None \
and len(sigmas) - 1 != len(ring_radii):
raise ValueError('`len(sigmas)-1 != len(ring_radii)`')
if ring_radii is not None:
rings = len(ring_radii)
radius = ring_radii[-1]
if sigmas is not None:
rings = len(sigmas) - 1
if sigmas is None:
sigmas = [radius * (i + 1) / float(2 * rings) for i in range(rings)]
if ring_radii is None:
ring_radii = [radius * (i + 1) / float(rings) for i in range(rings)]
if normalization not in ['l1', 'l2', 'daisy', 'off']:
raise ValueError('Invalid normalization method.')
# Compute image derivatives.
dx = np.zeros(image.shape)
dy = np.zeros(image.shape)
dx[:, :-1] = np.diff(image, n=1, axis=1)
dy[:-1, :] = np.diff(image, n=1, axis=0)
# Compute gradient orientation and magnitude and their contribution
# to the histograms.
grad_mag = sqrt(dx ** 2 + dy ** 2)
grad_ori = arctan2(dy, dx)
orientation_kappa = orientations / pi
orientation_angles = [2 * o * pi / orientations - pi
for o in range(orientations)]
hist = np.empty((orientations,) + image.shape, dtype=float)
for i, o in enumerate(orientation_angles):
# Weigh bin contribution by the circular normal distribution
hist[i, :, :] = exp(orientation_kappa * cos(grad_ori - o))
# Weigh bin contribution by the gradient magnitude
hist[i, :, :] = np.multiply(hist[i, :, :], grad_mag)
# Smooth orientation histograms for the center and all rings.
sigmas = [sigmas[0]] + sigmas
hist_smooth = np.empty((rings + 1,) + hist.shape, dtype=float)
for i in range(rings + 1):
for j in range(orientations):
hist_smooth[i, j, :, :] = gaussian_filter(hist[j, :, :],
sigma=sigmas[i])
# Assemble descriptor grid.
theta = [2 * pi * j / histograms for j in range(histograms)]
desc_dims = (rings * histograms + 1) * orientations
descs = np.empty((desc_dims, image.shape[0] - 2 * radius,
image.shape[1] - 2 * radius))
descs[:orientations, :, :] = hist_smooth[0, :, radius:-radius,
radius:-radius]
idx = orientations
for i in range(rings):
for j in range(histograms):
y_min = radius + int(round(ring_radii[i] * sin(theta[j])))
y_max = descs.shape[1] + y_min
x_min = radius + int(round(ring_radii[i] * cos(theta[j])))
x_max = descs.shape[2] + x_min
descs[idx:idx + orientations, :, :] = hist_smooth[i + 1, :,
y_min:y_max,
x_min:x_max]
idx += orientations
descs = descs[:, ::step, ::step]
descs = descs.swapaxes(0, 1).swapaxes(1, 2)
# Normalize descriptors.
if normalization != 'off':
descs += 1e-10
if normalization == 'l1':
descs /= np.sum(descs, axis=2)[:, :, np.newaxis]
elif normalization == 'l2':
descs /= sqrt(np.sum(descs ** 2, axis=2))[:, :, np.newaxis]
elif normalization == 'daisy':
for i in range(0, desc_dims, orientations):
norms = sqrt(np.sum(descs[:, :, i:i + orientations] ** 2,
axis=2))
descs[:, :, i:i + orientations] /= norms[:, :, np.newaxis]
if visualize:
descs_img = gray2rgb(image)
for i in range(descs.shape[0]):
for j in range(descs.shape[1]):
# Draw center histogram sigma
color = [1, 0, 0]
desc_y = i * step + radius
desc_x = j * step + radius
rows, cols, val = draw.circle_perimeter_aa(desc_y, desc_x, int(sigmas[0]))
draw.set_color(descs_img, (rows, cols), color, alpha=val)
max_bin = np.max(descs[i, j, :])
for o_num, o in enumerate(orientation_angles):
# Draw center histogram bins
bin_size = descs[i, j, o_num] / max_bin
dy = sigmas[0] * bin_size * sin(o)
dx = sigmas[0] * bin_size * cos(o)
rows, cols, val = draw.line_aa(desc_y, desc_x, int(desc_y + dy),
int(desc_x + dx))
draw.set_color(descs_img, (rows, cols), color, alpha=val)
for r_num, r in enumerate(ring_radii):
color_offset = float(1 + r_num) / rings
color = (1 - color_offset, 1, color_offset)
for t_num, t in enumerate(theta):
# Draw ring histogram sigmas
hist_y = desc_y + int(round(r * sin(t)))
hist_x = desc_x + int(round(r * cos(t)))
rows, cols, val = draw.circle_perimeter_aa(hist_y, hist_x,
int(sigmas[r_num + 1]))
draw.set_color(descs_img, (rows, cols), color, alpha=val)
for o_num, o in enumerate(orientation_angles):
# Draw histogram bins
bin_size = descs[i, j, orientations + r_num *
histograms * orientations +
t_num * orientations + o_num]
bin_size /= max_bin
dy = sigmas[r_num + 1] * bin_size * sin(o)
dx = sigmas[r_num + 1] * bin_size * cos(o)
rows, cols, val = draw.line_aa(hist_y, hist_x,
int(hist_y + dy),
int(hist_x + dx))
draw.set_color(descs_img, (rows, cols), color, alpha=val)
return descs, descs_img
else:
return descs