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import numpy as np
def line_to_border(line, size):
# line:(a,b,c), ax+by+c=0
# size:(W,H)
H, W = size[1], size[0]
a, b, c = line[0], line[1], line[2]
epsa = 1e-8 if a >= 0 else -1e-8
epsb = 1e-8 if b >= 0 else -1e-8
intersection_list = []
y_left = -c / (b + epsb)
y_right = (-c - a * (W - 1)) / (b + epsb)
x_top = -c / (a + epsa)
x_down = (-c - b * (H - 1)) / (a + epsa)
if y_left >= 0 and y_left <= H - 1:
intersection_list.append([0, y_left])
if y_right >= 0 and y_right <= H - 1:
intersection_list.append([W - 1, y_right])
if x_top >= 0 and x_top <= W - 1:
intersection_list.append([x_top, 0])
if x_down >= 0 and x_down <= W - 1:
intersection_list.append([x_down, H - 1])
if len(intersection_list) != 2:
return None
intersection_list = np.asarray(intersection_list)
return intersection_list
def find_point_in_line(end_point):
x_span, y_span = (
end_point[1, 0] - end_point[0, 0],
end_point[1, 1] - end_point[0, 1],
)
mv = np.random.uniform()
point = np.asarray([end_point[0, 0] + x_span * mv, end_point[0, 1] + y_span * mv])
return point
def epi_line(point, F):
homo = np.concatenate([point, np.ones([len(point), 1])], axis=-1)
epi = np.matmul(homo, F.T)
return epi
def dis_point_to_line(line, point):
homo = np.concatenate([point, np.ones([len(point), 1])], axis=-1)
dis = line * homo
dis = dis.sum(axis=-1) / (np.linalg.norm(line[:, :2], axis=-1) + 1e-8)
return abs(dis)
def SGD_oneiter(F1, F2, size1, size2):
H1, W1 = size1[1], size1[0]
factor1 = 1 / np.linalg.norm(size1)
factor2 = 1 / np.linalg.norm(size2)
p0 = np.asarray([(W1 - 1) * np.random.uniform(), (H1 - 1) * np.random.uniform()])
epi1 = epi_line(p0[np.newaxis], F1)[0]
border_point1 = line_to_border(epi1, size2)
if border_point1 is None:
return -1
p1 = find_point_in_line(border_point1)
epi2 = epi_line(p0[np.newaxis], F2)
d1 = dis_point_to_line(epi2, p1[np.newaxis])[0] * factor2
epi3 = epi_line(p1[np.newaxis], F2.T)
d2 = dis_point_to_line(epi3, p0[np.newaxis])[0] * factor1
return (d1 + d2) / 2
def compute_SGD(F1, F2, size1, size2):
np.random.seed(1234)
N = 1000
max_iter = N * 10
count, sgd = 0, 0
for i in range(max_iter):
d1 = SGD_oneiter(F1, F2, size1, size2)
if d1 < 0:
continue
d2 = SGD_oneiter(F2, F1, size1, size2)
if d2 < 0:
continue
count += 1
sgd += (d1 + d2) / 2
if count == N:
break
if count == 0:
return 1
else:
return sgd / count
def compute_inlier_rate(x1, x2, size1, size2, F_gt, th=0.003):
t1, t2 = np.linalg.norm(size1) * th, np.linalg.norm(size2) * th
epi1, epi2 = epi_line(x1, F_gt), epi_line(x2, F_gt.T)
dis1, dis2 = dis_point_to_line(epi1, x2), dis_point_to_line(epi2, x1)
mask_inlier = np.logical_and(dis1 < t2, dis2 < t1)
return mask_inlier.mean() if len(mask_inlier) != 0 else 0
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