├── AddToNewFamily.m ├── AlignRotationL1.m ├── AlignRotationL2.m ├── ChordalL1Mean.m ├── ClosestToChordalL1Mean.m ├── CreateSyntheticData.m ├── ExpMap.m ├── LICENSE ├── LocalOptimization.m ├── LogMap.m ├── ProjectOntoSO3.m ├── R2q.m ├── README.md ├── RandomRotation.m ├── RunHARA.m ├── RunHARA_usingNumberOfInlierMatches.m ├── SkewSymmetricMatrix.m ├── SortNonFamilyNeighbors.m ├── Test_HARA.m ├── UniformSampling.m └── q2R.m /AddToNewFamily.m: -------------------------------------------------------------------------------- 1 | function [newFamily, newFamily_nEdges] = AddToNewFamily(id_to_add, nEdges_of_id_to_add, newFamily, newFamily_nEdges) 2 | 3 | % Add to newFamily such that the one with fewer edges comes at the end. 4 | 5 | if (isempty(newFamily)) 6 | newFamily = id_to_add; 7 | newFamily_nEdges = nEdges_of_id_to_add; 8 | return; 9 | end 10 | 11 | if (nEdges_of_id_to_add <= newFamily_nEdges(end)) 12 | newFamily(end+1) = id_to_add; 13 | newFamily_nEdges(end+1) = nEdges_of_id_to_add; 14 | return; 15 | end 16 | 17 | newFamily_ = [newFamily 0]; 18 | newFamily_nEdges_ = [newFamily_nEdges 0]; 19 | 20 | for i = 1: length(newFamily) 21 | nE = newFamily_nEdges(i); 22 | if (nEdges_of_id_to_add >= nE) 23 | newFamily_(i) = id_to_add; 24 | newFamily_nEdges_(i) = nEdges_of_id_to_add; 25 | newFamily_(i+1:end) = newFamily(i:end); 26 | newFamily_nEdges_(i+1:end) = newFamily_nEdges(i:end); 27 | break; 28 | end 29 | end 30 | 31 | newFamily = newFamily_; 32 | newFamily_nEdges = newFamily_nEdges_; 33 | end -------------------------------------------------------------------------------- /AlignRotationL1.m: -------------------------------------------------------------------------------- 1 | function [R_geo1, errors, mean_error, rms_error] = AlignRotationL1(R_true, R_est) 2 | 3 | 4 | nViews = size(R_true,2); 5 | 6 | errors = zeros(1,nViews); 7 | R_transform = cell(1, nViews); 8 | 9 | for i = 1:nViews 10 | R_transform{i} = R_est{i}'*R_true{i}; 11 | end 12 | 13 | vectors_total = zeros(9,nViews); 14 | for i = 1:nViews 15 | vectors_total(:,i)= R_transform{i}(:); 16 | end 17 | med_vectors_total = median(vectors_total,2); 18 | [U,~,V] = svd(reshape(med_vectors_total, [3 3])); 19 | R_med = U*V.'; 20 | if (det(R_med) < 0) 21 | V(:,3) = -V(:,3); 22 | R_med = U*V.'; 23 | end 24 | 25 | R_geo1 = R_med; 26 | for j = 1:10 27 | step_num = 0; 28 | step_den = 0; 29 | for i = 1:nViews 30 | v = LogMap(R_transform{i}*R_geo1'); 31 | v_norm = norm(v); 32 | step_num = step_num + v/v_norm; 33 | step_den = step_den + 1/v_norm; 34 | end 35 | delta = step_num/step_den; 36 | delta_angle = norm(delta); 37 | 38 | delta_axis = delta/delta_angle; 39 | so3_delta = SkewSymmetricMatrix(delta_axis); 40 | R_delta = eye(3)+so3_delta*sin(delta_angle)+so3_delta^2*(1-cos(delta_angle)); 41 | R_geo1 = R_delta*R_geo1; 42 | end 43 | 44 | 45 | 46 | for i = 1:nViews 47 | error = abs(acosd((trace(R_true{i}*(R_est{i}*R_geo1)')-1)/2)); 48 | errors(i) = error; 49 | end 50 | mean_error = mean(errors); 51 | rms_error = sqrt(mean(errors.^2)); 52 | end -------------------------------------------------------------------------------- /AlignRotationL2.m: -------------------------------------------------------------------------------- 1 | function [R_geo2, mean_error, rms_error] = AlignRotationL2(R_true, R_est) 2 | 3 | nViews = size(R_true,2); 4 | errors = zeros(1,nViews); 5 | R_transform = cell(1, nViews); 6 | for i = 1:nViews 7 | R_transform{i} = R_est{i}'*R_true{i}; 8 | end 9 | 10 | R_sum = zeros(3,3); 11 | for i = 1:nViews 12 | R_sum = R_sum + R_transform{i}; 13 | end 14 | R_geo2 = ProjectOntoSO3(R_sum); 15 | 16 | for j = 1:10 17 | v = zeros(3,1); 18 | for i = 1:nViews 19 | v = v + LogMap(R_transform{i}*R_geo2'); 20 | end 21 | v = v/nViews; 22 | R_delta = ExpMap(v); 23 | R_geo2 = R_delta*R_geo2; 24 | end 25 | 26 | for i = 1:nViews 27 | error = abs(acosd((trace(R_true{i}*(R_est{i}*R_geo2)')-1)/2)); 28 | errors(i) = error; 29 | end 30 | 31 | mean_error = mean(errors); 32 | rms_error = sqrt(mean(errors.