├── GenerateUncertaintyData.m ├── LICENSE ├── README.md ├── RobustUncertaintyAwareMultiviewTriangulation_ReleaseCode.m └── uncertainty.mat /GenerateUncertaintyData.m: -------------------------------------------------------------------------------- 1 | clear all; close all; clc; 2 | 3 | load_precomputed_results = true; 4 | 5 | if (load_precomputed_results) 6 | load uncertainty.mat; 7 | load results_inliers.mat; 8 | else 9 | 10 | tic 11 | % Camera follows TUM rgb-d dataset parameters 12 | focal_length = 525; 13 | img_width = 640; 14 | img_height = 480; 15 | K = [focal_length 0 0; 0 focal_length 0; 0 0 1]; 16 | 17 | noise_levels = [1:10, 12:2:30]; 18 | dists = [1:9, 10:10:30]; 19 | 20 | n_cameras = [2:10, 12:2:30, 35:5:50]; 21 | 22 | n_simulations = []; 23 | for i = 1:length(n_cameras) 24 | 25 | if (n_cameras(i) <= 5) 26 | n_simulations = [n_simulations, 10]; 27 | continue; 28 | end 29 | 30 | if (n_cameras(i) <= 20) 31 | n_simulations = [n_simulations, 5]; 32 | continue; 33 | end 34 | 35 | n_simulations = [n_simulations, 3]; 36 | end 37 | 38 | n_simulations = 1000*n_simulations; 39 | 40 | n_total_run = length(noise_levels)*length(dists)*sum(n_simulations); 41 | 42 | all_error_3D = nan(1,n_total_run); 43 | all_error_2D = nan(1,n_total_run); 44 | all_min_level_of_degeneracy = nan(1,n_total_run); 45 | all_n_camera = nan(1,n_total_run); 46 | 47 | idx = 0; 48 | 49 | for noise_level = noise_levels 50 | 51 | for dist = dists 52 | point_w = [0;0;dist]; 53 | 54 | for n_camera = fliplr(n_cameras) 55 | 56 | disp(['noise_level = ', num2str(noise_level), ', dist = ', num2str(dist), ', n_camera = ', num2str(n_camera)]) 57 | 58 | 59 | n_simulation = n_simulations(n_cameras == n_camera); 60 | for simulation = 1:n_simulation 61 | 62 | idx = idx + 1; 63 | cam_pos = cell(1,n_camera); 64 | cam_pos_mat = nan(3,n_camera); 65 | R = cell(1,n_camera); 66 | t = cell(1,n_camera); 67 | uv = cell(1,n_camera); 68 | uv_measured = cell(1,n_camera); 69 | ray = cell(1,n_camera); 70 | AA = cell(1,n_camera); 71 | bb = cell(1,n_camera); 72 | 73 | for i = 1:n_camera 74 | 75 | % Camera is located randomly inside a unit sphere. 76 | cam_pos{i} = rand(3,1)-0.5; 77 | cam_pos{i} = rand(1)*0.5*cam_pos{i}/norm(cam_pos{i}); 78 | 79 | % The first two cameras are antipodal. 80 | if (i==1) 81 | cam_pos{1} = rand(3,1)-0.5; 82 | cam_pos{1} = 0.5*cam_pos{1}/norm(cam_pos{1}); 83 | elseif (i==2) 84 | cam_pos{2} = -cam_pos{1}; 85 | end 86 | 87 | while(true) 88 | R_temp = random_rotation(180); 89 | t_temp = -R_temp*cam_pos{i}; 90 | 91 | point_c = R_temp*point_w+t_temp; 92 | uv_temp = K*[point_c(1)/point_c(3); point_c(2)/point_c(3);1]; 93 | uv_temp = uv_temp(1:2); 94 | if (abs(uv_temp(1)) > img_width/2 || abs(uv_temp(2)) > img_height/2 || point_c(3) < 0) 95 | continue; 96 | end 97 | 98 | while(true) 99 | noise_dir = rand(2,1)-0.5; 100 | noise_dir = noise_dir/norm(noise_dir); 101 | uv_measured_temp = uv_temp+normrnd(0, noise_level)*noise_dir; 102 | if (abs(uv_measured_temp(1)) > img_width/2 || abs(uv_measured_temp(2)) > img_height/2) 103 | continue; 104 | end 105 | break; 106 | end 107 | 108 | 109 | break; 110 | end 111 | 112 | cam_pos_mat(:,i) = cam_pos{i}; 113 | R{i} = R_temp; 114 | t{i} = t_temp; 115 | uv{i} = uv_temp; 116 | uv_measured{i} = uv_measured_temp; 117 | ray{i} = K\[uv_measured{i};1]; 118 | ray{i} = ray{i}/norm(ray{i}); 119 | 120 | % Compute AA and bb necesary for computing the Jacobian: 121 | r11 = R{i}(1,1); r12 = R{i}(1,2); r13 = R{i}(1,3); 122 | r21 = R{i}(2,1); r22 = R{i}(2,2); r23 = R{i}(2,3); 123 | r31 = R{i}(3,1); r32 = R{i}(3,2); r33 = R{i}(3,3); 124 | tx = t{i}(1); ty = t{i}(2); tz = t{i}(3); 125 | fx = K(1,1); skew = K(1,2); fy = K(2,2); 126 | 127 | a11 = [... 128 | 0, ... 129 | fx*(r11*r32-r31*r12)+skew*(r21*r32-r31*r22), ... 130 | fx*(r11*r33-r31*r13)+skew*(r21*r33-r31*r23), ... 131 | fx*(r11*tz-r31*tx)+skew*(r21*tz-r31*ty)]; 132 | a21 = [... 133 | 0, ... 134 | fy*(r21*r32-r31*r22), ... 135 | fy*(r21*r33-r31*r23), ... 136 | +fy*(r21*tz-r31*ty)]; 137 | a12 = [... 138 | fx*(r12*r31-r32*r11)+skew*(r22*r31-r32*r21),... 139 | 0,... 140 | fx*(r12*r33-r32*r13)+skew*(r22*r33-r32*r23),... 141 | fx*(r12*tz-r32*tx)+skew*(r22*tz-r32*ty)]; 142 | a22 = [... 143 | fy*(r22*r31-r32*r21),... 144 | 0,... 145 | fy*(r22*r33-r32*r23),... 146 | fy*(r22*tz-r32*ty)]; 147 | a13 = [... 148 | fx*(r13*r31-r33*r11)+skew*(r23*r31-r33*r21),... 149 | fx*(r13*r32-r33*r12)+skew*(r23*r32-r33*r22),... 150 | 0,... 151 | fx*(r13*tz-r33*tx)+skew*(r23*tz-r33*ty)]; 152 | a23 = [... 153 | fy*(r23*r31-r33*r21),... 154 | fy*(r23*r32-r33*r22),... 155 | 0,... 156 | fy*(r23*tz-r33*ty)]; 157 | 158 | AA{i} = [a11;a21;a12;a22;a13;a23]; 159 | bb{i} = [r31, r32, r33, tz]; 160 | end 161 | 162 | 163 | % figure; 164 | % axis equal 165 | % hold on 166 | % for i=1:n_camera 167 | % if (i<= n_inlier) 168 | % scatter3(cam_pos{i}(1),cam_pos{i}(2),cam_pos{i}(3), 'ko') 169 | % text(cam_pos{i}(1), cam_pos{i}(2), cam_pos{i}(3),num2str(i),'HorizontalAlignment','left','FontSize',20); 170 | % 171 | % endpoint = 15*R{i}'*ray{i}+cam_pos{i}; 172 | % xx = [cam_pos{i}(1), endpoint(1)]; 173 | % yy = [cam_pos{i}(2), endpoint(2)]; 174 | % zz = [cam_pos{i}(3), endpoint(3)]; 175 | % plot3(xx, yy, zz, 'Color', [0 0 0 0.5]); 176 | % else 177 | % scatter3(cam_pos{i}(1),cam_pos{i}(2),cam_pos{i}(3), 'ro') 178 | % 179 | % endpoint = R{i}'*ray{i}+cam_pos{i}; 180 | % xx = [cam_pos{i}(1), endpoint(1)]; 181 | % yy = [cam_pos{i}(2), endpoint(2)]; 182 | % zz = [cam_pos{i}(3), endpoint(3)]; 183 | % plot3(xx, yy, zz, 'Color', [1 0 0 0.5]); 184 | % end 185 | % end 186 | % scatter3(point_w(1), point_w(2), point_w(3), 200, 'kx') 187 | % view(360,0) 188 | 189 | 190 | %% DLT + GN for all inliers 191 | 192 | % Prepare the matrices. 