File size: 16,996 Bytes
404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af 8b973ee 404d2af |
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 |
"""
Implementation of the line matching methods.
"""
import numpy as np
import cv2
import torch
import torch.nn.functional as F
from ..misc.geometry_utils import keypoints_to_grid
class WunschLineMatcher(object):
"""Class matching two sets of line segments
with the Needleman-Wunsch algorithm."""
def __init__(
self,
cross_check=True,
num_samples=10,
min_dist_pts=8,
top_k_candidates=10,
grid_size=8,
sampling="regular",
line_score=False,
):
self.cross_check = cross_check
self.num_samples = num_samples
self.min_dist_pts = min_dist_pts
self.top_k_candidates = top_k_candidates
self.grid_size = grid_size
self.line_score = line_score # True to compute saliency on a line
self.sampling_mode = sampling
if sampling not in ["regular", "d2_net", "asl_feat"]:
raise ValueError("Wrong sampling mode: " + sampling)
def forward(self, line_seg1, line_seg2, desc1, desc2):
"""
Find the best matches between two sets of line segments
and their corresponding descriptors.
"""
img_size1 = (desc1.shape[2] * self.grid_size, desc1.shape[3] * self.grid_size)
img_size2 = (desc2.shape[2] * self.grid_size, desc2.shape[3] * self.grid_size)
device = desc1.device
# Default case when an image has no lines
if len(line_seg1) == 0:
return np.empty((0), dtype=int)
if len(line_seg2) == 0:
return -np.ones(len(line_seg1), dtype=int)
# Sample points regularly along each line
if self.sampling_mode == "regular":
line_points1, valid_points1 = self.sample_line_points(line_seg1)
line_points2, valid_points2 = self.sample_line_points(line_seg2)
else:
line_points1, valid_points1 = self.sample_salient_points(
line_seg1, desc1, img_size1, self.sampling_mode
)
line_points2, valid_points2 = self.sample_salient_points(
line_seg2, desc2, img_size2, self.sampling_mode
)
line_points1 = torch.tensor(
line_points1.reshape(-1, 2), dtype=torch.float, device=device
)
line_points2 = torch.tensor(
line_points2.reshape(-1, 2), dtype=torch.float, device=device
)
# Extract the descriptors for each point
grid1 = keypoints_to_grid(line_points1, img_size1)
grid2 = keypoints_to_grid(line_points2, img_size2)
desc1 = F.normalize(F.grid_sample(desc1, grid1)[0, :, :, 0], dim=0)
desc2 = F.normalize(F.grid_sample(desc2, grid2)[0, :, :, 0], dim=0)
# Precompute the distance between line points for every pair of lines
# Assign a score of -1 for unvalid points
scores = desc1.t() @ desc2
scores[~valid_points1.flatten()] = -1
scores[:, ~valid_points2.flatten()] = -1
scores = scores.reshape(
len(line_seg1), self.num_samples, len(line_seg2), self.num_samples
)
scores = scores.permute(0, 2, 1, 3)
# scores.shape = (n_lines1, n_lines2, num_samples, num_samples)
# Pre-filter the line candidates and find the best match for each line
matches = self.filter_and_match_lines(scores)
# [Optionally] filter matches with mutual nearest neighbor filtering
if self.cross_check:
matches2 = self.filter_and_match_lines(scores.permute(1, 0, 3, 2))
mutual = matches2[matches] == np.arange(len(line_seg1))
matches[~mutual] = -1
return matches
def d2_net_saliency_score(self, desc):
"""Compute the D2-Net saliency score
on a 3D or 4D descriptor."""