^2)); 33 | end -------------------------------------------------------------------------------- /ChordalL1Mean.m: -------------------------------------------------------------------------------- 1 | function R = ChordalL1Mean(R_input, b_outlier_rejection, n_iterations, thr_convergence) 2 | % https://github.com/sunghoon031/RobustSingleRotationAveraging 3 | 4 | % 1. Initialize 5 | n_samples = length(R_input); 6 | 7 | vectors_total = zeros(9,n_samples); 8 | for i = 1:n_samples 9 | vectors_total(:,i)= R_input{i}(:); 10 | end 11 | 12 | 13 | s = median(vectors_total,2); 14 | 15 | 16 | % 2. Optimize 17 | for j = 1:n_iterations 18 | if (sum(sum(abs(vectors_total-repmat(s,1,n_samples)))==0) ~= 0) 19 | s = s+rand(size(s,1),1)*0.001; 20 | end 21 | 22 | v_norms = zeros(1,n_samples); 23 | for i = 1:n_samples 24 | v = vectors_total(:,i)-s; 25 | v_norm = norm(v); 26 | v_norms(i) = v_norm; 27 | end 28 | 29 | % Compute the inlier threshold (if we reject outliers). 30 | thr = inf; 31 | if (b_outlier_rejection) 32 | sorted_v_norms = sort(v_norms); 33 | v_norm_firstQ = sorted_v_norms(ceil(n_samples/4)); 34 | 35 | if (n_samples <= 50) 36 | thr = max(v_norm_firstQ, 1.356); 37 | % 2*sqrt(2)*sin(1/2) is approximately 1.356 38 | else 39 | thr = max(v_norm_firstQ, 0.7); 40 | % 2*sqrt(2)*sin(0.5/2) is approximately 0.7 41 | end 42 | end 43 | 44 | step_num = 0; 45 | step_den = 0; 46 | 47 | for i = 1:n_samples 48 | v_norm = v_norms(i); 49 | if (v_norm > thr) 50 | continue; 51 | end 52 | step_num = step_num + vectors_total(:,i)/v_norm; 53 | step_den = step_den + 1/v_norm; 54 | end 55 | 56 | 57 | s_prev = s; 58 | s = step_num/step_den; 59 | 60 | update_medvec = s-s_prev; 61 | if (norm(update_medvec) < thr_convergence) 62 | break; 63 | end 64 | 65 | end 66 | 67 | R = ProjectOntoSO3(reshape(s, [3 3])); 68 | 69 | end -------------------------------------------------------------------------------- /ClosestToChordalL1Mean.m: -------------------------------------------------------------------------------- 1 | function R = ClosestToChordalL1Mean(R_input, b_outlier_rejection, n_iterations, thr_convergence) 2 | 3 | R_ = ChordalL1Mean(R_input, b_outlier_rejection, n_iterations, thr_convergence); 4 | 5 | min_err = inf; 6 | for i = 1:length(R_input) 7 | delta_R = R_-R_input{i}; 8 | err_sq = sum(sum(delta_R.^2)); 9 | 10 | if (err_sq < min_err) 11 | min_err = err_sq; 12 | R = R_input{i}; 13 | end 14 | end 15 | 16 | end -------------------------------------------------------------------------------- /CreateSyntheticData.m: -------------------------------------------------------------------------------- 1 | function [R_gt, edge_IDs, RR] = CreateSyntheticData(nViews, connectivity, outlier_ratio, inlier_noise_deg) 2 | 3 | 4 | % Input: 5 | % - nViews = Number of absolute rotations (views) we simulate. 6 | % - connectivity = Proportion of the established edges among all 7 | % pairs of views. 8 | % - outlier_ratio = Outlier ratio in the edges. 9 | % - inlier_noise_deg = Noise level in the inlier edges. 10 | % 11 | % Output: 12 | % - R_gt = Ground-truth absolute rotations. 13 | % - edge_IDs = Edges between views. 14 | % If an i-th edge is established between view j and k, 15 | % edge_IDs(:,i) = [j;k]. 16 | % - RR = Relative rotations for all edges. 