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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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