is_3d = len(desc.shape) == 3
b_size = len(desc)
feat = F.relu(desc)
# Compute the soft local max
exp = torch.exp(feat)
if is_3d:
sum_exp = 3 * F.avg_pool1d(exp, kernel_size=3, stride=1, padding=1)
else:
sum_exp = 9 * F.avg_pool2d(exp, kernel_size=3, stride=1, padding=1)
soft_local_max = exp / sum_exp
# Compute the depth-wise maximum
depth_wise_max = torch.max(feat, dim=1)[0]
depth_wise_max = feat / depth_wise_max.unsqueeze(1)
# Total saliency score
score = torch.max(soft_local_max * depth_wise_max, dim=1)[0]
normalization = torch.sum(score.reshape(b_size, -1), dim=1)
if is_3d:
normalization = normalization.reshape(b_size, 1)
else:
normalization = normalization.reshape(b_size, 1, 1)
score = score / normalization
return score
def asl_feat_saliency_score(self, desc):
"""Compute the ASLFeat saliency score on a 3D or 4D descriptor."""
is_3d = len(desc.shape) == 3
b_size = len(desc)
# Compute the soft local peakiness
if is_3d:
local_avg = F.avg_pool1d(desc, kernel_size=3, stride=1, padding=1)
else:
local_avg = F.avg_pool2d(desc, kernel_size=3, stride=1, padding=1)
soft_local_score = F.softplus(desc - local_avg)
# Compute the depth-wise peakiness
depth_wise_mean = torch.mean(desc, dim=1).unsqueeze(1)
depth_wise_score = F.softplus(desc - depth_wise_mean)
# Total saliency score
score = torch.max(soft_local_score * depth_wise_score, dim=1)[0]
normalization = torch.sum(score.reshape(b_size, -1), dim=1)
if is_3d:
normalization = normalization.reshape(b_size, 1)
else:
normalization = normalization.reshape(b_size, 1, 1)
score = score / normalization
return score
def sample_salient_points(self, line_seg, desc, img_size, saliency_type="d2_net"):
"""
Sample the most salient points along each line segments, with a
minimal distance between each point. Pad the remaining points.
Inputs:
line_seg: an Nx2x2 torch.Tensor.
desc: a NxDxHxW torch.Tensor.
image_size: the original image size.
saliency_type: 'd2_net' or 'asl_feat'.
Outputs:
line_points: an Nxnum_samplesx2 np.array.
valid_points: a boolean Nxnum_samples np.array.
"""
device = desc.device
if not self.line_score:
# Compute the score map
if saliency_type == "d2_net":
score = self.d2_net_saliency_score(desc)
else:
score = self.asl_feat_saliency_score(desc)
num_lines = len(line_seg)
line_lengths = np.linalg.norm(line_seg[:, 0] - line_seg[:, 1], axis=1)
# The number of samples depends on the length of the line
num_samples_lst = np.clip(
line_lengths // self.min_dist_pts, 2, self.num_samples
)
line_points = np.empty((num_lines, self.num_samples, 2), dtype=float)
valid_points = np.empty((num_lines, self.num_samples), dtype=bool)
# Sample the score on a fixed number of points of each line
n_samples_per_region = 4
for n in np.arange(2, self.num_samples + 1):
sample_rate = n * n_samples_per_region
# Consider all lines where we can fit up to n points
cur_mask = num_samples_lst == n
cur_line_seg = line_seg[cur_mask]
cur_num_lines = len(cur_line_seg)
if cur_num_lines == 0:
continue
line_points_x = np.linspace(
cur_line_seg[:, 0, 0], cur_line_seg[:, 1, 0], sample_rate, axis=-1
)
line_points_y = np.linspace(
cur_line_seg[:, 0, 1], cur_line_seg[:, 1, 1], sample_rate, axis=-1
)
cur_line_points = np.stack([line_points_x, line_points_y], axis=-1).reshape(
-1, 2