17 | % If an i-th edge is established between view j and k, 18 | % RR(:,:,i) = Estimate of (R_j)*(R_k)^T. 19 | 20 | 21 | R_gt = cell(1, nViews); 22 | for i = 1:nViews 23 | R_gt{i} = RandomRotation(rand(1)*360); 24 | end 25 | 26 | nEdgesThr = round(connectivity*(nViews*(nViews-1)/2)); 27 | 28 | edge_IDs = []; 29 | RR = []; 30 | 31 | interval = 1; 32 | c = 0; 33 | while (true) 34 | 35 | for i = 1:nViews 36 | j = i + interval; 37 | if (j > nViews) 38 | j = j - nViews; 39 | end 40 | 41 | c = c + 1; 42 | 43 | edge_IDs(:,c) = [i;j]; 44 | RR(:,:,c) = R_gt{i}*R_gt{j}'*RandomRotation(normrnd(0, inlier_noise_deg)); 45 | 46 | 47 | if (size(edge_IDs,2) > nEdgesThr) 48 | break; 49 | end 50 | end 51 | 52 | if (size(edge_IDs,2) > nEdgesThr) 53 | break; 54 | end 55 | 56 | if (interval == 1) 57 | nSafeEdges = c; 58 | end 59 | 60 | interval = interval + 1; 61 | 62 | %disp(['Progress = ' num2str(size(edge_IDs,2)/nEdgesThr*100) '%']) 63 | end 64 | 65 | nEdges = size(edge_IDs,2); 66 | 67 | 68 | % Turn some of the edges into outliers 69 | nOutliersThr = round(outlier_ratio*nEdges); 70 | outlierIDs = []; 71 | 72 | while (true) 73 | 74 | i = randi(nEdges); 75 | 76 | if (i <= nSafeEdges) 77 | continue; 78 | end 79 | 80 | if (ismember(i, outlierIDs)) 81 | continue; 82 | end 83 | 84 | outlierIDs(end+1) = i; 85 | RR(:,:,i) = RandomRotation(rand(1)*360); 86 | 87 | if (length(outlierIDs) >= nOutliersThr) 88 | break; 89 | end 90 | end 91 | 92 | % Shuffle 93 | ii = randperm(nEdges); 94 | edge_IDs = edge_IDs(:,ii); 95 | RR = RR(:,:,ii); 96 | 97 | end -------------------------------------------------------------------------------- /ExpMap.m: -------------------------------------------------------------------------------- 1 | function out = ExpMap(in) 2 | angle = norm(in); 3 | if (angle == 0) 4 | out = eye(3); 5 | return; 6 | end 7 | axis = in/angle; 8 | so3 = SkewSymmetricMatrix(axis); 9 | R = eye(3)+so3*sin(angle)+so3^2*(1-cos(angle)); 10 | out = R; 11 | 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 | -------------------------------------------------------------------------------- /LocalOptimization.m: -------------------------------------------------------------------------------- 1 | function [R_est, time_iterations, iterations] = LocalOptimization(R_init, edge_IDs, RR, mode, nIterations) 2 | 3 | % For this part, I used Chatterjee's code as a reference: 4 | % https://ee.iisc.ac.in/labs/cvl/research/rotaveraging/ 5 | 6 | 7 | someVerySmallNumber = 1e-6; 8 | nEdges = size(edge_IDs, 2); 9 | nViews = length(R_init); 10 | 11 | % Fix the ambiguity (gauge freedom) by not updating the first view. 12 | nEntriesExceptAnchor = sum(sum(edge_IDs ~= 1)); 13 | row_A = zeros(1, nEntriesExceptAnchor); col_A = row_A; val_A = row_A; 14 | 15 | c = 0; 16 | for i = 1:nEdges 17 | j = edge_IDs(1,i)-1; 18 | k = edge_IDs(2,i)-1; 19 | 20 | if (j > 0) 21 | c = c + 1; 22 | row_A(c) = i; col_A(c) = j; val_A(c) = 1; %A(i, j) = 1 23 | end 24 | 25 | if (k > 0) 26 | c = c + 1; 27 | row_A(c) = i; col_A(c) = k; val_A(c) = -1; %A(i, k) = -1 28 | end 29 | end 30 | 31 | A = sparse(row_A, col_A, val_A); % [nEdges x (nViews-1)] 32 | 33 | w = ones(nEdges, 1); 34 | v = zeros(nViews, 3); % Update in terms of rotation vector. 35 | 36 | qjk_qk = zeros(4,nEdges); 37 | invOfqj_qjk_qk = zeros(4,nEdges); 38 | qjk_all = zeros(4,nEdges); 39 | for i = 1:nEdges 40 | qjk_all(:,i) = R2q(RR(:,:,i)); 41 | end 42 | q_all = zeros(4,nViews); 43 | for i = 1:nViews 44 | q_all(:,i) = R2q(R_init{i}); 45 | end 46 | q_all_updated = zeros(4,nViews); 47 | delta_q_all = zeros(4,nViews); 48 | 49 | js = edge_IDs(1,:); 50 | ks = edge_IDs(2,:); 51 | 52 | tIterations = tic; 53 | for it = 1:nIterations 54 | 55 | qjk_qk(1,:) = ... %scalar term of (q_jk)(q_k) 56 | qjk_all(1,:).*q_all(1,ks) - sum(qjk_all(2:4,:).