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import numpy as np
def norm_kpt(K, kp):
kp = np.concatenate([kp, np.ones([kp.shape[0], 1])], axis=1)
kp = np.matmul(kp, np.linalg.inv(K).T)[:, :2]
return kp
def unnorm_kp(K, kp):
kp = np.concatenate([kp, np.ones([kp.shape[0], 1])], axis=1)
kp = np.matmul(kp, K.T)[:, :2]
return kp
def interpolate_depth(pos, depth):
# pos:[y,x]
ids = np.array(range(0, pos.shape[0]))
h, w = depth.shape
i = pos[:, 0]
j = pos[:, 1]
valid_corner = np.logical_and(
np.logical_and(i > 0, i < h - 1), np.logical_and(j > 0, j < w - 1)
)
i, j = i[valid_corner], j[valid_corner]
ids = ids[valid_corner]
i_top_left = np.floor(i).astype(np.int32)
j_top_left = np.floor(j).astype(np.int32)
i_top_right = np.floor(i).astype(np.int32)
j_top_right = np.ceil(j).astype(np.int32)
i_bottom_left = np.ceil(i).astype(np.int32)
j_bottom_left = np.floor(j).astype(np.int32)
i_bottom_right = np.ceil(i).astype(np.int32)
j_bottom_right = np.ceil(j).astype(np.int32)
# Valid depth
depth_top_left, depth_top_right, depth_down_left, depth_down_right = (
depth[i_top_left, j_top_left],
depth[i_top_right, j_top_right],
depth[i_bottom_left, j_bottom_left],
depth[i_bottom_right, j_bottom_right],
)
valid_depth = np.logical_and(
np.logical_and(depth_top_left > 0, depth_top_right > 0),
np.logical_and(depth_down_left > 0, depth_down_left > 0),
)
ids = ids[valid_depth]
depth_top_left, depth_top_right, depth_down_left, depth_down_right = (
depth_top_left[valid_depth],
depth_top_right[valid_depth],
depth_down_left[valid_depth],
depth_down_right[valid_depth],
)
i, j, i_top_left, j_top_left = (
i[valid_depth],
j[valid_depth],
i_top_left[valid_depth],
j_top_left[valid_depth],
)
# Interpolation
dist_i_top_left = i - i_top_left.astype(np.float32)
dist_j_top_left = j - j_top_left.astype(np.float32)
w_top_left = (1 - dist_i_top_left) * (1 - dist_j_top_left)
w_top_right = (1 - dist_i_top_left) * dist_j_top_left
w_bottom_left = dist_i_top_left * (1 - dist_j_top_left)
w_bottom_right = dist_i_top_left * dist_j_top_left
interpolated_depth = (
w_top_left * depth_top_left
+ w_top_right * depth_top_right
+ w_bottom_left * depth_down_left
+ w_bottom_right * depth_down_right
)
return [interpolated_depth, ids]
def reprojection(depth_map, kpt, dR, dt, K1_img2depth, K1, K2):
# warp kpt from img1 to img2
def swap_axis(data):
return np.stack([data[:, 1], data[:, 0]], axis=-1)
kp_depth = unnorm_kp(K1_img2depth, kpt)
uv_depth = swap_axis(kp_depth)
z, valid_idx = interpolate_depth(uv_depth, depth_map)
norm_kp = norm_kpt(K1, kpt)
norm_kp_valid = np.concatenate(
[norm_kp[valid_idx, :], np.ones((len(valid_idx), 1))], axis=-1
)
xyz_valid = norm_kp_valid * z.reshape(-1, 1)
xyz2 = np.matmul(xyz_valid, dR.T) + dt.reshape(1, 3)
xy2 = xyz2[:, :2] / xyz2[:, 2:]
kp2, valid = np.ones(kpt.shape) * 1e5, np.zeros(kpt.shape[0])
kp2[valid_idx] = unnorm_kp(K2, xy2)
valid[valid_idx] = 1
return kp2, valid.astype(bool)
def reprojection_2s(kp1, kp2, depth1, depth2, K1, K2, dR, dt, size1, size2):
# size:H*W
depth_size1, depth_size2 = [depth1.shape[0], depth1.shape[1]], [
depth2.shape[0],
depth2.shape[1],
]
scale_1 = [float(depth_size1[0]) / size1[0], float(depth_size1[1]) / size1[1], 1]