193 | M0 = nan(1,n_camera); 194 | M1 = nan(1,n_camera); 195 | M2 = nan(4,n_camera); 196 | M3 = nan(4,n_camera); 197 | M4 = nan(4,n_camera); 198 | ray_w = cell(1,n_camera); 199 | for i = 1:n_camera 200 | ray_w{i} = K\[uv_measured{i};1]; 201 | ray_w{i} = ray_w{i}/norm(ray_w{i}); 202 | ray_w{i} = R{i}'*ray_w{i}; 203 | 204 | M0(1,i) = uv_measured{i}(1)-K(1,3); 205 | M1(1,i) = uv_measured{i}(2)-K(2,3); 206 | 207 | P = [R{i}, t{i}]; 208 | M2(:,i) = K(1,1)*P(1,:)'+K(1,2)*P(2,:)'; 209 | M3(:,i) = K(2,1)*P(1,:)'+K(2,2)*P(2,:)'; 210 | M4(:,i) = P(3,:)'; 211 | end 212 | 213 | % Do DLT. 214 | A = zeros(2*n_camera, 4); 215 | for i = 1:n_camera 216 | Q = K*[R{i}, t{i}]; 217 | u = uv_measured{i}(1); 218 | v = uv_measured{i}(2); 219 | A(2*i-1:2*i, :) = [u*Q(3,:)-Q(1,:); v*Q(3,:)-Q(2,:)]; 220 | end 221 | [~,S_,V_] = svd(A); 222 | [~, min_idx] = min(diag(S_)); 223 | x_dlt = V_(:, min_idx); 224 | x_dlt = x_dlt/x_dlt(end); 225 | x_dlt = x_dlt(1:3); 226 | 227 | % Do Gauss-Newton Optimization. 228 | mean_reproj_error = 0; 229 | x_gn = x_dlt; 230 | for it = 1:10 231 | N4 = [x_gn;1]'*M4; 232 | M5 = ([x_gn;1]'*M2)./N4 - M0; 233 | M6 = ([x_gn;1]'*M3)./N4 - M1; 234 | M5 = M5(1:n_camera); 235 | M6 = M6(1:n_camera); 236 | residuals = [M5;M6]; 237 | squared_reproj_error_all = M5.*M5+M6.*M6; 238 | 239 | mean_reproj_error_prev = mean_reproj_error; 240 | mean_reproj_error = mean(sqrt(squared_reproj_error_all)); 241 | 242 | if (it > 2 && abs(mean_reproj_error-mean_reproj_error_prev) < 0.1) 243 | break; 244 | end 245 | 246 | J_est = zeros(2*n_camera,3); 247 | for i = 1:n_camera 248 | J_temp = AA{i}*[x_gn;1]/(bb{i}*[x_gn;1])^2; 249 | J_est(2*i-1:2*i, :) = reshape(J_temp, [2,3]); 250 | end 251 | update = -pinv(J_est)*residuals(:); 252 | x_gn = x_gn+update; 253 | end 254 | 255 | % Evaluate the performance metrics. 256 | N4 = [x_gn;1]'*M4; 257 | M5 = ([x_gn;1]'*M2)./N4 - M0; 258 | M6 = ([x_gn;1]'*M3)./N4 - M1; 259 | squared_reproj_error_all = M5.*M5+M6.*M6; 260 | squared_reproj_error_inliers = squared_reproj_error_all(1:n_camera); 261 | 262 | 263 | all_error_3D(idx) = norm(point_w-x_gn); 264 | all_error_2D(idx) = mean(sqrt(squared_reproj_error_inliers)); 265 | all_min_level_of_degeneracy(idx) = GetMinimumLevelOfDegeneracy(cam_pos, ray_w, 1:n_camera); 266 | all_n_camera(idx) = n_camera; 267 | 268 | end 269 | 270 | end 271 | end 272 | end 273 | 274 | angle_bin_edges = fliplr([0:19; 1:20]); 275 | noise_bin_edges = [0:19; 1:20]; 276 | cell_colormap_results = cell(size(angle_bin_edges,2), size(noise_bin_edges,2), length(n_cameras)); 277 | 278 | for i = 1:length(all_error_3D) 279 | angle_of_degeneracy = acosd(all_min_level_of_degeneracy(i)); 280 | n_camera = all_n_camera(i); 281 | error_3D = all_error_3D(i); 282 | error_2D = all_error_2D(i); 283 | for j = 1:size(angle_bin_edges,2) 284 | if (angle_of_degeneracy < angle_bin_edges(1,j) || angle_of_degeneracy >= angle_bin_edges(2,j)) 285 | continue; 286 | end 287 | for k = 1:size(noise_bin_edges,2) 288 | if (error_2D < noise_bin_edges(1,k) || error_2D >= noise_bin_edges(2,k)) 289 | continue; 290 | end 291 | for l = 1:length(n_cameras) 292 | if (n_cameras(l) ~= n_camera) 293 | continue; 294 | end 295 | cell_colormap_results{j,k,l} = [cell_colormap_results{j,k,l}, error_3D]; 296 | end 297 | end 298 | end 299 | end 300 | 301 | mat_colormap_results = zeros(size(cell_colormap_results)); 302 | for j = 1:size(mat_colormap_results,1) 303 | for k = 1:size(mat_colormap_results,2) 304 | for l = 1:size(mat_colormap_results,3) 305 | mat_colormap_results(j,k,l) = min(1,sqrt(mean(cell_colormap_results{j,k,l}.^2))); 306 | end 307 | end 308 | end 309 | 310 | mat_colormap_results_smoothed = MonotoneSmooth(mat_colormap_results, 0.01, 1, 1, 0); 311 | 312 | uncertainty.angle_i = angle_bin_edges; 313 | uncertainty.reproj_j = noise_bin_edges; 314 | uncertainty.camera_k = n_cameras; 315 | uncertainty.result = mat_colormap_results_smoothed; 316 | 317 | save uncertainty.mat uncertainty 318 | save results_inliers.mat 319 | time_elsaped = toc; 320 | disp(['Took ', num2str(time_elsaped/3600), ' hours.']) 321 | 322 | end 323 | 324 | 325 | 326 | %out = TrilinearInterpolation(8.5, 3.5, 10, uncertainty) 327 | 328 | 329 | 330 | 331 | 332 | %% Plot 333 | 334 | figure; 335 | for i = 1:length(n_cameras) 336 | subplot(6,8,2*i-1) 337 | imagesc(mat_colormap_results(:,:,i)) 338 | colormap(jet) 339 | caxis([0 1]) 340 | set(gca,'xticklabel',{[]}) 341 | set(gca,'yticklabel',{[]}) 342 | title([num2str(n_cameras(i)), ' cams']) 343 | 344 | subplot(6,8,2*i) 345 | imagesc(mat_colormap_results_smoothed(:,:,i)) 346 | colormap(jet) 347 | caxis([0 1]) 348 | set(gca,'xticklabel',{[]}) 349 | set(gca,'yticklabel',{[]}) 350 | title([num2str(n_cameras(i)), ' cams (smoothed)']) 351 | end 352 | 353 | 354 | figure; 355 | plot_idx = 0; 356 | for i = 1:length(n_cameras) 357 | n_camera = n_cameras(i); 358 | if (ismember(n_cameras(i), [2, 3, 4, 5, 10, 20,30,50])) 359 | plot_idx = plot_idx + 1; 360 | subplot(2,4,plot_idx) 361 | imagesc(mat_colormap_results_smoothed(:,:,i)) 362 | axis equal 363 | colormap(jet) 364 | colorbar 365 | caxis([0 1]) 366 | xticks(0.5:5:20.5) 367 | xticklabels({'0', '5', '10', '15', '20'}) 368 | xlabel('Mean 2D error (pix)') 369 | yticks(0.5:5:20.5) 370 | yticklabels({'20','15', '10', '5','0'}) 371 | ylabel('Angle of Degeneracy (deg)') 372 | title([num2str(n_cameras(i)), ' cams']) 373 | end 374 | end 375 | 376 | % for i = 1:length(n_cameras) 377 | % disp(['n_camera = ', num2str(n_cameras(i))]) 378 | % latex_table_raw = latex(vpa(sym(mat_colormap_results(:,:,i)),2)) 379 | % latex_table_smoothed = latex(vpa(sym(mat_colormap_results_smoothed(:,:,i)),2)) 380 | % end 381 | 382 | 383 | %% 384 | function out = random_rotation(max_angle_deg) 385 | 386 | axis = rand(3,1)-0.5; 387 | axis = axis/norm(axis); 388 | angle = rand*max_angle_deg/180*pi; 389 | rotvec = angle*axis; 390 | out = rotation_from_rotvec(rotvec); 391 | 392 | end 393 | 394 | function R = rotation_from_rotvec(in) 395 | angle = norm(in); 396 | 397 | if (angle==0) 398 | R = eye(3); 399 | else 400 | unit_axis = in/angle; 401 | so3 = SkewSymmetricMatrix(unit_axis); 402 | R = eye(3)+so3*sin(angle)+so3^2*(1-cos(angle)); 403 | end 404 | end 405 | 406 | 407 | function out = SkewSymmetricMatrix(in) 408 | out=[0 -in(3) in(2) ; in(3) 0 -in(1) ; -in(2) in(1) 0 ]; 409 | end 410 | 411 | 412 | function mLoD = GetMinimumLevelOfDegeneracy(cam_pos, ray_w, idx) 413 | 414 | idx = reshape(idx, [1, numel(idx)]); 415 | 416 | mLoD = inf; 417 | for i = idx 418 | for j = idx 419 | if (j<=i) 420 | continue; 421 | end 422 | t_ij = cam_pos{i}-cam_pos{j}; 423 | t_ij = t_ij/norm(t_ij); 424 | f_i = ray_w{i}; 425 | f_j = ray_w{j}; 426 | 427 | LoD = abs(f_i'*f_j); 428 | % LoD = max(abs([t_ij'*f_i, t_ij'*f_j, f_i'*f_j])); 429 | if (LoD < mLoD) 430 | mLoD = LoD; 431 | end 432 | end 433 | end 434 | 435 | end 436 | 437 | 438 | function out = MonotoneSmooth(in, thr, x_increasing, y_increasing, z_increasing) 439 | 440 | out = in; 441 | for it = 1:100000 442 | out_prev = out; 443 | 444 | for i = 1:size(out_prev,1) 445 | for j = 1:size(out_prev,2) 446 | for k = 1:size(out_prev,3) 447 | candidates = []; 448 | 449 | if (x_increasing) 450 | if (i-1 >= 1) 451 | if (out_prev(i-1,j,k) <= out_prev(i,j,k)) 452 | candidates = [candidates, out_prev(i,j,k)]; 453 | else 454 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i-1,j,k))]; 455 | end 456 | end 457 | if (i+1 <= size(out_prev,1)) 458 | if (out_prev(i+1,j,k) >= out_prev(i,j,k)) 459 | candidates = [candidates, out_prev(i,j,k)]; 460 | else 461 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i+1,j,k))]; 462 | end 463 | end 464 | else 465 | if (i-1 >= 1) 466 | if (out_prev(i-1,j,k) >= out_prev(i,j,k)) 467 | candidates = [candidates, out_prev(i,j,k)]; 468 | else 469 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i-1,j,k))]; 470 | end 471 | end 472 | if (i+1 <= size(out_prev,1)) 473 | if (out_prev(i+1,j,k) <= out_prev(i,j,k)) 474 | candidates = [candidates, out_prev(i,j,k)]; 475 | else 476 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i+1,j,k))]; 477 | end 478 | end 479 | end 480 | 481 | if (y_increasing) 482 | if (j-1 >= 1) 483 | if (out_prev(i,j-1,k) <= out_prev(i,j,k)) 484 | candidates = [candidates, out_prev(i,j,k)]; 485 | else 486 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i,j-1,k))]; 487 | end 488 | end 489 | if (j+1 <= size(out_prev,2)) 490 | if (out_prev(i,j+1,k) >= out_prev(i,j,k)) 491 | candidates = [candidates, out_prev(i,j,k)]; 492 | else 493 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i,j+1,k))]; 494 | end 495 | end 496 | else 497 | if (j-1 >= 1) 498 | if (out_prev(i,j-1,k) >= out_prev(i,j,k)) 499 | candidates = [candidates, out_prev(i,j,k)]; 500 | else 501 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i,j-1,k))]; 502 | end 503 | end 504 | if (j+1 <= size(out_prev,2)) 505 | if (out_prev(i,j+1,k) <= out_prev(i,j,k)) 506 | candidates = [candidates, out_prev(i,j,k)]; 507 | else 508 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i,j+1,k))]; 509 | end 510 | end 511 | end 512 | 513 | if (z_increasing) 514 | if (k-1 >= 1) 515 | if (out_prev(i,j,k-1) <= out_prev(i,j,k)) 516 | candidates = [candidates, out_prev(i,j,k)]; 517 | else 518 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i,j,k-1))]; 519 | end 520 | end 521 | if (k+1 <= size(out_prev,3)) 522 | if (out_prev(i,j,k+1) >= out_prev(i,j,k)) 523 | candidates = [candidates, out_prev(i,j,k)]; 524 | else 525 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i,j,k+1))]; 526 | end 527 | end 528 | else 529 | if (k-1 >= 1) 530 | if (out_prev(i,j,k-1) >= out_prev(i,j,k)) 531 | candidates = [candidates, out_prev(i,j,k)]; 532 | else 533 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i,j,k-1))]; 534 | end 535 | end 536 | if (k+1 <= size(out_prev,3)) 537 | if (out_prev(i,j,k+1) <= out_prev(i,j,k)) 538 | candidates = [candidates, out_prev(i,j,k)]; 539 | else 540 | candidates = [candidates, 0.5*(out_prev(i,j,k)+out_prev(i,j,k+1))]; 541 | end 542 | end 543 | end 544 | 545 | out(i,j,k) = mean(candidates); 546 | end 547 | end 548 | end 549 | 550 | 551 | % Check if monotonicity is enforced for every value 552 | 553 | completed = true; 554 | for i = 1:size(out,1) 555 | if (~completed) 556 | break; 557 | end 558 | for j = 1:size(out,2) 559 | if (~completed) 560 | break; 561 | end 562 | for k = 1:size(out,3) 563 | if (~completed) 564 | break; 565 | end 566 | 567 | if (x_increasing) 568 | if (out(max(1,i-1),j,k) > out(i,j,k)+thr) 569 | completed = false; 570 | break; 571 | end 572 | if (out(min(size(out,1),i+1),j,k) < out(i,j,k)-thr) 573 | completed = false; 574 | break; 575 | end 576 | else 577 | if (out(max(1,i-1),j,k) < out(i,j,k)-thr) 578 | completed = false; 579 | break; 580 | end 581 | if (out(min(size(out,1),i+1),j,k) > out(i,j,k)+thr) 582 | completed = false; 583 | break; 584 | end 585 | end 586 | 587 | if (y_increasing) 588 | if (out(i,max(1,j-1),k) > out(i,j,k)+thr) 589 | completed = false; 590 | break; 591 | end 592 | if (out(i,min(size(out,2),j+1),k) < out(i,j,k)-thr) 593 | completed = false; 594 | break; 595 | end 596 | else 597 | if (out(i,max(1,j-1),k) < out(i,j,k)-thr) 598 | completed = false; 599 | break; 600 | end 601 | if (out(i,min(size(out,2),j+1),k) > out(i,j,k)+thr) 602 | completed = false; 603 | break; 604 | end 605 | end 606 | 607 | if (z_increasing) 608 | if (out(i,j,max(1,k-1)) > out(i,j,k)+thr) 609 | completed = false; 610 | break; 611 | end 612 | if (out(i,j,min(size(out,3),k+1)) < out(i,j,k)-thr) 613 | completed = false; 614 | break; 615 | end 616 | else 617 | if (out(i,j,max(1,k-1)) < out(i,j,k)-thr) 618 | completed = false; 619 | break; 620 | end 621 | if (out(i,j,min(size(out,3),k+1)) > out(i,j,k)+thr) 622 | completed = false; 623 | break; 624 | end 625 | end 626 | 627 | end 628 | end 629 | end 630 | 631 | 632 | 633 | 634 | if (completed) 635 | it 636 | break; 637 | end 638 | 639 | 640 | 641 | 642 | end 643 | 644 | end 645 | 646 | 647 | function [out] = TrilinearInterpolation(angle, reproj, n_cam, uncertainty) 648 | 649 | if (reproj > max(uncertainty.reproj_j(2,:))) 650 | out = 1; 651 | return; 652 | end 653 | 654 | angle_i = mean(uncertainty.angle_i); 655 | reproj_j = mean(uncertainty.reproj_j); 656 | camera_k = uncertainty.camera_k; 657 | 658 | [angle_lb, i_lb] = min(angle_i); 659 | [angle_ub, i_ub] = max(angle_i); 660 | for i = 1:length(angle_i) 661 | angle_candidate = angle_i(i); 662 | if (angle-angle_candidate >= 0 && angle_candidate > angle_lb) 663 | angle_lb = angle_candidate; 664 | i_lb = i; 665 | end 666 | if (angle-angle_candidate <= 0 && angle_candidate < angle_ub) 667 | angle_ub = angle_candidate; 668 | i_ub = i; 669 | end 670 | end 671 | 672 | [reproj_lb, j_lb] = min(reproj_j); 673 | [reproj_ub, j_ub] = max(reproj_j); 674 | for j = 1:length(reproj_j) 675 | reproj_candidate = reproj_j(j); 676 | if (reproj-reproj_candidate >= 0 && reproj_candidate > reproj_lb) 677 | reproj_lb = reproj_candidate; 678 | j_lb = j; 679 | end 680 | if (reproj-reproj_candidate <= 0 && reproj_candidate < reproj_ub) 681 | reproj_ub = reproj_candidate; 682 | j_ub = j; 683 | end 684 | end 685 | 686 | [n_cam_lb, k_lb] = min(camera_k); 687 | [n_cam_ub, k_ub] = max(camera_k); 688 | for k = 1:length(camera_k) 689 | n_cam_candidate = camera_k(k); 690 | if (n_cam-n_cam_candidate >= 0 && n_cam_candidate > n_cam_lb) 691 | n_cam_lb = n_cam_candidate; 692 | k_lb = k; 693 | end 694 | if (n_cam-n_cam_candidate <= 0 && n_cam_candidate < n_cam_ub) 695 | n_cam_ub = n_cam_candidate; 696 | k_ub = k; 697 | end 698 | end 699 | 700 | 701 | if (angle_ub == angle_lb) 702 | x_d = 0; 703 | else 704 | x_d = (angle-angle_lb)/(angle_ub-angle_lb); 705 | end 706 | if (reproj_ub == reproj_lb) 707 | y_d = 0; 708 | else 709 | y_d = (reproj-reproj_lb)/(reproj_ub-reproj_lb); 710 | end 711 | if (n_cam_ub == n_cam_lb) 712 | z_d = 0; 713 | else 714 | z_d = (n_cam-n_cam_lb)/(n_cam_ub-n_cam_lb); 715 | end 716 | 717 | c_000 = uncertainty.result(i_lb,j_lb,k_lb); 718 | c_001 = uncertainty.result(i_lb,j_lb,k_ub); 719 | c_010 = uncertainty.result(i_lb,j_ub,k_lb); 720 | c_011 = uncertainty.result(i_lb,j_ub,k_ub); 721 | c_100 = uncertainty.result(i_ub,j_lb,k_lb); 722 | c_101 = uncertainty.result(i_ub,j_lb,k_ub); 723 | c_110 = uncertainty.result(i_ub,j_ub,k_lb); 724 | c_111 = uncertainty.result(i_ub,j_ub,k_ub); 725 | 726 | c_00 = c_000*(1-x_d)+c_100*x_d; 727 | c_01 = c_001*(1-x_d)+c_101*x_d; 728 | c_10 = c_010*(1-x_d)+c_110*x_d; 729 | c_11 = c_011*(1-x_d)+c_111*x_d; 730 | 731 | c_0 = c_00*(1-y_d)+c_10*y_d; 732 | c_1 = c_01*(1-y_d)+c_11*y_d; 733 | 734 | out = c_0*(1-z_d)+c_1*z_d; 735 | 736 | % disp(['angle = ', num2str(angle), ', lb = ', num2str(angle_lb), ', ub = ', num2str(angle_ub), ' angle(i_lb) = ', num2str(angle_i(i_lb)), ', angle(i_ub) = ', num2str(angle_i(i_ub))]) 737 | % disp(['reproj = ', num2str(reproj), ', lb = ', num2str(reproj_lb), ', ub = ', num2str(reproj_ub), ' reproj(j_lb) = ', num2str(reproj_j(j_lb)), ', reproj(j_ub) = ', num2str(reproj_j(j_ub))]) 738 | % disp(['n_cam = ', num2str(n_cam), ', lb = ', num2str(n_cam_lb), ', ub = ', num2str(n_cam_ub), ' camera_k(k_lb) = ', num2str(camera_k(k_lb)), ', camera_k(k_ub) = ', num2str(camera_k(k_ub))]) 739 | 740 | 741 | end -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # RobustUncertaintyAwareMultiviewTriangulation 2 | MATLAB implementation of our multiview triangulation method proposed in "Robust Uncertainty-Aware Multiview Triangulation" ([arXiv](https://arxiv.org/abs/2008.01258)). 3 | 4 | #### Instruction to run the triangulation code: 5 | 6 | 1. Download the 3D uncertainty grid (learned from the simulations): [uncertainty.mat](https://github.com/sunghoon031/RobustUncertaintyAwareMultiviewTriangulation/blob/master/uncertainty.mat). 