*q_all(2:4,ks),1); 57 | 58 | qjk_qk(2:4,:) = ... % vector term of (q_jk)(q_k) 59 | qjk_all(1,:).*q_all(2:4,ks) + q_all(1,ks).*qjk_all(2:4,:) ... 60 | + [qjk_all(3,:).*q_all(4,ks) - qjk_all(4,:).*q_all(3,ks);... 61 | qjk_all(4,:).*q_all(2,ks) - qjk_all(2,:).*q_all(4,ks);... 62 | qjk_all(2,:).*q_all(3,ks) - qjk_all(3,:).*q_all(2,ks)]; 63 | 64 | invOfqj_qjk_qk(1,:) = ... %scalar term of inv(q_j)(q_jk)(q_k) 65 | -q_all(1,js).*qjk_qk(1,:) - sum(q_all(2:4,js).*qjk_qk(2:4,:),1); 66 | 67 | invOfqj_qjk_qk(2:4,:) = ... %vector term of inv(q_j)(q_jk)(q_k) 68 | -q_all(1,js).*qjk_qk(2:4,:) + qjk_qk(1,:).*q_all(2:4,js) ... 69 | + [q_all(3,js).*qjk_qk(4,:) - q_all(4,js).*qjk_qk(3,:);... 70 | q_all(4,js).*qjk_qk(2,:) - q_all(2,js).*qjk_qk(4,:);... 71 | q_all(2,js).*qjk_qk(3,:) - q_all(3,js).*qjk_qk(2,:)]; 72 | 73 | vij_norm = sqrt(sum(invOfqj_qjk_qk(2:4,:).^2, 1)); 74 | vij_theta = 2*atan2(vij_norm, invOfqj_qjk_qk(1,:)); 75 | 76 | ids_theta_smaller_than_minus_pi = vij_theta < -pi; 77 | vij_theta(ids_theta_smaller_than_minus_pi) = vij_theta(ids_theta_smaller_than_minus_pi) + 2*pi; 78 | ids_theta_larger_than_pi = vij_theta > pi; 79 | vij_theta(ids_theta_larger_than_pi) = vij_theta(ids_theta_larger_than_pi) - 2*pi; 80 | 81 | % The three lines below prevent division by near-zero. 82 | ids_theta_too_small = vij_norm < someVerySmallNumber; 83 | vij_norm(ids_theta_too_small) = 1; 84 | vij_theta(ids_theta_too_small) = 0; 85 | 86 | B = (vij_theta./vij_norm).*invOfqj_qjk_qk(2:4,:); 87 | B = B'; 88 | 89 | WB = w.*B; % [nEdges x 3] 90 | W = sparse(1:length(w), 1:length(w), w, length(w), length(w)); 91 | WA =W*A; % [nEdges x (nViews-1)] 92 | 93 | % We replace the following line... 94 | % v(2:end,:) = WA\WB; % [(nViews-1) x 3] 95 | % ... by the following two lines, as it is much faster due to MATLAB's specialized procedure involving a positive symmetric matrix. 96 | 97 | ATWTWA = WA'*WA; 98 | v(2:end,:) = ATWTWA\(WA'*WB); % [(nViews-1) x 3] 99 | 100 | 101 | residuals_sq = A*v(2:end,:)-B; 102 | residuals_sq = sum(residuals_sq.^2, 2); 103 | 104 | 105 | 106 | if (strcmp(mode, 'L1')) 107 | % w = min(1e4, residuals.^(-1/2)); % sqrt of weight from L1 norm 108 | w = min(1e4, residuals_sq.^(-1/4)); % sqrt of weight from L1 norm 109 | elseif (strcmp(mode, 'L0.5')) 110 | % w = min(1e4, residuals.^(-3/4)); % sqrt of weight from L0.5 norm 111 | w = min(1e4, residuals_sq.^(-3/8)); % sqrt of weight from L0.5 norm 112 | end 113 | 114 | 115 | v = v'; %[nViews x 3] 116 | v_theta = sqrt(sum(v.*v, 1)); 117 | sin_half_theta = sin(v_theta/2); 118 | cos_half_theta = cos(v_theta/2); 119 | 120 | mean_theta = mean(v_theta(2:end)); 121 | 122 | % The four lines below prevent division by near-zero. 123 | ids_theta_too_small = v_theta < someVerySmallNumber; 124 | sin_half_theta(ids_theta_too_small) = 0; 125 | cos_half_theta(ids_theta_too_small) = 1; 126 | v_theta(ids_theta_too_small) = 1; 127 | 128 | delta_q_all(1,:) = cos_half_theta; 129 | delta_q_all(2:4,:) = (sin_half_theta./v_theta).*v; 130 | v = v'; %[3 x nViews] 131 | 132 | 133 | q_all_updated(1,:) = ... %scalar term of q*delta_q 134 | q_all(1,:).*delta_q_all(1,:) - sum(q_all(2:4,:).*delta_q_all(2:4,:),1); 135 | 136 | q_all_updated(2:4,:) = ... % vector term of q*delta_q 137 | q_all(1,:).*delta_q_all(2:4,:) + delta_q_all(1,:).*q_all(2:4,:) ... 138 | + [q_all(3,:).*delta_q_all(4,:) - q_all(4,:).*delta_q_all(3,:);... 139 | q_all(4,:).*delta_q_all(2,:) - q_all(2,:).*delta_q_all(4,:);... 140 | q_all(2,:).*delta_q_all(3,:) - q_all(3,:).