File size: 7,304 Bytes
59b2a81
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
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