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In [2]:

%run ../common.ipynb
from skimage.feature import hog

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Populating the interactive namespace from numpy and matplotlib

WARNING: pylab import has clobbered these variables: ['imread', 'imsave']
`%matplotlib` prevents importing * from pylab and numpy

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In [3]:

size = 256
img = np.zeros((size,size), dtype=np.uint8)
t = linspace(start=0, stop=50*pi, endpoint=False, num=size)s
x,y = meshgrid(t, t)
img[:,:] = 127 + 127*sin(x+y)
#img[:,:] = 127 + 127*sin(sqrt((80-x)**2+(80-y)**2))
#img = rot90(img)
gimshow(img)
a, hog_img = hog(img, orientations=8, cells_per_block=(4,4), visualise=True)
imshow(hog_img);

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In [187]:

yy = ndimage.sobel(img, axis=0)
xx = ndimage.sobel(img, axis=-1)
angles = arctan2(xx,yy) / pi * 180 # in degrees
%matplotlib qt
imshow(angles, cmap='hot')

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Out[187]:

(<matplotlib.figure.Figure at 0x10d390b38>,
<matplotlib.axes._subplots.AxesSubplot at 0x10c6a3358>,
<matplotlib.image.AxesImage at 0x109668208>)

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In [201]:

plt.hist(angles.flatten(), bins=360, normed=True);

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In [76]:

def anglehist(img):
"Plot angles in image as histogram."
amax = angles.max()
amin = angles.min()
r = amax - amin + 1
figure()
h = plt.hist(angles.flatten(), bins=r, range=(amin, amax), normed=True)
xlim(amin, amax)
return h

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In [67]:

anglehist(img);

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plt.rcParams['image.interpolation'] = 'none' img = np.zeros((size,size)) img[:,:] = 127 + 127sin(x-3y) img = img.astype(np.int) imshow(img[0:10,0:10]) colorbar() figure() grad = gradient(img) angle = arctan2(img[0], img[1]) / pi * 180 figure() plt.hist(angle);

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In [179]:

a, hog_img = hog(img, visualise=True)
anglehist(img)
img = smooth(img)
anglehist(img);

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In [405]:

figure(figsize=(14,14))
plt.bar(range(180), h, width=0.8)

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Out[405]:

<Container object of 180 artists>

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In [414]:

hf = ndimage.uniform_filter1d(h, size=9)
figure(figsize=(14,14))
plt.bar(range(180), hf)
np.where(hf > hf.max()*0.9)

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Out[414]:

(array([22, 29, 30, 59, 60, 67]),)

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In [2]:

def g():
ori = 180 # every 2 degrees
# histogram of gradient 20 orientations
ihog = hog(img, orientations=ori)
# sum up magnitudes for each orientation
h = np.zeros((ori))
for i in range(ori):
h[i] = ihog[i::ori].sum()
plt.bar(range(ori), h)
h2 = np.where(h > h.max()*0.8, 0, h) # remove the highest (0,45,90,135 degrees)
figure()
plt.bar(range(ori), h2)

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In [13]:

%lprun -f hog2 hog2(img, orientations=180)

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In [11]:

def hog2(image, orientations=9, pixels_per_cell=(8, 8),
cells_per_block=(3, 3), visualise=False, normalise=False):
"""Extract Histogram of Oriented Gradients (HOG) for a given image.

Compute a Histogram of Oriented Gradients (HOG) by

1. (optional) global image normalisation
2. computing the gradient image in x and y
4. normalising across blocks
5. flattening into a feature vector

Parameters
----------
image : (M, N) ndarray
Input image (greyscale).
orientations : int
Number of orientation bins.
pixels_per_cell : 2 tuple (int, int)
Size (in pixels) of a cell.
cells_per_block  : 2 tuple (int,int)
Number of cells in each block.
visualise : bool, optional
Also return an image of the HOG.
normalise : bool, optional
Apply power law compression to normalise the image before
processing.