*delta_q_all(2,:)]; 141 | 142 | q_all = q_all_updated; 143 | 144 | if (mean_theta < 1e-3) % Same as Chatterjee's 145 | break; 146 | end 147 | end 148 | time_iterations = toc(tIterations); 149 | iterations = it; 150 | 151 | R_est = cell(1,nViews); 152 | for i = 1:nViews 153 | R_est{i} = q2R(q_all(:,i)); 154 | end 155 | end 156 | -------------------------------------------------------------------------------- /LogMap.m: -------------------------------------------------------------------------------- 1 | function out = LogMap(in) 2 | if (in(1,1) == 1 && in(2,2) == 1 && in(3,3) == 1) 3 | out = [0;0;0]; 4 | return; 5 | end 6 | 7 | cos_theta = (trace(in)-1)/2; 8 | sin_theta = sqrt(1-cos_theta^2); 9 | theta = acos(cos_theta); 10 | ln_R = theta/(2*sin_theta)*(in-in'); 11 | out = [ln_R(3,2);ln_R(1,3);ln_R(2,1)]; 12 | end -------------------------------------------------------------------------------- /ProjectOntoSO3.m: -------------------------------------------------------------------------------- 1 | function R = ProjectOntoSO3(M) 2 | [U,~,V] = svd(M); 3 | R = U*V.'; 4 | if (det(R) < 0) 5 | V(:,3) = -V(:,3); 6 | R = U*V.'; 7 | end 8 | end -------------------------------------------------------------------------------- /R2q.m: -------------------------------------------------------------------------------- 1 | function q = R2q(R) 2 | % https://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/ 3 | q = zeros(4,1); 4 | tr = trace(R); 5 | if (tr > 0) 6 | s = sqrt(1+tr)*2; %s = 4*qw 7 | q(1) = 0.25*s; 8 | q(2) = (R(3,2)-R(2,3))/s; 9 | q(3) = (R(1,3)-R(3,1))/s; 10 | q(4) = (R(2,1)-R(1,2))/s; 11 | elseif (R(1,1) > R(2,2) && R(1,1) > R(3,3)) 12 | s = sqrt(1+R(1,1)-R(2,2)-R(3,3))*2; %s = 4*qx 13 | q(1) = (R(3,2)-R(2,3))/s; 14 | q(2) = 0.25*s; 15 | q(3) = (R(1,2)+R(2,1))/s; 16 | q(4) = (R(1,3)+R(3,1))/s; 17 | elseif (R(2,2) > R(3,3)) 18 | s = sqrt(1+R(2,2)-R(1,1)-R(3,3))*2; %s = 4*qy 19 | q(1) = (R(1,3)-R(3,1))/s; 20 | q(2) = (R(1,2)+R(2,1))/s; 21 | q(3) = 0.25*s; 22 | q(4) = (R(2,3)+R(3,2))/s; 23 | else 24 | s = sqrt(1+R(3,3)-R(1,1)-R(2,2))*2; %s = 4*qz 25 | q(1) = (R(2,1)-R(1,2))/s; 26 | q(2) = (R(1,3)+R(3,1))/s; 27 | q(3) = (R(2,3)+R(3,2))/s; 28 | q(4) = 0.25*s; 29 | end 30 | end -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # HARA: A Hierarchical Approach for Robust Rotation Averaging 2 | 3 | [Paper](https://arxiv.org/abs/2111.08831), [Video](https://www.youtube.com/watch?v=oAR-LMStRS4), [Supplementary material](https://github.com/seonghun-lee/seonghun-lee.github.io/blob/master/pdf/SupplementaryMaterial_HARA_A_Hierarchical_Approach_for_Robust_Rotation_Averaging.pdf) 4 | 5 | In this repository, we provide the implementation of HARA. If you use our code, please cite it as follows: 6 | 7 | ```` 8 | @InProceedings{Lee_2022_CVPR, 9 | author = {Lee, Seong Hun and Civera, Javier}, 10 | title = {{HARA}: A Hierarchical Approach for Robust Rotation Averaging}, 11 | booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, 12 | month = {June}, 13 | year = {2022}, 14 | pages = {15777--15786} 15 | } 16 | ```` 17 | ### Update (January 8th 2023) 18 | 19 | [This recent change in the code](https://github.com/sunghoon031/HARA/commit/00d88296a6be1e2693d4f1e50397f84bad21003b) leads to a significant speedup of the local optimization step compared to the version used for the CVPR paper. We thank Chitturi Sidhartha, the first author of a 3DV paper titled ['It Is All In The Weights: Robust Rotation Averaging Revisited'](https://ieeexplore.ieee.org/document/9665962), for the discussion that led to this finding. 20 | 21 | ### Quick start 22 | Run `Test_HARA.m` to try it on a synthetic data WITHOUT using the number of inlier matches. 23 | 24 | ### Main functions: 25 | 1. `CreateSyntheticData.m`: Generate a synthetic dataset, as described in the main paper. 26 | 2. `RunHARA.m`: Run HARA without using the number of inlier matches. 