7 | 2. In the same folder, download the [script](https://github.com/sunghoon031/RobustUncertaintyAwareMultiviewTriangulation/blob/master/RobustUncertaintyAwareMultiviewTriangulation_ReleaseCode.m). 8 | 3. Run the script on Matlab. 9 | 10 | #### Instruction to run the uncertainty generation code: 11 | 12 | 1. Open GenerateUncertaintyData.m 13 | 2. Set `load_precomputed_results = false;` 14 | 3. Set `n_simulations` to the number of simulations you want to run for each number of cameras in `n_cameras`. 15 | 4. Run. If you use the default `n_simulations`, it will take a very long time to finish (possibly, more than a few days)... 16 | 5. This will create two files, `uncertainty.mat` and `results_inliers.mat`. **Caution: this will overwrite the original `uncertainty.mat`! Make sure you rename the filename if you want to avoid this!** 17 | 6. Set `load_precomputed_results = true;` and run. Then it will plot some of the results. 18 | -------------------------------------------------------------------------------- /RobustUncertaintyAwareMultiviewTriangulation_ReleaseCode.m: -------------------------------------------------------------------------------- 1 | clc; 2 | 3 | %% Load the 3D uncertainty grid 4 | load uncertainty.mat; 5 | 6 | %% World point to be triangulated 7 | dist = 2+rand(1)*8; % between 2 and 10 unit 8 | point_w = [0;0;dist]; 9 | 10 | %% Set up the cameras (50 cameras with inlying measurements + 50 cameras with outlying measurements) 11 | focal_length = 525; 12 | img_width = 640; 13 | img_height = 480; 14 | 15 | noise_level = 3; % pixel (Gaussian noise level) 16 | outlier_min_noise = 10; % pixel (Outliers contain noise greater than this) 17 | 18 | n_inliers = 50; 19 | n_outliers = 50; 20 | n_cameras = n_inliers + n_outliers; 21 | 22 | [R, t, K, uv_measured] = SimulateCameras(point_w, n_inliers, n_cameras, img_width, img_height, focal_length, noise_level, outlier_min_noise); 23 | 24 | %% Triangulate the point using our method. 25 | 26 | % Precomputation indepndent of the point 27 | tic; 28 | [cam_pos, P, A, M3, M4, M5] = Precompute(n_cameras, K, R, t); 29 | time_precompute = toc; 30 | 31 | % Gauss-Newton optimization: 32 | tic; 33 | [x_gn, uncertainty_3D_gn] = RunMultiviewTriangulation('GN', uncertainty, cam_pos, R,P,K,uv_measured,A, M3, M4, M5); 34 | time_gn = toc; 35 | 36 | % DLT optimization: 37 | tic; 38 | [x_dlt, uncertainty_3D_dlt] = RunMultiviewTriangulation('DLT', uncertainty, cam_pos, R,P,K,uv_measured,A, M3, M4, M5); 39 | time_dlt = toc; 40 | 41 | 42 | %% Evaluate the performance 43 | 44 | error_2D_gn = GetMean2DErrorOfTrueInliers(x_gn, n_cameras, n_inliers, K, P, uv_measured); 45 | error_2D_dlt = GetMean2DErrorOfTrueInliers(x_dlt, n_cameras, n_inliers, K, P, uv_measured); 46 | 47 | error_3D_gn = norm(x_gn-point_w); 48 | error_3D_dlt = norm(x_dlt-point_w); 49 | 50 | disp(['Point distance = ', num2str(dist), ' unit (1 unit = geometric span of the cameras).']) 51 | disp(['Number of cameras = ', num2str(n_cameras), ', Outlier ratio = ', num2str(n_outliers/n_cameras*100), '%.']) 52 | disp(['Precomputation took ', num2str(time_precompute*1000), ' ms.']) 53 | disp(['GN optimization: 2D error = ', num2str(error_2D_gn), ' pix, 3D error = ', num2str(error_3D_gn), ' unit, uncertainty = ', num2str(uncertainty_3D_gn), ', took ', num2str(time_gn*1000), ' ms.']) 54 | disp(['DLT optimization: 2D error = ', num2str(error_2D_dlt), ' pix, 3D error = ', num2str(error_3D_dlt), ' unit, uncertainty = ', num2str(uncertainty_3D_dlt), ', took ', num2str(time_dlt*1000), ' ms.']) 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | %% Function definitions 63 | 64 | function R = RandomRotation(max_angle_rad) 65 | 66 | unit_axis = rand(3,1)-0.5; 67 | unit_axis = unit_axis/norm(unit_axis); 68 | angle = rand*max_angle_rad; 69 | R = RotationFromUnitAxisAngle(unit_axis, angle); 70 | 71 | end 72 | 73 | function R = RotationFromUnitAxisAngle(unit_axis, angle) 74 | 75 | if (angle==0) 76 | R = eye(3); 77 | else 78 | so3 = SkewSymmetricMatrix(unit_axis); 79 | R = eye(3)+so3*sin(angle)+so3^2*(1-cos(angle)); 80 | end 81 | end 82 | 83 | 84 | function out = SkewSymmetricMatrix(in) 85 | out=[0 -in(3) in(2) ; in(3) 0 -in(1) ; -in(2) in(1) 0 ]; 86 | end 87 | 88 | function [R, t, K, uv_measured] = SimulateCameras(point_w, n_inlier, n_cameras, img_width, img_height, focal_length, noise_level, outlier_min_noise) 89 | 90 | K_cam = [focal_length 0 0; 0 focal_length 0; 0 0 1]; 91 | 92 | 93 | R = cell(1,n_cameras); 94 | t = cell(1,n_cameras); 95 | K = cell(1,n_cameras); 96 | uv_measured = cell(1,n_cameras); 97 | 98 | for i = 1:n_cameras 99 | 100 | K{i} = K_cam; 101 | 102 | % Camera is located randomly inside a unit sphere. 103 | cam_pos = rand(3,1)-0.5; 104 | cam_pos = rand(1)*0.5*cam_pos/norm(cam_pos); 105 | 106 | % The first two cameras are antipodal. 