def test_skeletonize_num_neighbours(self):
# an empty image
image = np.zeros((300, 300))
# foreground object 1
image[10:-10, 10:100] = 1
image[-100:-10, 10:-10] = 1
image[10:-10, -100:-10] = 1
# foreground object 2
rs, cs = draw.bresenham(250, 150, 10, 280)
for i in range(10):
image[rs + i, cs] = 1
rs, cs = draw.bresenham(10, 150, 250, 280)
for i in range(20):
image[rs + i, cs] = 1
# foreground object 3
ir, ic = np.indices(image.shape)
circle1 = (ic - 135)**2 + (ir - 150)**2 < 30**2
circle2 = (ic - 135)**2 + (ir - 150)**2 < 20**2
image[circle1] = 1
image[circle2] = 0
result = skeletonize(image)
# there should never be a 2x2 block of foreground pixels in a skeleton
mask = np.array([[1, 1],
[1, 1]], np.uint8)
blocks = correlate(result, mask, mode='constant')
assert not numpy.any(blocks == 4)
def test_skeletonize_num_neighbours(self):
# an empty image
image = np.zeros((300, 300))
# foreground object 1
image[10:-10, 10:100] = 1
image[-100:-10, 10:-10] = 1
image[10:-10, -100:-10] = 1
# foreground object 2
rs, cs = draw.bresenham(250, 150, 10, 280)
for i in range(10):
image[rs + i, cs] = 1
rs, cs = draw.bresenham(10, 150, 250, 280)
for i in range(20):
image[rs + i, cs] = 1
# foreground object 3
ir, ic = np.indices(image.shape)
circle1 = (ic - 135)**2 + (ir - 150)**2 < 30**2
circle2 = (ic - 135)**2 + (ir - 150)**2 < 20**2
image[circle1] = 1
image[circle2] = 0
result = skeletonize(image)
# there should never be a 2x2 block of foreground pixels in a skeleton
mask = np.array([[1, 1], [1, 1]], np.uint8)
blocks = correlate(result, mask, mode='constant')
assert not numpy.any(blocks == 4)
def test_diag():
img = np.zeros((5, 5))
rr, cc = bresenham(0, 0, 4, 4)
img[rr, cc] = 1
img_ = np.eye(5)
assert_array_equal(img, img_)
def test_bresenham_vertical():
img = np.zeros((10, 10))
rr, cc = bresenham(0, 0, 9, 0)
img[rr, cc] = 1
img_ = np.zeros((10, 10))
img_[:, 0] = 1
assert_array_equal(img, img_)
def test_reverse():
img = np.zeros((10, 10))
rr, cc = bresenham(0, 9, 0, 0)
img[rr, cc] = 1
img_ = np.zeros((10, 10))
img_[0, :] = 1
assert_array_equal(img, img_)
def merge_bounding_boxes(image, scores, positions, threshold=0.5, dist=5):
"""
Merges bounding boxes
"""
image = image.copy()
num = 0
calc = scores > threshold
correct_positions = positions[calc]
correct_scores = scores[calc]
for position, score in zip(correct_positions, correct_scores):
num += 1
x0 = position[0]
y0 = position[1]
image[bresenham(x0, y0, x0 + 24, y0)] = 0
image[bresenham(x0, y0, x0, y0 + 24)] = 0
image[bresenham(x0 + 24, y0, x0 + 24, y0 + 24)] = 0
image[bresenham(x0, y0 + 24, x0 + 24, y0 + 24)] = 0
print "detected %d faces" % num
return image, correct_positions, correct_scores
def test_bresenham_horizontal():
img = np.zeros((10, 10))
rr, cc = bresenham(0, 0, 0, 9)
img[rr, cc] = 1
img_ = np.zeros((10, 10))
img_[0, :] = 1
assert_array_equal(img, img_)
def show_positive_boxes(image, labels, positions):
"""
Returns an image with the positive bounding boxes drawn
params
-------
image
labels
returns
-------
image
"""
image = image.copy()
for i, label in enumerate(labels):
if label:
x0 = positions[i, 0]
y0 = positions[i, 1]
image[bresenham(x0, y0, x0 + 24, y0)] = 0
image[bresenham(x0, y0, x0, y0 + 24)] = 0
image[bresenham(x0 + 24, y0, x0 + 24, y0 + 24)] = 0
image[bresenham(x0, y0 + 24, x0 + 24, y0 + 24)] = 0
return image
def _generate(self):
backprojection = np.zeros((self.width, self.width))
sinogram = np.zeros((self.num_steps, self.num_detectors))
filter = self._generate_filter(self.num_detectors)
angular_step = np.pi / self.num_steps
for step in range(self.num_steps):
#obliczenie kąta zerowego emitera