27 | 3. `RunHARA_usingNumberOfInlierMatches.m`: Run HARA using the number of inlier matches. Note that we only provide the function, without the test script or a sample dataset. This function is quite similar to `RunHARA.m`, so it shouldn't be too difficult to use on your own dataset. 28 | -------------------------------------------------------------------------------- /RandomRotation.m: -------------------------------------------------------------------------------- 1 | function out = RandomRotation(angle_deg) 2 | axis = rand(3,1)-0.5; 3 | axis = axis/norm(axis); 4 | angle = angle_deg/180*pi; 5 | rotvec = angle*axis; 6 | out = ExpMap(rotvec); 7 | end -------------------------------------------------------------------------------- /RunHARA.m: -------------------------------------------------------------------------------- 1 | function [R_est, time_initialization, time_optimization] = ... 2 | RunHARA(... 3 | nViews, ... 4 | edge_IDs, ... 5 | RR, ... 6 | nSamples, ... 7 | s_init, ... 8 | thrs_proportion, ... 9 | triplet_thr, ... 10 | median_thr, ... 11 | err_sq_thr) 12 | 13 | 14 | %% Definitions: 15 | % Input: 16 | % - nViews = Number of absolute rotations (views) we want to estimate. 17 | % - edge_IDs = Edges between views. 18 | % If an i-th edge is established between view j and k, 19 | % edge_IDs(:,i) = [j;k]. 20 | % - RR = Relative rotations for all edges. 21 | % If an i-th edge is established between view j and k, 22 | % RR(:,:,i) = Estimate of (R_j)*(R_k)^T. 23 | % - nSamples = Number of triplets we sample per edge (default = 10). 24 | % - s_init = Initial support threshold (default = 10). 25 | % - thrs_proportion = Related to the percentiles of the sampled loop 26 | % errors. We use it to set the loop thresholds. 27 | % If thrs_proportion = [0.1 0.2 0.3], it means that 28 | % we set the loop thresholds (thrs) to the 10th, 29 | % 20th, and 30th percentile of the collected 30 | % errors. 31 | % (default = [0.1, 0.2, 0.3]) 32 | % - triplet_thr = When compute the loop thresholds from the sampled 33 | % loop errors, we ignore the errors above this 34 | % threshiold. This is because we assume that any loop 35 | % error above this level is likely to be caused by one 36 | % or more outliers in the triplet. 37 | % (default = 1.0) 38 | % - median_thr = If the median of all sampled loop errors is greater 39 | % than this threshold, we skip edge filtering. 40 | % (default = 1.0) 41 | % - err_sq_thr = Corresponds to tau^2 (tau is explained in the paper). 42 | % If the edge does not conform to our initial solution, 43 | % we filter this edge. This is the threshold we use for 44 | % this check. 45 | % (default = 1.0). 46 | % 47 | % Output: 48 | % - R_est = Estimated absolute rotations. 49 | % - time_initialization = Time taken to obtain the initial solution. 50 | % - time_optimization = Time taken to filter edges and perform the 51 | % local refinement. 52 | 53 | %% Step 0: Preprocessing 54 | 55 | t_init = tic; 56 | 57 | nEdges = size(edge_IDs,2); 58 | 59 | edge_info = cell(1, nViews); % Lists the views connected to each view. 60 | for i = 1:nEdges 61 | j = edge_IDs(1,i); 62 | k = edge_IDs(2,i); 63 | edge_info{j} = [edge_info{j}, k]; 64 | edge_info{k} = [edge_info{k}, j]; 65 | end 66 | 67 | nEdgesForEachView = zeros(1, nViews); 68 | for i = 1:nViews 69 | nEdgesForEachView(i) = length(edge_info{i}); 70 | end 71 | 72 | A = zeros(nViews,nViews); 73 | G = eye(3*nViews); 74 | for i = 1:nEdges 75 | j = edge_IDs(1,i); 76 | k = edge_IDs(2,i); 77 | R_jk = RR(:,:,i); 78 | G(3*j-2:3*j, 3*k-2:3*k) = R_jk; 79 | G(3*k-2:3*k, 3*j-2:3*j) = R_jk'; 80 | A(j,k) = 1; 81 | A(k,j) = 1; 82 | end 83 | 84 | % Sample loop errors: 85 | errs = []; 86 | errs_total = []; 87 | for i = 1:nEdges 88 | j = edge_IDs(1,i); 89 | k = edge_IDs(2,i); 90 | R_jk = G(3*j-2:3*j, 3*k-2:3*k); 91 | 92 | ls = intersect(edge_info{j}, edge_info{k}); 93 | ls = UniformSampling(ls, nSamples); 94 | 95 | for l = ls 96 | R_jl = G(3*j-2:3*j, 3*l-2:3*l); 97 | R_kl = G(3*k-2:3*k, 3*l-2:3*l); 98 | 99 | delta_R = R_jk - (R_jl*R_kl'); 100 | err_sq = sum(sum(delta_R.