def expand_im(im, filter_vec, expand_shape):
"""
reduce image by taking the even pixel in the even row
Parameters
----------
:param im: array_like
:param filter_vec: array_like
:param expand_shape: tuple
Returns
-------
:return the expand image
"""
# step 1: expand
M, N = expand_shape
expanded_im = np.zeros((M, N))
expanded_im[::2, 1::2] = im
# step 2: blur
expanded_im = conv(expanded_im, filter_vec) # convolution with horizontal filter
expanded_im = conv(expanded_im, filter_vec.transpose()) # convolution with vertical filter
return expanded_im
def compute_derivatives(frame, next_frame, kernelX, kernelY, kernelT,
are_phases=False, kernel_center=None):
if are_phases:
fx = phase_conv2D(frame, kernelX, kernel_center) \
+ phase_conv2D(next_frame, kernelX, kernel_center)
fy = phase_conv2D(frame, kernelY, kernel_center) \
+ phase_conv2D(next_frame, kernelY, kernel_center)
ft = norm_angle(frame - next_frame)
else:
fx = conv(frame, kernelX) + conv(next_frame, kernelX)
fy = conv(frame, kernelY) + conv(next_frame, kernelY)
# ft = conv(frame, kernelT) + conv(next_frame, -kernelT)
ft = frame - next_frame
def horn_schunck_step(frame, next_frame, alpha, max_Niter, convergence_limit,
kernelHS, kernelT, kernelX, kernelY):
"""
Parameters
----------
frame: numpy.ndarray
image at t=0
next_frame: numpy.ndarray
image at t=1
alpha: float
regularization constant
max_Niter: int
maximum number of iteration
convergence_limit: float
the maximum absolute change between iterations defining convergence
"""
# set up initial velocities
vx = np.zeros_like(frame)
vy = np.zeros_like(frame)
# Estimate derivatives
[fx, fy, ft] = compute_derivatives(frame,
next_frame,
kernelX=kernelX,
kernelY=kernelY,
kernelT=kernelT)
# Iteration to reduce error
for i in range(max_Niter):
# Compute local averages of the flow vectors (smoothness constraint)
vx_avg = conv(vx, kernelHS)
vy_avg = conv(vy, kernelHS)
# common part of update step (brightness constancy)
der = (fx * vx_avg + fy * vy_avg + ft) / (alpha**2 + fx**2 + fy**2)
# iterative step
new_vx = vx_avg - fx * der
new_vy = vy_avg - fy * der
# check convergence
max_dv = np.max(
[np.max(np.abs(vx - new_vx)),
np.max(np.abs(vy - new_vy))])
vx, vy = new_vx, new_vy
if max_dv < convergence_limit:
break
return vx + vy * 1j
def reduce_im(im, filter_vec):
"""
reduce image by taking the even pixel in the even row
Parameters
----------
:param im: array_like
:param filter_vec: array_like
Returns
-------
:return the reduced image
"""
# step 1: blur
im = conv(im, filter_vec) # convolution with horizontal filter
im = conv(im, filter_vec.transpose()) # convolution with vertical filter
# step 2: reduce
return im[::2, 1::2]
def _get_status2(self):
a = np.array(self.matrix).reshape(4, 4)
n = 1
k = np.ones(n, dtype=int)
v = (conv((a[1:] == a[:-1]).astype(int), k, axis=0, mode='constant') >=
n).any()
h = (conv(
(a[:, 1:] == a[:, :-1]).astype(int), k, axis=1, mode='constant') >=
n).any()
if a.max() >= 256:
return "win"
if v | h:
return "not_over"
nzeros = np.count_nonzero(a)
if nzeros >= 16:
return "lose"
def normalized(img,window_shape=None):
if window_shape is None:
mfunc = lambda img: img.mean(axis=(0,1))
else:
box = np.ones(window_shape)/(window_shape[0]*window_shape[1])
if len(img.shape) == 3:
box = box[...,None]
mfunc = lambda img: conv(img,box)
diff = img-mfunc(img)
std = np.sqrt(mfunc(diff**2))
normalized_img = diff/(std+1e-6)
return normalized_img
def energy_map_w_filter(self):
"""
Counts energy map of image, using convolution and filter matrices.
:return: energy map of image
"""
if self._image is None:
raise ValueError
else:
dx = np.array([
[1., 2., 1.],
[0., 0., 0.],
[-1., -2., -1.]
])
dy = dx.transpose()
RGB = np.split(self._image, 3, axis=2)
energy_map = np.zeros(self._image.shape[:2])
for i in RGB:
i = i.reshape(self._image.shape[:2])
energy_map += np.absolute(conv(i, dx)) + np.absolute(conv(i, dy))
self._energy_map = energy_map
return energy_map
def compute_derivatives(frame, next_frame, kernelX, kernelY, kernelT):
fx = conv(frame, kernelX) + conv(next_frame, kernelX)
fy = conv(frame, kernelY) + conv(next_frame, kernelY)
ft = conv(frame, kernelT) + conv(next_frame, -kernelT)
from skimage import data, img_as_float, color from skimage.feature import corner_harris, corner_peaks from scipy import ndimage as ndi from scipy.ndimage.filters import convolve as conv from scipy.ndimage.filters import gaussian_filter as gauss import numpy as np import matplotlib.pyplot as plt I = data.camera() I = img_as_float(I) Gx = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]]) Gy = np.transpose(Gx) Ix = conv(I, Gx, mode='constant') Iy = conv(I, Gy, mode='constant') plt.figure(1) plt.subplot(1,2,1) plt.imshow(Ix) plt.subplot(1,2,2) plt.imshow(Iy) # Tenseur Axx = gauss(Ix*Ix, 1, mode='constant') Ayy = gauss(Iy*Iy, 1, mode='constant') Axy = gauss(Ix*Iy, 1, mode='constant') # determinant detA = Axx * Ayy - Axy ** 2
