/
_hog.py
251 lines (211 loc) · 10.3 KB
/
_hog.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
from __future__ import division
import numpy as np
from .._shared.utils import assert_nD
from .._shared.utils import skimage_deprecation, warn
from . import _hoghistogram
def _hog_normalize_block(block, method, eps=1e-5):
if method == 'L1':
out = block / (np.sum(np.abs(block)) + eps)
elif method == 'L1-sqrt':
out = np.sqrt(block / (np.sum(np.abs(block)) + eps))
elif method == 'L2':
out = block / np.sqrt(np.sum(block ** 2) + eps ** 2)
elif method == 'L2-Hys':
out = block / np.sqrt(np.sum(block ** 2) + eps ** 2)
out = np.minimum(out, 0.2)
out = out / np.sqrt(np.sum(block ** 2) + eps ** 2)
else:
raise ValueError('Selected block normalization method is invalid.')
return out
def hog(image, orientations=9, pixels_per_cell=(8, 8), cells_per_block=(3, 3),
block_norm='L1', visualise=False, transform_sqrt=False,
feature_vector=True, normalise=None):
"""Extract Histogram of Oriented Gradients (HOG) for a given image.
Compute a Histogram of Oriented Gradients (HOG) by
1. (optional) global image normalization
2. computing the gradient image in x and y
3. computing gradient histograms
4. normalizing across blocks
5. flattening into a feature vector
Parameters
----------
image : (M, N) ndarray
Input image (greyscale).
orientations : int, optional
Number of orientation bins.
pixels_per_cell : 2-tuple (int, int), optional
Size (in pixels) of a cell.
cells_per_block : 2-tuple (int, int), optional
Number of cells in each block.
block_norm : str {'L1', 'L1-sqrt', 'L2', 'L2-Hys'}, optional
Block normalization method:
``L1``
Normalization using L1-norm. (default)
``L1-sqrt``
Normalization using L1-norm, followed by square root.
``L2``
Normalization using L2-norm.
``L2-Hys``
Normalization using L2-norm, followed by limiting the
maximum values to 0.2 (`Hys` stands for `hysteresis`) and
renormalization using L2-norm.
For details, see [3]_, [4]_.
visualise : bool, optional
Also return an image of the HOG.
transform_sqrt : bool, optional
Apply power law compression to normalize the image before
processing. DO NOT use this if the image contains negative
values. Also see `notes` section below.
feature_vector : bool, optional
Return the data as a feature vector by calling .ravel() on the result
just before returning.
normalise : bool, deprecated
The parameter is deprecated. Use `transform_sqrt` for power law
compression. `normalise` has been deprecated.
Returns
-------
newarr : ndarray
HOG for the image as a 1D (flattened) array.
hog_image : ndarray (if visualise=True)
A visualisation of the HOG image.
References
----------
.. [1] http://en.wikipedia.org/wiki/Histogram_of_oriented_gradients
.. [2] Dalal, N and Triggs, B, Histograms of Oriented Gradients for
Human Detection, IEEE Computer Society Conference on Computer
Vision and Pattern Recognition 2005 San Diego, CA, USA,
https://lear.inrialpes.fr/people/triggs/pubs/Dalal-cvpr05.pdf,
DOI:10.1109/CVPR.2005.177
.. [3] Lowe, D.G., Distinctive image features from scale-invatiant
keypoints, International Journal of Computer Vision (2004) 60: 91,
http://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf,
DOI:10.1023/B:VISI.0000029664.99615.94
.. [4] Dalal, N, Finding People in Images and Videos,
Human-Computer Interaction [cs.HC], Institut National Polytechnique
de Grenoble - INPG, 2006,
https://tel.archives-ouvertes.fr/tel-00390303/file/NavneetDalalThesis.pdf
Notes
-----
The presented code implements the HOG extraction method from [2]_ with
the following changes: (I) blocks of (3, 3) cells are used ((2, 2) in the
paper; (II) no smoothing within cells (Gaussian spatial window with sigma=8pix
in the paper); (III) L1 block normalization is used (L2-Hys in the paper).
Power law compression, also known as Gamma correction, is used to reduce
the effects of shadowing and illumination variations. The compression makes
the dark regions lighter. When the kwarg `transform_sqrt` is set to
``True``, the function computes the square root of each color channel
and then applies the hog algorithm to the image.
"""
if block_norm == 'L1':
warn('Default value of `block_norm`==`L1` is deprecated and will '
'be changed to `L2-Hys` in v0.15', skimage_deprecation)
image = np.atleast_2d(image)
"""
The first stage applies an optional global image normalization
equalisation that is designed to reduce the influence of illumination
effects. In practice we use gamma (power law) compression, either
computing the square root or the log of each colour channel.