)
# cur_line_points is of shape (n_cur_lines * sample_rate, 2)
cur_line_points = torch.tensor(
cur_line_points, dtype=torch.float, device=device
)
grid_points = keypoints_to_grid(cur_line_points, img_size)
if self.line_score:
# The saliency score is high when the activation are locally
# maximal along the line (and not in a square neigborhood)
line_desc = F.grid_sample(desc, grid_points).squeeze()
line_desc = line_desc.reshape(-1, cur_num_lines, sample_rate)
line_desc = line_desc.permute(1, 0, 2)
if saliency_type == "d2_net":
scores = self.d2_net_saliency_score(line_desc)
else:
scores = self.asl_feat_saliency_score(line_desc)
else:
scores = F.grid_sample(score.unsqueeze(1), grid_points).squeeze()
# Take the most salient point in n distinct regions
scores = scores.reshape(-1, n, n_samples_per_region)
best = torch.max(scores, dim=2, keepdim=True)[1].cpu().numpy()
cur_line_points = cur_line_points.reshape(-1, n, n_samples_per_region, 2)
cur_line_points = np.take_along_axis(
cur_line_points, best[..., None], axis=2
)[:, :, 0]
# Pad
cur_valid_points = np.ones((cur_num_lines, self.num_samples), dtype=bool)
cur_valid_points[:, n:] = False
cur_line_points = np.concatenate(
[
cur_line_points,
np.zeros((cur_num_lines, self.num_samples - n, 2), dtype=float),
],
axis=1,
)
line_points[cur_mask] = cur_line_points
valid_points[cur_mask] = cur_valid_points
return line_points, valid_points
def sample_line_points(self, line_seg):
"""
Regularly sample points along each line segments, with a minimal
distance between each point. Pad the remaining points.
Inputs:
line_seg: an Nx2x2 torch.Tensor.
Outputs:
line_points: an Nxnum_samplesx2 np.array.
valid_points: a boolean Nxnum_samples np.array.
"""
num_lines = len(line_seg)
line_lengths = np.linalg.norm(line_seg[:, 0] - line_seg[:, 1], axis=1)
# Sample the points separated by at least min_dist_pts along each line
# The number of samples depends on the length of the line
num_samples_lst = np.clip(
line_lengths // self.min_dist_pts, 2, self.num_samples
)
line_points = np.empty((num_lines, self.num_samples, 2), dtype=float)
valid_points = np.empty((num_lines, self.num_samples), dtype=bool)
for n in np.arange(2, self.num_samples + 1):
# Consider all lines where we can fit up to n points
cur_mask = num_samples_lst == n
cur_line_seg = line_seg[cur_mask]
line_points_x = np.linspace(
cur_line_seg[:, 0, 0], cur_line_seg[:, 1, 0], n, axis=-1
)
line_points_y = np.linspace(
cur_line_seg[:, 0, 1], cur_line_seg[:, 1, 1], n, axis=-1
)
cur_line_points = np.stack([line_points_x, line_points_y], axis=-1)
# Pad
cur_num_lines = len(cur_line_seg)
cur_valid_points = np.ones((cur_num_lines, self.num_samples), dtype=bool)
cur_valid_points[:, n:] = False
cur_line_points = np.concatenate(
[
cur_line_points,
np.zeros((cur_num_lines, self.num_samples - n, 2), dtype=float),
],
axis=1,
)
line_points[cur_mask] = cur_line_points
valid_points[cur_mask] = cur_valid_points
return line_points, valid_points
def filter_and_match_lines(self, scores):
"""
Use the scores to keep the top k best lines, compute the Needleman-
Wunsch algorithm on each candidate pairs, and keep the highest score.
Inputs:
scores: a (N, M, n, n) torch.Tensor containing the pairwise scores
of the elements to match.
