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import numpy as np
def make_colorwheel():
"""
Generates a color wheel for optical flow visualization as presented in:
Baker et al. "A Database and Evaluation Methodology for Optical Flow" (ICCV, 2007)
URL: http://vision.middlebury.edu/flow/flowEval-iccv07.pdf
Code follows the original C++ source code of Daniel Scharstein.
Code follows the the Matlab source code of Deqing Sun.
Returns:
np.ndarray: Color wheel
"""
RY = 15
YG = 6
GC = 4
CB = 11
BM = 13
MR = 6
ncols = RY + YG + GC + CB + BM + MR
colorwheel = np.zeros((ncols, 3))
col = 0
# RY
colorwheel[0:RY, 0] = 255
colorwheel[0:RY, 1] = np.floor(255*np.arange(0,RY)/RY)
col = col+RY
# YG
colorwheel[col:col+YG, 0] = 255 - np.floor(255*np.arange(0,YG)/YG)
colorwheel[col:col+YG, 1] = 255
col = col+YG
# GC
colorwheel[col:col+GC, 1] = 255
colorwheel[col:col+GC, 2] = np.floor(255*np.arange(0,GC)/GC)
col = col+GC
# CB
colorwheel[col:col+CB, 1] = 255 - np.floor(255*np.arange(CB)/CB)
colorwheel[col:col+CB, 2] = 255
col = col+CB
# BM
colorwheel[col:col+BM, 2] = 255
colorwheel[col:col+BM, 0] = np.floor(255*np.arange(0,BM)/BM)
col = col+BM
# MR
colorwheel[col:col+MR, 2] = 255 - np.floor(255*np.arange(MR)/MR)
colorwheel[col:col+MR, 0] = 255
return colorwheel
def flow_uv_to_colors(u, v, convert_to_bgr=False):
"""
Applies the flow color wheel to (possibly clipped) flow components u and v.
According to the C++ source code of Daniel Scharstein
According to the Matlab source code of Deqing Sun
Args:
u (np.ndarray): Input horizontal flow of shape [H,W]
v (np.ndarray): Input vertical flow of shape [H,W]
convert_to_bgr (bool, optional): Convert output image to BGR. Defaults to False.
Returns:
np.ndarray: Flow visualization image of shape [H,W,3] in range [0, 255]
"""
flow_image = np.zeros((u.shape[0], u.shape[1], 3), np.uint8)
colorwheel = make_colorwheel() # shape [55x3]
ncols = colorwheel.shape[0]
rad = np.sqrt(np.square(u) + np.square(v))
a = np.arctan2(-v, -u)/np.pi
fk = (a+1) / 2*(ncols-1)
k0 = np.floor(fk).astype(np.int32)
k1 = k0 + 1
k1[k1 == ncols] = 0
f = fk - k0
for i in range(colorwheel.shape[1]):
tmp = colorwheel[:,i]
col0 = tmp[k0] / 255.0
col1 = tmp[k1] / 255.0
col = (1-f)*col0 + f*col1
idx = (rad <= 1)
col[idx] = 1 - rad[idx] * (1-col[idx])
col[~idx] = col[~idx] * 0.75 # out of range
# Note the 2-i => BGR instead of RGB
ch_idx = 2-i if convert_to_bgr else i
flow_image[:,:,ch_idx] = np.floor(255 * col)
return flow_image
def flow_to_image(flow_uv, clip_flow=None, convert_to_bgr=False):
"""
Expects a two dimensional flow image of shape.
Args:
flow_uv (np.ndarray): Flow UV image of shape [H,W,2]
clip_flow (float, optional): Clip maximum of flow values. Defaults to None.
convert_to_bgr (bool, optional): Convert output image to BGR. Defaults to False.