Image texture strength is typically proportional to the local surface
illumination so this compression helps to reduce the effects of local
shadowing and illumination variations.
"""
assert_nD(image, 2)
if normalise is not None:
raise ValueError("The ``normalise`` parameter was removed due to "
"incorrect behavior: it only applied a square root "
"instead of a true normalization. "
"If you wish to duplicate the old behavior, set "
"``transform_sqrt=True``. ``normalise`` will be "
"completely removed in v0.14.")
if transform_sqrt:
image = np.sqrt(image)
"""
The second stage computes first order image gradients. These capture
contour, silhouette and some texture information, while providing
further resistance to illumination variations. The locally dominant
colour channel is used, which provides colour invariance to a large
extent. Variant methods may also include second order image derivatives,
which act as primitive bar detectors - a useful feature for capturing,
e.g. bar like structures in bicycles and limbs in humans.
"""
if image.dtype.kind == 'u':
# convert uint image to float
# to avoid problems with subtracting unsigned numbers
image = image.astype('float')
gy, gx = [np.ascontiguousarray(g, dtype=np.double)
for g in np.gradient(image)]
"""
The third stage aims to produce an encoding that is sensitive to
local image content while remaining resistant to small changes in
pose or appearance. The adopted method pools gradient orientation
information locally in the same way as the SIFT [Lowe 2004]
feature. The image window is divided into small spatial regions,
called "cells". For each cell we accumulate a local 1-D histogram
of gradient or edge orientations over all the pixels in the
cell. This combined cell-level 1-D histogram forms the basic
"orientation histogram" representation. Each orientation histogram
divides the gradient angle range into a fixed number of
predetermined bins. The gradient magnitudes of the pixels in the
cell are used to vote into the orientation histogram.
"""
sy, sx = image.shape
cx, cy = pixels_per_cell
bx, by = cells_per_block
n_cellsx = int(sx // cx) # number of cells in x
n_cellsy = int(sy // cy) # number of cells in y
# compute orientations integral images
orientation_histogram = np.zeros((n_cellsy, n_cellsx, orientations))
_hoghistogram.hog_histograms(gx, gy, cx, cy, sx, sy, n_cellsx, n_cellsy,
orientations, orientation_histogram)
# now compute the histogram for each cell
hog_image = None
if visualise:
from .. import draw
radius = min(cx, cy) // 2 - 1
orientations_arr = np.arange(orientations)
dx_arr = radius * np.cos(orientations_arr / orientations * np.pi)
dy_arr = radius * np.sin(orientations_arr / orientations * np.pi)
hog_image = np.zeros((sy, sx), dtype=float)
for x in range(n_cellsx):
for y in range(n_cellsy):
for o, dx, dy in zip(orientations_arr, dx_arr, dy_arr):
centre = tuple([y * cy + cy // 2, x * cx + cx // 2])
rr, cc = draw.line(int(centre[0] - dx),
int(centre[1] + dy),
int(centre[0] + dx),
int(centre[1] - dy))
hog_image[rr, cc] += orientation_histogram[y, x, o]
"""
The fourth stage computes normalization, which takes local groups of
cells and contrast normalizes their overall responses before passing
to next stage. Normalization introduces better invariance to illumination,
shadowing, and edge contrast. It is performed by accumulating a measure
of local histogram "energy" over local groups of cells that we call
"blocks". The result is used to normalize each cell in the block.
Typically each individual cell is shared between several blocks, but
its normalizations are block dependent and thus different. The cell
thus appears several times in the final output vector with different
normalizations. This may seem redundant but it improves the performance.
We refer to the normalized block descriptors as Histogram of Oriented
Gradient (HOG) descriptors.
"""
n_blocksx = (n_cellsx - bx) + 1
n_blocksy = (n_cellsy - by) + 1
normalized_blocks = np.zeros((n_blocksy, n_blocksx,
by, bx, orientations))
for x in range(n_blocksx):
for y in range(n_blocksy):
block = orientation_histogram[y:y + by, x:x + bx, :]
normalized_blocks[y, x, :] = \
_hog_normalize_block(block, method=block_norm)
"""
The final step collects the HOG descriptors from all blocks of a dense
overlapping grid of blocks covering the detection window into a combined
feature vector for use in the window classifier.
"""
if feature_vector:
normalized_blocks = normalized_blocks.ravel()
if visualise:
return normalized_blocks, hog_image
else:
return normalized_blocks