Outputs:
matches: a (N) np.array containing the indices of the best match
"""
# Pre-filter the pairs and keep the top k best candidate lines
line_scores1 = scores.max(3)[0]
valid_scores1 = line_scores1 != -1
line_scores1 = (line_scores1 * valid_scores1).sum(2) / valid_scores1.sum(2)
line_scores2 = scores.max(2)[0]
valid_scores2 = line_scores2 != -1
line_scores2 = (line_scores2 * valid_scores2).sum(2) / valid_scores2.sum(2)
line_scores = (line_scores1 + line_scores2) / 2
topk_lines = torch.argsort(line_scores, dim=1)[:, -self.top_k_candidates :]
scores, topk_lines = scores.cpu().numpy(), topk_lines.cpu().numpy()
# topk_lines.shape = (n_lines1, top_k_candidates)
top_scores = np.take_along_axis(scores, topk_lines[:, :, None, None], axis=1)
# Consider the reversed line segments as well
top_scores = np.concatenate([top_scores, top_scores[..., ::-1]], axis=1)
# Compute the line distance matrix with Needleman-Wunsch algo and
# retrieve the closest line neighbor
n_lines1, top2k, n, m = top_scores.shape
top_scores = top_scores.reshape(n_lines1 * top2k, n, m)
nw_scores = self.needleman_wunsch(top_scores)
nw_scores = nw_scores.reshape(n_lines1, top2k)
matches = np.mod(np.argmax(nw_scores, axis=1), top2k // 2)
matches = topk_lines[np.arange(n_lines1), matches]
return matches
def needleman_wunsch(self, scores):
"""
Batched implementation of the Needleman-Wunsch algorithm.
The cost of the InDel operation is set to 0 by subtracting the gap
penalty to the scores.
Inputs:
scores: a (B, N, M) np.array containing the pairwise scores
of the elements to match.
"""
b, n, m = scores.shape
# Recalibrate the scores to get a gap score of 0
gap = 0.1
nw_scores = scores - gap
# Run the dynamic programming algorithm
nw_grid = np.zeros((b, n + 1, m + 1), dtype=float)
for i in range(n):
for j in range(m):
nw_grid[:, i + 1, j + 1] = np.maximum(
np.maximum(nw_grid[:, i + 1, j], nw_grid[:, i, j + 1]),
nw_grid[:, i, j] + nw_scores[:, i, j],
)
return nw_grid[:, -1, -1]
def get_pairwise_distance(self, line_seg1, line_seg2, desc1, desc2):
"""
Compute the OPPOSITE of the NW score for pairs of line segments
and their corresponding descriptors.
"""
num_lines = len(line_seg1)
assert num_lines == len(
line_seg2
), "The same number of lines is required in pairwise score."
img_size1 = (desc1.shape[2] * self.grid_size, desc1.shape[3] * self.grid_size)
img_size2 = (desc2.shape[2] * self.grid_size, desc2.shape[3] * self.grid_size)
device = desc1.device
# Sample points regularly along each line
line_points1, valid_points1 = self.sample_line_points(line_seg1)
line_points2, valid_points2 = self.sample_line_points(line_seg2)
line_points1 = torch.tensor(
line_points1.reshape(-1, 2), dtype=torch.float, device=device
)
line_points2 = torch.tensor(
line_points2.reshape(-1, 2), dtype=torch.float, device=device
)
# Extract the descriptors for each point
grid1 = keypoints_to_grid(line_points1, img_size1)
grid2 = keypoints_to_grid(line_points2, img_size2)
desc1 = F.normalize(F.grid_sample(desc1, grid1)[0, :, :, 0], dim=0)
desc1 = desc1.reshape(-1, num_lines, self.num_samples)
desc2 = F.normalize(F.grid_sample(desc2, grid2)[0, :, :, 0], dim=0)
desc2 = desc2.reshape(-1, num_lines, self.num_samples)
# Compute the distance between line points for every pair of lines
# Assign a score of -1 for unvalid points
scores = torch.einsum("dns,dnt->nst", desc1, desc2).cpu().numpy()
scores = scores.reshape(num_lines * self.num_samples, self.num_samples)
scores[~valid_points1.flatten()] = -1
scores = scores.reshape(num_lines, self.num_samples, self.num_samples)
scores = scores.transpose(1, 0, 2).reshape(self.num_samples, -1)
scores[:, ~valid_points2.flatten()] = -1
scores = scores.reshape(self.num_samples, num_lines, self.num_samples)
scores = scores.transpose(1, 0, 2)
# scores.shape = (num_lines, num_samples, num_samples)
# Compute the NW score for each pair of lines
pairwise_scores = np.array([self.needleman_wunsch(s) for s in scores])
return -pairwise_scores
|