Returns:
np.ndarray: Flow visualization image of shape [H,W,3]
"""
assert flow_uv.ndim == 3, 'input flow must have three dimensions'
assert flow_uv.shape[2] == 2, 'input flow must have shape [H,W,2]'
if clip_flow is not None:
flow_uv = np.clip(flow_uv, 0, clip_flow)
u = flow_uv[:,:,0]
v = flow_uv[:,:,1]
rad = np.sqrt(np.square(u) + np.square(v))
rad_max = np.max(rad)
epsilon = 1e-5
u = u / (rad_max + epsilon)
v = v / (rad_max + epsilon)
return flow_uv_to_colors(u, v, convert_to_bgr)
def filter_uv(flow, threshold_factor = 0.1, sample_prob = 1.0):
'''
Args:
flow (numpy): A 2-dim array that stores x and y change in optical flow
threshold_factor (float): Prob of discarding outliers vector
sample_prob (float): The selection rate of how much proportion of points we need to store
'''
u = flow[:,:,0]
v = flow[:,:,1]
# Filter out those less than the threshold
rad = np.sqrt(np.square(u) + np.square(v))
rad_max = np.max(rad)
threshold = threshold_factor * rad_max
flow[:,:,0][rad < threshold] = 0
flow[:,:,1][rad < threshold] = 0
# Randomly sample based on sample_prob
zero_prob = 1 - sample_prob
random_array = np.random.randn(*flow.shape)
random_array[random_array < zero_prob] = 0
random_array[random_array >= zero_prob] = 1
flow = flow * random_array
return flow
############################################# The following is for dilation method in optical flow ######################################
def sigma_matrix2(sig_x, sig_y, theta):
"""Calculate the rotated sigma matrix (two dimensional matrix).
Args:
sig_x (float):
sig_y (float):
theta (float): Radian measurement.
Returns:
ndarray: Rotated sigma matrix.
"""
d_matrix = np.array([[sig_x**2, 0], [0, sig_y**2]])
u_matrix = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])
return np.dot(u_matrix, np.dot(d_matrix, u_matrix.T))
def mesh_grid(kernel_size):
"""Generate the mesh grid, centering at zero.
Args:
kernel_size (int):
Returns:
xy (ndarray): with the shape (kernel_size, kernel_size, 2)
xx (ndarray): with the shape (kernel_size, kernel_size)
yy (ndarray): with the shape (kernel_size, kernel_size)
"""
ax = np.arange(-kernel_size // 2 + 1., kernel_size // 2 + 1.)
xx, yy = np.meshgrid(ax, ax)
xy = np.hstack((xx.reshape((kernel_size * kernel_size, 1)), yy.reshape(kernel_size * kernel_size,
1))).reshape(kernel_size, kernel_size, 2)
return xy, xx, yy
def pdf2(sigma_matrix, grid):
"""Calculate PDF of the bivariate Gaussian distribution.
Args:
sigma_matrix (ndarray): with the shape (2, 2)
grid (ndarray): generated by :func:`mesh_grid`,
with the shape (K, K, 2), K is the kernel size.
Returns:
kernel (ndarrray): un-normalized kernel.
"""
inverse_sigma = np.linalg.inv(sigma_matrix)
kernel = np.exp(-0.5 * np.sum(np.dot(grid, inverse_sigma) * grid, 2))
return kernel
def bivariate_Gaussian(kernel_size, sig_x, sig_y, theta, grid=None, isotropic=True):
"""Generate a bivariate isotropic or anisotropic Gaussian kernel.
In the isotropic mode, only `sig_x` is used. `sig_y` and `theta` is ignored.
Args:
kernel_size (int):
sig_x (float):
sig_y (float):
theta (float): Radian measurement.
grid (ndarray, optional): generated by :func:`mesh_grid`,
with the shape (K, K, 2), K is the kernel size. Default: None
isotropic (bool):
Returns:
kernel (ndarray): normalized kernel.
"""
if grid is None:
grid, _, _ = mesh_grid(kernel_size)
if isotropic:
sigma_matrix = np.array([[sig_x**2, 0], [0, sig_x**2]])
else:
sigma_matrix = sigma_matrix2(sig_x, sig_y, theta)
kernel = pdf2(sigma_matrix, grid)
kernel = kernel / np.sum(kernel)
return kernel
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