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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 | |