^2)); 101 | 102 | errs_total(end+1) = err_sq; 103 | 104 | if (err_sq < triplet_thr) 105 | errs(end+1) = err_sq; 106 | end 107 | end 108 | end 109 | 110 | med_err = median(errs_total); 111 | 112 | errs = sort(errs); 113 | nErrs = length(errs); 114 | thrs = errs(round(nErrs*thrs_proportion)); 115 | 116 | 117 | %% Step 1: Initialization 118 | 119 | thr_idx = 1; 120 | s = s_init; 121 | 122 | isFamily = zeros(1, nViews); 123 | R_init = cell(1,nViews); 124 | 125 | % Find the most connected node: 126 | [~, id_to_check] = max(nEdgesForEachView); 127 | 128 | % Add it to family. 129 | newFamily = id_to_check; 130 | newFamily_nEdges = nEdgesForEachView(id_to_check); 131 | 132 | isFamily(id_to_check) = 1; 133 | R_init{id_to_check} = eye(3); 134 | 135 | 136 | supportedNeighborsTable = zeros(nViews, length(thrs), s_init); 137 | % Example: For each view, it's the transpose of the following table: 138 | % 139 | % | thr1 | thr2 | thr3 | ... 140 | % #nbors supported by 1 other neighbor | 12 | 14 | 10 | ... 141 | % #nbors supported by 2 other neighbors | 20 | 31 | 24 | ... 142 | % ... 143 | % #nbors supported by s_init neighbors | 50 | 100 | 80 | ... 144 | 145 | votes = zeros(1,nViews); 146 | has_voted = zeros(1,nViews); 147 | 148 | while(min(isFamily)==0) 149 | 150 | % If the neighbors of the first one in newFamily are consistent 151 | % with each other, add them to the family. 152 | 153 | while(~isempty(newFamily)) 154 | id_to_check = newFamily(1); 155 | newFamily(1) = []; 156 | newFamily_nEdges(1) = []; 157 | 158 | % Set the non-family neighbors' rotations: 159 | 160 | neighbors = edge_info{id_to_check}; 161 | 162 | all_neighbors_are_family = true; 163 | for j = neighbors 164 | if (~isFamily(j)) 165 | all_neighbors_are_family = false; 166 | R_ji = G(3*j-2:3*j, 3*id_to_check-2:3*id_to_check); 167 | R_init{j} = R_ji*R_init{id_to_check}; 168 | end 169 | end 170 | 171 | if (all_neighbors_are_family) 172 | supportedNeighborsTable(id_to_check, :, :) = zeros(length(thrs), s_init); 173 | continue; 174 | end 175 | 176 | consistent_neighbors = cell(1, length(thrs)); 177 | % Example: 178 | % If (1, 2), (1, 3), (2, 3) have error less than thrs(1), 179 | % and (1, 2), (1, 3), (2, 3), (2, 4), (3, 4) have error less 180 | % than thrs(2), then we have 181 | % consistent_neighbors{1} = [1, 2, 1, 3, 2, 3] 182 | % consistent_neighbors{2} = [1, 2, 1, 3, 2, 3, 2, 4, 3, 4] 183 | 184 | 185 | % Check consistency between them: 186 | for jj = 1:length(neighbors)-1 187 | j = neighbors(jj); 188 | for kk = jj + 1:length(neighbors) 189 | k = neighbors(kk); 190 | if (A(j,k)==0) 191 | continue; 192 | end 193 | if (isFamily(j) && isFamily(k)) 194 | continue; 195 | end 196 | 197 | R_jk = G(3*j-2:3*j, 3*k-2:3*k); 198 | delta_R = R_init{j}*R_init{k}'-R_jk; 199 | err_sq = sum(sum(delta_R.^2)); 200 | 201 | for ii = 1:length(thrs) 202 | if (err_sq < thrs(ii)) 203 | consistent_neighbors{ii} = [consistent_neighbors{ii}, j, k]; 204 | end 205 | end 206 | end 207 | end 208 | 209 | % Next, we find out how many times each neighbor appears in 210 | % consistent_neighbors at the current loop threshold. 211 | % If a neighbor appears s or more times, we add it to family. 