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
----------

* 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

"""
image = np.atleast_2d(image)

"""
The first stage applies an optional global image normalisation
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
"""

if image.ndim > 2:
raise ValueError("Currently only supports grey-level images")

if normalise:
image = 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 in np.diff()
image = image.astype('float')

gx = np.zeros(image.shape)
gy = np.zeros(image.shape)
gx[:, :-1] = np.diff(image, n=1, axis=1)
gy[:-1, :] = np.diff(image, n=1, axis=0)

"""
The third stage aims to produce an encoding that is sensitive to
local image content while remaining resistant to small changes in
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.
"""

magnitude = sqrt(gx**2 + gy**2)
orientation = arctan2(gy, gx) * (180 / pi) % 180

sy, sx = image.shape
cx, cy = pixels_per_cell
bx, by = cells_per_block

n_cellsx = int(np.floor(sx // cx))  # number of cells in x
n_cellsy = int(np.floor(sy // cy))  # number of cells in y

# compute orientations integral images
orientation_histogram = np.zeros((n_cellsy, n_cellsx, orientations))
subsample = np.index_exp[cy // 2:cy * n_cellsy:cy,
cx // 2:cx * n_cellsx:cx]
for i in range(orientations):
#create new integral image for this orientation
# isolate orientations in this range

temp_ori = np.where(orientation < 180.0 / orientations * (i + 1),
orientation, -1)
temp_ori = np.where(orientation >= 180.0 / orientations * i,
temp_ori, -1)
# select magnitudes for those orientations
cond2 = temp_ori > -1
temp_mag = np.where(cond2, magnitude, 0)

orientation_histogram[:, :, i] = temp_filt[subsample]

# now for each cell, compute the histogram
hog_image = None

if visualise:
from skimage import draw

radius = min(cx, cy) // 2 - 1
hog_image = np.zeros((sy, sx), dtype=float)
for x in range(n_cellsx):
for y in range(n_cellsy):
for o in range(orientations):
centre = tuple([y * cy + cy // 2, x * cx + cx // 2])
dx = radius * cos(float(o) / orientations * np.pi)
dy = radius * sin(float(o) / orientations * np.pi)
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 normalisation, which takes local groups of
cells and contrast normalises their overall responses before passing
to next stage. Normalisation 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 normalise each cell in the block.
Typically each individual cell is shared between several blocks, but
its normalisations are block dependent and thus different. The cell
thus appears several times in the final output vector with different
normalisations. This may seem redundant but it improves the performance.
We refer to the normalised block descriptors as Histogram of Oriented
"""

n_blocksx = (n_cellsx - bx) + 1
n_blocksy = (n_cellsy - by) + 1
normalised_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, :]
eps = 1e-5
normalised_blocks[y, x, :] = block / sqrt(block.sum()**2 + eps)

"""
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 visualise:
return normalised_blocks.ravel(), hog_image
else:
return normalised_blocks.ravel()

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In [457]:

np.where(h > h.max()*0.09)

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Out[457]:

(array([  0,  45,  90, 135]),)

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In [459]:

%matplotlib qt
imshow(img)

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Out[459]:

<matplotlib.image.AxesImage at 0x1569bc240>

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In [19]:

def anglehist(img):
"Plot angles in image as histogram."

# imports
from numpy import zeros_like, arctan2, ravel, histogram, pi

# as signed integer (dx,dy negative values too)
img = img.astype(np.int16)

# calculate difference in x-y direction
dx = zeros_like(img)
dy = zeros_like(img)
dx[:,1:-1] = img[:,2:] - img[:,0:-2]
dy[1:-1,:] = img[2:,:] - img[0:-2,:]

#magnitude = sqrt(dx**2+dy**2)

angles = arctan2(dy, dx, ) / pi * 180 % 180

# exclude weak orientations
#angles[magnitude < magnitude.mean()] = 0

# exclude n*45 angles
mask = ~((angles == 0) +
(angles == 45) +
(angles == 90) +
(angles == 135))
angles = ravel(angles[mask]) # flatten also

# calculate histogram of angles
return histogram(angles, bins=180, range=(0,180))

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In [ ]:

%timeit anglehist(img)

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In [ ]:

%lprun -s -f anglehist anglehist(img)

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In [ ]:

from skimage import filter

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In [14]:

sy = img.shape[0] // 40
sx = img.shape[1] // 40
for i in range(20,25):
for j in range(5,10):
temp_img = img[i*sy:(i+1)*sy, j*sx:(j+1)*sx]
figure(figsize=(14,7))
subplot(122)
matplotlib.pylab.imshow(temp_img)
#h = anglehist(temp_img)
h = hog(temp_img, orientations=180)
hh = np.zeros(180)
for x in range(180):
if x==0 or x==45 or x==90 or x==135:
continue
hh[x] = h[x::180].sum()
subplot(121)
plt.bar(range(180), hh)
t = 'cm:{:3.1f}, mean:{:0.2}, var:{:0.2}'.format(ndimage.center_of_mass(hh)[0],hh.mean(),hh.var())
title(t)

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/Users/arve/.virtualenvs/3.4/lib/python3.4/site-packages/matplotlib/pyplot.py:424: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).
max_open_warning, RuntimeWarning)

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