scale_2 = [float(depth_size2[0]) / size2[0], float(depth_size2[1]) / size2[1], 1]
K1_img2depth, K2_img2depth = np.diag(np.asarray(scale_1)), np.diag(
np.asarray(scale_2)
)
kp1_2_proj, valid1_2 = reprojection(depth1, kp1, dR, dt, K1_img2depth, K1, K2)
kp2_1_proj, valid2_1 = reprojection(
depth2, kp2, dR.T, -np.matmul(dR.T, dt), K2_img2depth, K2, K1
)
return [kp1_2_proj, kp2_1_proj], [valid1_2, valid2_1]
def make_corr(
kp1,
kp2,
desc1,
desc2,
depth1,
depth2,
K1,
K2,
dR,
dt,
size1,
size2,
corr_th,
incorr_th,
check_desc=False,
):
# make reprojection
[kp1_2, kp2_1], [valid1_2, valid2_1] = reprojection_2s(
kp1, kp2, depth1, depth2, K1, K2, dR, dt, size1, size2
)
num_pts1, num_pts2 = kp1.shape[0], kp2.shape[0]
# reprojection error
dis_mat1 = np.sqrt(
abs(
(kp1**2).sum(1, keepdims=True)
+ (kp2_1**2).sum(1, keepdims=False)[np.newaxis]
- 2 * np.matmul(kp1, kp2_1.T)
)
)
dis_mat2 = np.sqrt(
abs(
(kp2**2).sum(1, keepdims=True)
+ (kp1_2**2).sum(1, keepdims=False)[np.newaxis]
- 2 * np.matmul(kp2, kp1_2.T)
)
)
repro_error = np.maximum(dis_mat1, dis_mat2.T) # n1*n2
# find corr index
nn_sort1 = np.argmin(repro_error, axis=1)
nn_sort2 = np.argmin(repro_error, axis=0)
mask_mutual = nn_sort2[nn_sort1] == np.arange(kp1.shape[0])
mask_inlier = (
np.take_along_axis(
repro_error, indices=nn_sort1[:, np.newaxis], axis=-1
).squeeze(1)
< corr_th
)
mask = mask_mutual & mask_inlier
corr_index = np.stack(
[np.arange(num_pts1)[mask], np.arange(num_pts2)[nn_sort1[mask]]], axis=-1
)
if check_desc:
# filter kpt in same pos using desc distance(e.g. DoG kpt)
x1_valid, x2_valid = kp1[corr_index[:, 0]], kp2[corr_index[:, 1]]
mask_samepos1 = np.logical_and(
x1_valid[:, 0, np.newaxis] == kp1[np.newaxis, :, 0],
x1_valid[:, 1, np.newaxis] == kp1[np.newaxis, :, 1],
)
mask_samepos2 = np.logical_and(
x2_valid[:, 0, np.newaxis] == kp2[np.newaxis, :, 0],
x2_valid[:, 1, np.newaxis] == kp2[np.newaxis, :, 1],
)
duplicated_mask = np.logical_or(
mask_samepos1.sum(-1) > 1, mask_samepos2.sum(-1) > 1
)
duplicated_index = np.nonzero(duplicated_mask)[0]
unique_corr_index = corr_index[~duplicated_mask]
clean_duplicated_corr = []
for index in duplicated_index:
cur_desc1, cur_desc2 = (
desc1[mask_samepos1[index]],
desc2[mask_samepos2[index]],
)
cur_desc_mat = np.matmul(cur_desc1, cur_desc2.T)
cur_max_index = [
np.argmax(cur_desc_mat) // cur_desc_mat.shape[1],
np.argmax(cur_desc_mat) % cur_desc_mat.shape[1],
]
clean_duplicated_corr.append(
np.stack(
[
np.arange(num_pts1)[mask_samepos1[index]][cur_max_index[0]],
np.arange(num_pts2)[mask_samepos2[index]][cur_max_index[1]],
]
)
)
clean_corr_index = unique_corr_index
if len(clean_duplicated_corr) != 0:
clean_duplicated_corr = np.stack(clean_duplicated_corr, axis=0)
clean_corr_index = np.concatenate(
[clean_corr_index, clean_duplicated_corr], axis=0
)
else:
clean_corr_index = corr_index
# find incorr
mask_incorr1 = np.min(dis_mat2.T[valid1_2], axis=-1) > incorr_th
mask_incorr2 = np.min(dis_mat1.T[valid2_1], axis=-1) > incorr_th
incorr_index1, incorr_index2 = (
np.arange(num_pts1)[valid1_2][mask_incorr1.squeeze()],
np.arange(num_pts2)[valid2_1][mask_incorr2.squeeze()],
)
return clean_corr_index, incorr_index1, incorr_index2
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