107 | if (i==1) 108 | cam_pos = rand(3,1)-0.5; 109 | cam_pos = 0.5*cam_pos/norm(cam_pos); 110 | elseif (i==2) 111 | cam_pos = -cam_pos; 112 | end 113 | 114 | while(true) 115 | R_temp = RandomRotation(pi); 116 | t_temp = -R_temp*cam_pos; 117 | 118 | point_c = R_temp*point_w+t_temp; 119 | uv = K{i}*[point_c(1)/point_c(3); point_c(2)/point_c(3);1]; 120 | uv = uv(1:2); 121 | if (abs(uv(1)) > img_width/2 || abs(uv(2)) > img_height/2 || point_c(3) < 0) 122 | continue; 123 | end 124 | 125 | if (i <= n_inlier) 126 | while(true) 127 | noise_dir = rand(2,1)-0.5; 128 | noise_dir = noise_dir/norm(noise_dir); 129 | uv_with_noise = uv+normrnd(0, noise_level)*noise_dir; 130 | if (abs(uv_with_noise(1)) > img_width/2 || abs(uv_with_noise(2)) > img_height/2) 131 | continue; 132 | end 133 | break; 134 | end 135 | else 136 | while(true) 137 | uv_with_noise = [img_width*(rand(1)-0.5); img_height*(rand(1)-0.5)]; 138 | noise_magnitude = norm(uv-uv_with_noise); 139 | if (noise_magnitude < outlier_min_noise) 140 | continue; 141 | end 142 | break; 143 | end 144 | end 145 | 146 | break; 147 | end 148 | 149 | R{i} = R_temp; 150 | t{i} = t_temp; 151 | uv_measured{i} = uv_with_noise; 152 | end 153 | end 154 | 155 | 156 | function [cam_pos, P, A, M3, M4, M5] = Precompute(n_cameras, K, R, t) 157 | 158 | 159 | cam_pos = cell(1,n_cameras); 160 | P = cell(1,n_cameras); 161 | A = cell(1,n_cameras); % necessary for computing the Jacobian 162 | M3 = nan(4,n_cameras); 163 | M4 = nan(4,n_cameras); 164 | M5 = nan(4,n_cameras); 165 | 166 | for i = 1:n_cameras 167 | r11 = R{i}(1,1); r12 = R{i}(1,2); r13 = R{i}(1,3); 168 | r21 = R{i}(2,1); r22 = R{i}(2,2); r23 = R{i}(2,3); 169 | r31 = R{i}(3,1); r32 = R{i}(3,2); r33 = R{i}(3,3); 170 | tx = t{i}(1); ty = t{i}(2); tz = t{i}(3); 171 | k11 = K{i}(1,1); k12 = K{i}(1,2); k21 = K{i}(2,1); k22 = K{i}(2,2); 172 | 173 | b1 = r11*[0;r32;r33;tz]-r31*[0;r12;r13;tx]; 174 | b2 = r21*[0;r32;r33;tz]-r31*[0;r22;r23;ty]; 175 | b3 = r12*[r31;0;r33;tz]-r32*[r11;0;r13;tx]; 176 | b4 = r22*[r31;0;r33;tz]-r32*[r21;0;r23;ty]; 177 | b5 = r13*[r31;r32;0;tz]-r33*[r11;r12;0;tx]; 178 | b6 = r23*[r31;r32;0;tz]-r33*[r21;r22;0;ty]; 179 | a1 = k11*b1+k12*b2; 180 | a2 = k21*b1+k22*b2; 181 | a3 = k11*b3+k12*b4; 182 | a4 = k21*b3+k22*b4; 183 | a5 = k11*b5+k12*b6; 184 | a6 = k21*b5+k22*b6; 185 | A{i} = [a1,a2,a3,a4,a5,a6]; 186 | 187 | cam_pos{i} = -R{i}'*t{i}; 188 | P{i} = [R{i}, t{i}]; 189 | 190 | M3(:,i) = K{i}(1,1)*P{i}(1,:)'+K{i}(1,2)*P{i}(2,:)'; 191 | M4(:,i) = K{i}(2,1)*P{i}(1,:)'+K{i}(2,2)*P{i}(2,:)'; 192 | M5(:,i) = P{i}(3,:)'; 193 | end 194 | 195 | end 196 | 197 | 198 | 199 | function [output_pairs] = GetSamplePairs(input_vec, max_n_samples, bool_random_forced) 200 | n_sample = length(input_vec); 201 | possible_n_pairs = n_sample*(n_sample-1)/2; 202 | if(~bool_random_forced && possible_n_pairs <= max_n_samples) 203 | output_pairs = zeros(2,possible_n_pairs); 204 | c = 0; 205 | for i = input_vec 206 | for j = input_vec 207 | if (i<=j) 208 | continue; 209 | end 210 | c = c + 1; 211 | output_pairs(:,c) = [i,j]; 212 | end 213 | end 214 | else 215 | max_n_samples = min(max_n_samples, possible_n_pairs); 216 | output_pairs = zeros(2,max_n_samples); 217 | idx_shuffled = input_vec(randperm(n_sample)); 218 | c = 0; 219 | gap = 1; 220 | sample1_idx = 0; 221 | while (c n_sample || sample2_idx > n_sample) 225 | sample1_idx = 0; 226 | gap = gap + 1; 227 | continue; 228 | end 229 | sample1 = idx_shuffled(sample1_idx); 230 | sample2 = idx_shuffled(sample2_idx); 231 | c = c + 1; 232 | output_pairs(:,c) = [sample1,sample2]; 233 | end 234 | end 235 | end 236 | 237 | function error_2D = GetMean2DErrorOfTrueInliers(x, n_cameras, n_inlier, K, P, uv_measured) 238 | 239 | M1 = nan(1,n_cameras); 240 | M2 = nan(1,n_cameras); 241 | M3 = nan(4,n_cameras); 242 | M4 = nan(4,n_cameras); 243 | M5 = nan(4,n_cameras); 244 | for i = 1:n_cameras 245 | M1(1,i) = K{i}(1,3)-uv_measured{i}(1); 246 | M2(1,i) = K{i}(2,3)-uv_measured{i}(2); 247 | M3(:,i) = K{i}(1,1)*P{i}(1,:)'+K{i}(1,2)*P{i}(2,:)'; 248 | M4(:,i) = K{i}(2,1)*P{i}(1,:)'+K{i}(2,2)*P{i}(2,:)'; 249 | M5(:,i) = P{i}(3,:)'; 250 | end 251 | 252 | M6 = [x;1]'*M5; 253 | M7 = M1+([x;1]'*M3)./M6; 254 | M8 = M2+([x;1]'*M4)./M6; 255 | squared_reproj_error_all = M7.*M7+M8.*M8; 256 | 257 | error_2D = 0; 258 | c = 0; 259 | for i = 1:n_inlier 260 | if (M6(i) <= 0) 261 | continue; 262 | end 263 | error_2D = error_2D + sqrt(squared_reproj_error_all(i)); 264 | c = c + 1; 265 | end 266 | error_2D = error_2D/c; 267 | 268 | if (error_2D == 0) 269 | error_2D = nan; 270 | end 271 | end 272 | 273 | function error_2D = GetMean2DErrorOfEstimatedInliers(x, M1, M2, M3, M4, M5, idx_inlier) 274 | M6 = [x;1]'*M5; 275 | M7 = M1+([x;1]'*M3)./M6; 276 | M8 = M2+([x;1]'*M4)./M6; 277 | squared_reproj_error_all = M7.*M7+M8.*M8; 278 | 279 | error_2D = 0; 280 | c = 0; 281 | for i = idx_inlier 282 | if (M6(i) <= 0) 283 | continue; 284 | end 285 | error_2D = error_2D + sqrt(squared_reproj_error_all(i)); 286 | c = c + 1; 287 | end 288 | error_2D = error_2D/c; 289 | 290 | if (error_2D == 0) 291 | error_2D = nan; 292 | end 293 | end 294 | 295 | 296 | function [min_level_of_degeneracy] = GetMinLevelOfDegeneracy(cam_pos, ray_w, K, uv_measured, R, idx, n_sample_mLoD) 297 | 298 | min_level_of_degeneracy = inf; 299 | idx = reshape(idx, [1, numel(idx)]); 300 | 301 | sample_pairs = GetSamplePairs(idx, n_sample_mLoD, false); 302 | 303 | for k = 1:size(sample_pairs,2) 304 | i = sample_pairs(1,k); 305 | j = sample_pairs(2,k); 306 | 307 | ray_i = ray_w(:,i); 308 | if (ray_i(1)==0 && ray_i(2)==0 && ray_i(3)==0) 309 | ray_i = K{i}\[uv_measured{i};1]; 310 | ray_i = ray_i/norm(ray_i); 311 | ray_i = R{i}'*ray_i; 312 | ray_w(:,i) = ray_i; 313 | end 314 | 315 | ray_j = ray_w(:,j); 316 | if (ray_j(1)==0 && ray_j(2)==0 && ray_j(3)==0) 317 | ray_j = K{j}\[uv_measured{j};1]; 318 | ray_j = ray_j/norm(ray_j); 319 | ray_j = R{j}'*ray_j; 320 | ray_w(:,j) = ray_j; 321 | end 322 | 323 | t_ij = cam_pos{i}-cam_pos{j}; 324 | t_ij = t_ij/norm(t_ij); 325 | f_i = ray_i; 326 | f_j = ray_j; 327 | 328 | level_of_degeneracy = max(abs([t_ij'*f_i, t_ij'*f_j, f_i'*f_j])); 329 | 330 | if (level_of_degeneracy < min_level_of_degeneracy) 331 | min_level_of_degeneracy = level_of_degeneracy; 332 | end 333 | end 334 | 335 | end 336 | 337 | 338 | 339 | function [x_est, idx_consensus, max_n_consensus, min_cost, k_max, ray_w] = TwoViewRansac(j, k, x_est, idx_consensus, max_n_consensus, min_cost, k_max, confidence, n_cameras, epipolar_thr, cos_angle_thr, reproj_thr, M1, M2, M3, M4, M5, K, R, P, cam_pos, uv_measured,ray_w) 340 | 341 | ray_j = ray_w(:,j); 342 | if (ray_j(1)==0 && ray_j(2)==0 && ray_j(3)==0) 343 | ray_j = K{j}\[uv_measured{j};1]; 344 | ray_j = ray_j/norm(ray_j); 345 | ray_j = R{j}'*ray_j; 346 | 347 | ray_w(:,j) = ray_j; 348 | end 349 | 350 | ray_k = ray_w(:,k); 351 | if (ray_k(1)==0 && ray_k(2)==0 && ray_k(3)==0) 352 | ray_k = K{k}\[uv_measured{k};1]; 353 | ray_k = ray_k/norm(ray_k); 354 | ray_k = R{k}'*ray_k; 355 | 356 | ray_w(:,k) = ray_k; 357 | end 358 | 359 | 360 | 361 | 362 | % Epipolar error should be below threshold 363 | t_jk = cam_pos{j}-cam_pos{k}; 364 | t_norm = norm(t_jk); 365 | t_jk = t_jk/t_norm; 366 | cross_fj_fk = [... 367 | ray_j(2)*ray_k(3)-ray_j(3)*ray_k(2);... 368 | ray_j(3)*ray_k(1)-ray_j(1)*ray_k(3);... 369 | ray_j(1)*ray_k(2)-ray_j(2)*ray_k(1)]; 370 | e_epipolar = abs(t_jk'*cross_fj_fk); 371 | 372 | if (e_epipolar > epipolar_thr) 373 | return; 374 | end 375 | 376 | % Parallax must be below 90 deg, above threshold. 377 | p_jk = ray_j'*ray_k; 378 | if (p_jk < 0 || p_jk > cos_angle_thr) 379 | %disp(['Skip I:' num2str(i), ', ', num2str(j)]) 380 | return; 381 | end 382 | 383 | % Point must be far from the epipoles 384 | q_jk = t_jk'*ray_j; 385 | r_jk = t_jk'*ray_k; 386 | if (abs(q_jk) > cos_angle_thr || abs(r_jk) > cos_angle_thr) 387 | %disp(['Skip II:' num2str(i), ', ', num2str(j)]) 388 | return; 389 | end 390 | 391 | % Midpoint should satisfy the cheirality. 392 | tau_i = p_jk*r_jk-q_jk; 393 | tau_j = -p_jk*q_jk+r_jk; 394 | if (tau_i < 0 || tau_j < 0) 395 | %disp(['Skip III:' num2str(i), ', ', num2str(j)]) 396 | return; 397 | end 398 | 399 | % Obtain the midpoint. 400 | s_jk = t_norm/(1-p_jk'*p_jk); 401 | lambda_j = s_jk*tau_i; 402 | lambda_k = s_jk*tau_j; 403 | x_anchor_j = cam_pos{j}+lambda_j*ray_j; 404 | x_anchor_k= cam_pos{k}+lambda_k*ray_k; 405 | x_mid = 0.5*(x_anchor_j+x_anchor_k); 406 | 407 | 408 | % Cheirality 409 | 410 | x_j = P{j}*[x_mid;1]; 411 | x_k = P{k}*[x_mid;1]; 412 | 413 | if (x_j(3) < 0 || x_k(3) < 0) 414 | %disp(['Skip III:' num2str(i), ', ', num2str(j)]) 415 | return; 416 | end 417 | 418 | % Small reprojection error 419 | u_j = uv_measured{j}(1); v_j = uv_measured{j}(2); 420 | u_k = uv_measured{k}(1); v_k = uv_measured{k}(2); 421 | 422 | uv_reproj_j = K{j}*x_j/x_j(3); 423 | uv_error_j = [u_j;v_j;1]-uv_reproj_j; 424 | reproj_error_j = uv_error_j'*uv_error_j; 425 | if (reproj_error_j > reproj_thr) 426 | return; 427 | end 428 | 429 | uv_reproj_k = K{k}*x_k/x_k(3); 430 | uv_error_k = [u_k;v_k;1]-uv_reproj_k; 431 | reproj_error_k = uv_error_k'*uv_error_k; 432 | if (reproj_error_k > reproj_thr) 433 | return; 434 | end 435 | 436 | % Count the consensus. 437 | M6 = [x_mid;1]'*M5; 438 | M7 = M1 + ([x_mid;1]'*M3)./M6; 439 | M8 = M2 + ([x_mid;1]'*M4)./M6; 440 | squared_reproj_error_all = M7.*M7+M8.*M8; 441 | squared_reproj_error_all(M6<=0) = inf; 442 | 443 | cost = 0; 444 | for ii = 1:length(squared_reproj_error_all) 445 | cost = cost + min(squared_reproj_error_all(ii), reproj_thr); 446 | end 447 | 448 | bool_consensus = squared_reproj_error_all 0; 539 | 540 | if (bool_consensus_changed) 541 | c = 0; 542 | else 543 | c = c +1; 544 | end 545 | 546 | if (sum(bool_consensus) < 2) 547 | break; 548 | end 549 | 550 | if (c == 2 && abs(mean_reproj_error-mean_reproj_error_prev) < 0.1) 551 | break; 552 | end 553 | 554 | residuals_new = []; 555 | J_est = []; 556 | 557 | for i = 1:n_cameras 558 | if (bool_consensus(i)) 559 | residuals_new = [residuals_new; residuals(:,i)]; 560 | 561 | J_temp = A{i}'*[x_gn;1]; 562 | J_temp = reshape(J_temp, [2,3])/((P{i}(3,:)*[x_gn;1])^2); 563 | J_est = [J_est; J_temp]; 564 | end 565 | end 566 | 567 | update = -pinv(J_est)*residuals_new; 568 | 569 | x_gn = x_gn+update; 570 | 571 | end 572 | 573 | x_est = x_gn; 574 | idx_consensus = find(bool_consensus); 575 | max_n_consensus = sum(bool_consensus); 576 | end 577 | 578 | function [out] = TrilinearInterpolation(angle, reproj, n_cam, uncertainty) 579 | 580 | if (reproj > max(uncertainty.reproj_j(2,:))) 581 | out = 1; 582 | return; 583 | end 584 | 585 | angle_i = mean(uncertainty.angle_i); 586 | reproj_j = mean(uncertainty.reproj_j); 587 | camera_k = uncertainty.camera_k; 588 | 589 | [angle_lb, i_lb] = min(angle_i); 590 | [angle_ub, i_ub] = max(angle_i); 591 | for i = 1:length(angle_i) 592 | angle_candidate = angle_i(i); 593 | if (angle-angle_candidate >= 0 && angle_candidate > angle_lb) 594 | angle_lb = angle_candidate; 595 | i_lb = i; 596 | end 597 | if (angle-angle_candidate <= 0 && angle_candidate < angle_ub) 598 | angle_ub = angle_candidate; 599 | i_ub = i; 600 | end 601 | end 602 | 603 | [reproj_lb, j_lb] = min(reproj_j); 604 | [reproj_ub, j_ub] = max(reproj_j); 605 | for j = 1:length(reproj_j) 606 | reproj_candidate = reproj_j(j); 607 | if (reproj-reproj_candidate >= 0 && reproj_candidate > reproj_lb) 608 | reproj_lb = reproj_candidate; 609 | j_lb = j; 610 | end 611 | if (reproj-reproj_candidate <= 0 && reproj_candidate < reproj_ub) 612 | reproj_ub = reproj_candidate; 613 | j_ub = j; 614 | end 615 | end 616 | 617 | [n_cam_lb, k_lb] = min(camera_k); 618 | [n_cam_ub, k_ub] = max(camera_k); 619 | for k = 1:length(camera_k) 620 | n_cam_candidate = camera_k(k); 621 | if (n_cam-n_cam_candidate >= 0 && n_cam_candidate > n_cam_lb) 622 | n_cam_lb = n_cam_candidate; 623 | k_lb = k; 624 | end 625 | if (n_cam-n_cam_candidate <= 0 && n_cam_candidate < n_cam_ub) 626 | n_cam_ub = n_cam_candidate; 627 | k_ub = k; 628 | end 629 | end 630 | 631 | 632 | if (angle_ub == angle_lb) 633 | x_d = 0; 634 | else 635 | x_d = (angle-angle_lb)/(angle_ub-angle_lb); 636 | end 637 | if (reproj_ub == reproj_lb) 638 | y_d = 0; 639 | else 640 | y_d = (reproj-reproj_lb)/(reproj_ub-reproj_lb); 641 | end 642 | if (n_cam_ub == n_cam_lb) 643 | z_d = 0; 644 | else 645 | z_d = (n_cam-n_cam_lb)/(n_cam_ub-n_cam_lb); 646 | end 647 | 648 | c_000 = uncertainty.result(i_lb,j_lb,k_lb); 649 | c_001 = uncertainty.result(i_lb,j_lb,k_ub); 650 | c_010 = uncertainty.result(i_lb,j_ub,k_lb); 651 | c_011 = uncertainty.result(i_lb,j_ub,k_ub); 652 | c_100 = uncertainty.result(i_ub,j_lb,k_lb); 653 | c_101 = uncertainty.result(i_ub,j_lb,k_ub); 654 | c_110 = uncertainty.result(i_ub,j_ub,k_lb); 655 | c_111 = uncertainty.result(i_ub,j_ub,k_ub); 656 | 657 | c_00 = c_000*(1-x_d)+c_100*x_d; 658 | c_01 = c_001*(1-x_d)+c_101*x_d; 659 | c_10 = c_010*(1-x_d)+c_110*x_d; 660 | c_11 = c_011*(1-x_d)+c_111*x_d; 661 | 662 | c_0 = c_00*(1-y_d)+c_10*y_d; 663 | c_1 = c_01*(1-y_d)+c_11*y_d; 664 | 665 | out = c_0*(1-z_d)+c_1*z_d; 666 | 667 | % disp(['angle = ', num2str(angle), ', lb = ', num2str(angle_lb), ', ub = ', num2str(angle_ub), ' angle(i_lb) = ', num2str(angle_i(i_lb)), ', angle(i_ub) = ', num2str(angle_i(i_ub))]) 668 | % disp(['reproj = ', num2str(reproj), ', lb = ', num2str(reproj_lb), ', ub = ', num2str(reproj_ub), ' reproj(j_lb) = ', num2str(reproj_j(j_lb)), ', reproj(j_ub) = ', num2str(reproj_j(j_ub))]) 669 | % disp(['n_cam = ', num2str(n_cam), ', lb = ', num2str(n_cam_lb), ', ub = ', num2str(n_cam_ub), ' camera_k(k_lb) = ', num2str(camera_k(k_lb)), ', camera_k(k_ub) = ', num2str(camera_k(k_ub))]) 670 | 671 | 672 | end 673 | 674 | 675 | 676 | 677 | 678 | function [x_est, uncertainty_3D] = RunMultiviewTriangulation(method, uncertainty, cam_pos, R,P,K,uv_measured,A, M3, M4, M5) 679 | 680 | %% 1. Initialize 681 | 682 | uncertainty_3D = nan; 683 | x_est = nan; 684 | idx_consensus = []; 685 | 686 | n_cameras = numel(cam_pos); 687 | 688 | % Construct matrix M1 and M2 689 | M1 = nan(1,n_cameras); 690 | M2 = nan(1,n_cameras); 691 | for i = 1:n_cameras 692 | M1(1,i) = K{i}(1,3)-uv_measured{i}(1); 693 | M2(1,i) = K{i}(2,3)-uv_measured{i}(2); 694 | end 695 | 696 | 697 | ray_w = zeros(3,n_cameras); 698 | 699 | 700 | 701 | %% 2. Run two-view RANSAC 702 | 703 | confidence = 0.99; 704 | cos_angle_thr = cosd(4); 705 | reproj_thr = 10^2; 706 | epipolar_thr = 0.01; 707 | 708 | n_sample = min(10000, n_cameras*(n_cameras-1)/2); 709 | n_sample_mLoD = 100; 710 | n_consensus_thr = 2; 711 | 712 | min_cost = inf; 713 | inlier_ratio_est = 3/n_cameras; 714 | k_max = log(1-confidence)/log(1-inlier_ratio_est^2); 715 | max_n_consensus = 0; 716 | 717 | sample_pairs = GetSamplePairs(1:n_cameras, inf, true); 718 | 719 | for k = 1:size(sample_pairs,2) 720 | if (k == n_sample) 721 | break; 722 | end 723 | if (k > k_max && max_n_consensus >= n_consensus_thr) 724 | break; 725 | end 726 | i = sample_pairs(1,k); 727 | j = sample_pairs(2,k); 728 | [x_est, idx_consensus, max_n_consensus, min_cost, k_max, ray_w] = TwoViewRansac(i, j, x_est, idx_consensus, max_n_consensus, min_cost, k_max, confidence, n_cameras, epipolar_thr, cos_angle_thr, reproj_thr, M1, M2, M3, M4, M5, K, R, P, cam_pos, uv_measured,ray_w); 729 | 730 | end 731 | 732 | if (max_n_consensus < n_consensus_thr) 733 | disp('Not enough inliers!') 734 | return; 735 | end 736 | 737 | 738 | %% 3. Refine the initial solution and the inlier set: 739 | switch method 740 | case 'GN' 741 | [x_est, idx_consensus, max_n_consensus] = GaussNewton(x_est, idx_consensus, A, P, n_cameras, reproj_thr, M1, M2, M3, M4, M5); 742 | case 'DLT' 743 | [x_est, idx_consensus, max_n_consensus] = DLT(x_est, idx_consensus, n_cameras, reproj_thr, M1, M2, M3, M4, M5, K, P, uv_measured); 744 | end 745 | 746 | %% 4. Estimate the 3D uncertainty: 747 | error_2D_estimated_inliers = GetMean2DErrorOfEstimatedInliers(x_est, M1, M2, M3, M4, M5, idx_consensus); 748 | mLoD_approx = GetMinLevelOfDegeneracy(cam_pos, ray_w, K, uv_measured, R, idx_consensus, n_sample_mLoD); 749 | uncertainty_3D = TrilinearInterpolation(acosd(mLoD_approx), error_2D_estimated_inliers, max_n_consensus, uncertainty); 750 | 751 | 752 | end 753 | -------------------------------------------------------------------------------- /uncertainty.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sunghoon031/RobustUncertaintyAwareMultiviewTriangulation/fbc437f0a6e59aaf42c50f541bf4a650fddcfba9/uncertainty.mat --------------------------------------------------------------------------------