alpha = step * angular_step
step_lines = []
sinogram_row = np.zeros((self.num_detectors), dtype=np.int32)
for detector in range(self.num_detectors):
#obliczenie pozycji kolejnego detektora
detector_angle = alpha + np.pi - self.theta / 2 + detector * (
self.theta / (self.num_detectors - 1))
detector_x, detector_y = self._get_coords(detector_angle)
#obliczenie pozycji odpowiadającego emitera
emitter_angle = alpha + self.theta / 2 - detector * (
self.theta / (self.num_detectors - 1))
emitter_x, emitter_y = self._get_coords(emitter_angle)
#wygenerowanie linii
rr, cc = bresenham(emitter_y, emitter_x, detector_y,
detector_x)
#zsumowanie wartości pikseli oraz zapisanie linii do użycia w rekonstrukcji
sinogram_row[detector] = np.array(self.image[rr, cc]).sum()
step_lines.append((rr, cc))
sinogram[step] = sinogram_row
#filtruj wiersz sinogramu
if self.filter:
sinogram_row = np.array(np.convolve(sinogram_row, filter,
'same'),
dtype=np.int32)
for detector in range(self.num_detectors):
rr, cc = step_lines[detector]
backprojection[rr, cc] += sinogram_row[detector]
if (self.gaussian):
self.backprojections.append(
self._normalize_image(
cv2.GaussianBlur(backprojection, (3, 3), 3)))
else:
self.backprojections.append(
self._normalize_image(backprojection))
self.sinogram = cv2.normalize(sinogram, None, 0, 255, cv2.NORM_MINMAX)
def show_matched_desc(image1, image2, matched_desc):
image = np.zeros((image1.shape[0], image2.shape[1] + 10 + image2.shape[1]))
image[:, :image1.shape[1]] = image1
image[:, 10 + image2.shape[1]:] = image2
placed_desc = matched_desc
placed_desc[:, -1] = matched_desc[:, -1] + 10 + image2.shape[1]
from skimage.draw import bresenham
for el in placed_desc:
try:
draw_point(image, el[0], el[1])
draw_point(image, el[2], el[3])
image[bresenham(el[0], el[1], el[2], el[3])] = 0
except IndexError:
pass
return image
def bresenham_line(start, end):
"""Find the cells that should be selected to form a straight line
Use scikit-image implementation of the Bresenham line algorithm
Args:
start: (x, y) INDEX coordinates of the starting point
end: ((x, y), n) INDEX coordinates of the ending points
Returns:
List of (x, y) INDEX coordinates that form the straight lines
"""
path = list()
for target in end.T: # TODO: delete for loop
tmp = bresenham(start[0], start[1], target[0], target[1])
path += (list(zip(tmp[0], tmp[1]))[1:-1]) # start + end points removed
return path
def hog2image(hogArray,
imageSize=[32, 32],
orientations=9,
pixels_per_cell=(8, 8),
cells_per_block=(3, 3)):
from scipy import cos, sin
from skimage import draw
sy, sx = imageSize
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
n_blocksx = (n_cellsx - bx) + 1
n_blocksy = (n_cellsy - by) + 1
hogArray = hogArray.reshape([n_blocksy, n_blocksx, by, bx, orientations])
orientation_histogram = np.zeros((n_cellsy, n_cellsx, orientations))
for x in range(n_blocksx):
for y in range(n_blocksy):
block = hogArray[y, x, :]
orientation_histogram[y:y + by, x:x + bx, :] = block
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 = int(radius * cos(float(o) / orientations * np.pi))
dy = int(radius * sin(float(o) / orientations * np.pi))
# rr, cc = draw.bresenham(centre[0] - dy, centre[1] - dx,
# centre[0] + dy, centre[1] + dx)
rr, cc = draw.bresenham(centre[0] - dx, centre[1] - dy,
centre[0] + dx, centre[1] + dy)
hog_image[rr, cc] += orientation_histogram[y, x, o]
return hog_image
def show_matched_desc(image1, image2, matched_desc):
"""
Draw lines between matched descriptors of two images
params
------
image1: ndarray
image2: ndarray
"""
# Working on grayscale images
if len(image1.shape) == 3:
image1 = image1.mean(axis=2)
if len(image2.shape) == 3:
image2 = image2.mean(axis=2)
# FIXME doesn't work with images of different size
h = max(image1.shape[0], image2.shape[0])
image = np.zeros((h,
image1.shape[1] + 10 + image2.shape[1]))
image[:image1.shape[0], :image1.shape[1]] = image1
image[:image2.shape[0], 10 + image1.shape[1]:] = image2
placed_desc = matched_desc
placed_desc[:, -1] = matched_desc[:, -1] + 10 + image1.shape[1]
for el in placed_desc:
try:
draw_point(image, el[0], el[1])
draw_point(image, el[2], el[3])
image[bresenham(el[0], el[1], el[2], el[3])] = 0
except IndexError:
pass
fig = plt.figure()
ax = fig.add_subplot(111)
ax.xaxis.set_visible(False)
ax.yaxis.set_visible(False)
ax.imshow(image, cmap=cm.gray)
plt.show()
def show_matched_desc(image1, image2, matched_desc):
"""
Draw lines between matched descriptors of two images
params
------
image1: ndarray
image2: ndarray
"""
# Working on grayscale images
if len(image1.shape) == 3:
image1 = image1.mean(axis=2)
if len(image2.shape) == 3:
image2 = image2.mean(axis=2)
# FIXME doesn't work with images of different size
h = max(image1.shape[0], image2.shape[0])
image = np.zeros((h, image1.shape[1] + 10 + image2.shape[1]))
image[:image1.shape[0], :image1.shape[1]] = image1
image[:image2.shape[0], 10 + image1.shape[1]:] = image2
placed_desc = matched_desc
placed_desc[:, -1] = matched_desc[:, -1] + 10 + image1.shape[1]
for el in placed_desc:
try:
draw_point(image, el[0], el[1])
draw_point(image, el[2], el[3])
image[bresenham(el[0], el[1], el[2], el[3])] = 0
except IndexError:
pass
fig = plt.figure()
ax = fig.add_subplot(111)
ax.xaxis.set_visible(False)
ax.yaxis.set_visible(False)
ax.imshow(image, cmap=cm.gray)
plt.show()
def hog2image(hogArray, imageSize=[32,32],orientations=9,pixels_per_cell=(8, 8),cells_per_block=(3, 3)):
from scipy import sqrt, pi, arctan2, cos, sin
from skimage import draw
sy, sx = imageSize
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
n_blocksx = (n_cellsx - bx) + 1
n_blocksy = (n_cellsy - by) + 1
hogArray = hogArray.reshape([n_blocksy, n_blocksx, by, bx, orientations])
orientation_histogram = np.zeros((n_cellsy, n_cellsx, orientations))
for x in range(n_blocksx):
for y in range(n_blocksy):
block = hogArray[y, x, :]
orientation_histogram[y:y + by, x:x + bx, :] = block
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 = int(radius * cos(float(o) / orientations * np.pi))
dy = int(radius * sin(float(o) / orientations * np.pi))
# rr, cc = draw.bresenham(centre[0] - dy, centre[1] - dx,
# centre[0] + dy, centre[1] + dx)
rr, cc = draw.bresenham(centre[0] - dx, centre[1] - dy,\
centre[0] + dx, centre[1] + dy)
hog_image[rr, cc] += orientation_histogram[y, x, o]
return hog_image
""" from skimage.morphology import skeletonize from skimage import draw import numpy as np import matplotlib.pyplot as plt # an empty image image = np.zeros((400, 400)) # foreground object 1 image[10:-10, 10:100] = 1 image[-100:-10, 10:-10] = 1 image[10:-10, -100:-10] = 1 # foreground object 2 rs, cs = draw.bresenham(250, 150, 10, 280) for i in range(10): image[rs+i, cs] = 1 rs, cs = draw.bresenham(10, 150, 250, 280) for i in range(20): image[rs+i, cs] = 1 # foreground object 3 ir, ic = np.indices(image.shape) circle1 = (ic - 135)**2 + (ir - 150)**2 < 30**2 circle2 = (ic - 135)**2 + (ir - 150)**2 < 20**2 image[circle1] = 1 image[circle2] = 0 # perform skeletonization skeleton = skeletonize(image) # display results
def hof(flow, orientations=9, pixels_per_cell=(8, 8),
cells_per_block=(3, 3), visualise=False, normalise=False, motion_threshold=1.):
"""Extract Histogram of Optical Flow (HOF) for a given image.
Key difference between this and HOG is that flow is MxNx2 instead of MxN
Compute a Histogram of Optical Flow (HOF) by
1. (optional) global image normalisation
2. computing the dense optical flow
3. computing flow histograms
4. normalising across blocks
5. flattening into a feature vector
Parameters
----------
Flow : (M, N) ndarray
Input image (x and y flow images).
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 hof.
normalise : bool, optional
Apply power law compression to normalise the image before
processing.
static_threshold : threshold for no motion
Returns
-------
newarr : ndarray
hof for the image as a 1D (flattened) array.
hof_image : ndarray (if visualise=True)
A visualisation of the hof image.
References
----------
* http://en.wikipedia.org/wiki/Histogram_of_oriented_gradients
* 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
"""
flow = np.atleast_2d(flow)
"""
-1-
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
shadowing and illumination variations.
"""
if flow.ndim < 3:
raise ValueError("Requires dense flow in both directions")
if normalise:
flow = sqrt(flow)
"""
-2-
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 flow.dtype.kind == 'u':
# convert uint image to float
# to avoid problems with subtracting unsigned numbers in np.diff()
flow = flow.astype('float')
gx = np.zeros(flow.shape[:2])
gy = np.zeros(flow.shape[:2])
# gx[:, :-1] = np.diff(flow[:,:,1], n=1, axis=1)
# gy[:-1, :] = np.diff(flow[:,:,0], n=1, axis=0)
gx = flow[:,:,1]
gy = flow[:,:,0]
"""
-3-
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.
"""
magnitude = sqrt(gx**2 + gy**2)
orientation = arctan2(gy, gx) * (180 / pi) % 180
sy, sx = flow.shape[:2]
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-1):
#create new integral image for this orientation
# isolate orientations in this range
temp_ori = np.where(orientation < 180 / orientations * (i + 1),
orientation, -1)
temp_ori = np.where(orientation >= 180 / orientations * i,
temp_ori, -1)
# select magnitudes for those orientations
cond2 = (temp_ori > -1) * (magnitude > motion_threshold)
temp_mag = np.where(cond2, magnitude, 0)
temp_filt = uniform_filter(temp_mag, size=(cy, cx))
orientation_histogram[:, :, i] = temp_filt[subsample]
''' Calculate the no-motion bin '''
temp_mag = np.where(magnitude <= motion_threshold, magnitude, 0)
temp_filt = uniform_filter(temp_mag, size=(cy, cx))
orientation_histogram[:, :, -1] = temp_filt[subsample]
# now for each cell, compute the histogram
hof_image = None
if visualise:
from skimage import draw
radius = min(cx, cy) // 2 - 1
hof_image = np.zeros((sy, sx), dtype=float)
for x in range(n_cellsx):
for y in range(n_cellsy):
for o in range(orientations-1):
centre = tuple([y * cy + cy // 2, x * cx + cx // 2])
dx = int(radius * cos(float(o) / orientations * np.pi))
dy = int(radius * sin(float(o) / orientations * np.pi))
rr, cc = draw.bresenham(centre[0] - dy, centre[1] - dx,
centre[0] + dy, centre[1] + dx)
hof_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
Gradient (hog) descriptors.
"""
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 hof 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(), hof_image
else:
return normalised_blocks.ravel()
def hog(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
3. computing gradient histograms
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
----------
* http://en.wikipedia.org/wiki/Histogram_of_oriented_gradients
* 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
shadowing and illumination variations.
"""
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
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.
"""
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 / orientations * (i + 1),
orientation, -1)
temp_ori = np.where(orientation >= 180 / orientations * i, temp_ori,
-1)
# select magnitudes for those orientations
cond2 = temp_ori > -1
temp_mag = np.where(cond2, magnitude, 0)
temp_filt = uniform_filter(temp_mag, size=(cy, cx))
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.bresenham(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
Gradient (HOG) descriptors.
"""
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()
def hog(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
3. computing gradient histograms
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
----------
* http://en.wikipedia.org/wiki/Histogram_of_oriented_gradients
* 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
shadowing and illumination variations.
"""
if image.ndim > 3:
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.
"""
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
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.
"""
magnitude = sqrt(gx ** 2 + gy ** 2)
orientation = arctan2(gy, (gx + 1e-15)) * (180 / pi) + 90
sx, sy = 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_cellsx, n_cellsy, orientations))
for i in range(orientations):
#create new integral image for this orientation
# isolate orientations in this range
temp_ori = np.where(orientation < 180 / orientations * (i + 1),
orientation, 0)
temp_ori = np.where(orientation >= 180 / orientations * i,
temp_ori, 0)
# select magnitudes for those orientations
cond2 = temp_ori > 0
temp_mag = np.where(cond2, magnitude, 0)
orientation_histogram[:,:,i] = uniform_filter(temp_mag, size=(cx, cy))[cx/2::cx, cy/2::cy].T
# now for each cell, compute the histogram
#orientation_histogram = np.zeros((n_cellsx, n_cellsy, orientations))
radius = min(cx, cy) // 2 - 1
hog_image = None
if visualise:
hog_image = np.zeros((sy, sx), dtype=float)
if visualise:
from skimage import draw
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.bresenham(centre[0] - dx, centre[1] - dy,
centre[0] + dx, centre[1] + dy)
hog_image[rr, cc] += orientation_histogram[x, y, 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
Gradient (HOG) descriptors.
"""
n_blocksx = (n_cellsx - bx) + 1
n_blocksy = (n_cellsy - by) + 1
normalised_blocks = np.zeros((n_blocksx, n_blocksy,
bx, by, orientations))
for x in range(n_blocksx):
for y in range(n_blocksy):
block = orientation_histogram[x:x + bx, y:y + by, :]
eps = 1e-5
normalised_blocks[x, y, :] = 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()
def hog(image, orientations=9, pixels_per_cell=(8, 8),
cells_per_block=(3, 3), visualise=False, normalise=False):
image = np.atleast_2d(image)
if image.ndim > 3:
raise ValueError("Currently only supports grey-level images")
if normalise:
image = sqrt(image)
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)
magnitude = sqrt(gx ** 2 + gy ** 2)
orientation = arctan2(gy, (gx + 1e-15)) * (180 / pi) + 90
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))
for i in range(orientations):
temp_ori = np.where(orientation < 180 / orientations * (i + 1),
orientation, 0)
temp_ori = np.where(orientation >= 180 / orientations * i,
temp_ori, 0)
# select magnitudes for those orientations
cond2 = temp_ori > 0
temp_mag = np.where(cond2, magnitude, 0)
#orientation_histogram[:,:,i] = uniform_filter(temp_mag, size=(cy, cx))[cy/2::cy,cx/2::cx]
orientation_histogram[:,:,i] = uniform_filter(temp_mag, size=(cy, cx))[cy/2::cy,cx/2::cx]
radius = min(cx, cy) // 2 - 1
hog_image = None
if visualise:
hog_image = np.zeros((sy, sx), dtype=float)
if visualise:
from skimage import draw
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.bresenham(centre[0] - dx, centre[1] - dy,
centre[0] + dx, centre[1] + dy)
hog_image[rr, cc] += orientation_histogram[y, x, o]
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)
if visualise:
return normalised_blocks.ravel(), hog_image
else:
return normalised_blocks.ravel()
def hog(image,
orientations=9,
pixels_per_cell=(8, 8),
cells_per_block=(2, 2),
visualise=False,
normalise=True):
image = np.atleast_2d(image)
if image.ndim > 2:
raise ValueError("Only supports greyscale images")
if normalise:
image = sqrt(image)
if image.dtype.kind == 'u':
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)
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
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):
temp_ori = np.where(orientation < 180 / orientations * (i + 1),
orientation, -1)
temp_ori = np.where(orientation >= 180 / orientations * i, temp_ori,
-1)
cond2 = temp_ori > -1
temp_mag = np.where(cond2, magnitude, 0)
temp_filt = uniform_filter(temp_mag, size=(cy, cx))
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.bresenham(centre[0] - dy, centre[1] - dx,
centre[0] + dy, centre[1] + dx)
hog_image[rr, cc] += orientation_histogram[y, x, o]
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)
# print normalised_blocks.shape
if visualise:
return normalised_blocks.ravel(), hog_image
else:
return normalised_blocks.ravel()
def draw_line(p1,p2):
cc,rr = bresenham(x=p1[0],y=p1[1],x2=p2[0],y2=p2[1])
new_data[rr,cc] = 0