212 | 213 | [consistent_neighbors_sorted, freqs_sorted] = SortNonFamilyNeighbors(consistent_neighbors{thr_idx}, isFamily); 214 | 215 | 216 | family_candidates = []; 217 | for i = 1:length(consistent_neighbors_sorted) 218 | if (freqs_sorted(i) >= s) 219 | if (~isFamily(consistent_neighbors_sorted(i))) 220 | family_candidates(end+1) = consistent_neighbors_sorted(i); 221 | end 222 | else 223 | break; 224 | end 225 | end 226 | 227 | 228 | for i = 1:length(family_candidates) 229 | j = family_candidates(i); 230 | 231 | isFamily(j) = 1; 232 | [newFamily, newFamily_nEdges] = AddToNewFamily(... 233 | j, ... 234 | nEdgesForEachView(j), ... 235 | newFamily, ... 236 | newFamily_nEdges); 237 | 238 | % Reset thr and s (since new family member is added). 239 | s = s_init; 240 | thr_idx = 1; 241 | end 242 | 243 | 244 | % Now that consistent_neighbors have been updted, update 245 | % supportedNeighborsTable too: 246 | 247 | for ii = 1:length(thrs) 248 | [~, freq_sorted] = SortNonFamilyNeighbors(consistent_neighbors{ii}, isFamily); 249 | 250 | for i = 1:s_init 251 | supportedNeighborsTable(id_to_check, ii, i) = sum(freq_sorted >= i); 252 | end 253 | end 254 | 255 | end 256 | % newFamily is now empty. 257 | 258 | 259 | % Either (1) move on to the next base node, (2) increase the loop 260 | % threshold, or (3) decrease the support threshold, s: 261 | 262 | [max_support, id_min] = max(supportedNeighborsTable(:, thr_idx, s)); 263 | 264 | if (max_support > 0) 265 | newFamily = id_min; 266 | newFamily_nEdges = nEdgesForEachView(id_min); 267 | else 268 | if (thr_idx < length(thrs)) 269 | thr_idx = thr_idx + 1; 270 | else 271 | s = s-1; 272 | thr_idx = 1; 273 | end 274 | end 275 | 276 | if (s > 0) 277 | continue; 278 | end 279 | 280 | % Here, s = 0. Do SRA (single rotation averaging)! 281 | % Let every family member vote for nonfamily neighbors. 282 | % The one with the most votes gets added to family through SRA. 283 | votes(isFamily==1) = 0; 284 | voters = 1:nViews; 285 | voters = voters(~has_voted & isFamily); 286 | for i = voters 287 | for j = edge_info{i} 288 | if (~isFamily(j)) 289 | votes(j) = votes(j) + 1; 290 | end 291 | end 292 | end 293 | has_voted(voters) = 1; 294 | 295 | 296 | % Add the one with the most votes to the family. 297 | [maxVotes, id_to_check] = max(votes); 298 | if (maxVotes == 0) 299 | break; 300 | end 301 | isFamily(id_to_check) = 1; 302 | newFamily = id_to_check; 303 | newFamily_nEdges = nEdgesForEachView(id_to_check); 304 | 305 | 306 | % Determine the rotation of the new family member. 307 | c = 0; 308 | R_i = cell(1,1); 309 | for j = edge_info{id_to_check} 310 | if (isFamily(j)) 311 | c = c + 1; 312 | R_ij = G(3*id_to_check-2:3*id_to_check, 3*j-2:3*j); 313 | R_i{c} = R_ij*R_init{j}; 314 | end 315 | end 316 | R_init{id_to_check} = ClosestToChordalL1Mean(R_i, true, 10, 0.001); 317 | 318 | % Reset thr and s (since new family member is added). 319 | s = s_init; 320 | thr_idx = 1; 321 | end 322 | 323 | 324 | time_initialization = toc(t_init); 325 | 326 | 327 | %% Step 2: Edge filtering 328 | 329 | t_opti = tic; 330 | 331 | if (med_err > median_thr) 332 | edge_IDs_ = edge_IDs; 333 | RR_ = RR; 334 | else 335 | RR_ = zeros(3,3); 336 | edge_IDs_ = zeros(2,1); 337 | 338 | cc = 0; 339 | for i = 1:nEdges 340 | j = edge_IDs(1,i); 341 | k = edge_IDs(2,i); 342 | 343 | R_jk = RR(:,:,i); 344 | R_jk_est = R_init{j}*R_init{k}'; 345 | 346 | delta_R = R_jk_est-R_jk; 347 | err_sq = sum(sum(delta_R.^2)); 348 | 349 | if (err_sq < err_sq_thr) 350 | cc = cc + 1; 351 | RR_(:,:,cc) = RR(:,:,i); 352 | edge_IDs_(:,cc) = [j;k]; 353 | end 354 | end 355 | %disp(['Edges removed = ', num2str((nEdges-cc)/nEdges*100), '%']) 356 | end 357 | 358 | %% Step 3: Local optimization 359 | 360 | nIterations = 250; 361 | [R_est, ~, ~] = LocalOptimization(R_init, edge_IDs_, RR_, 'L0.5', nIterations); 362 | 363 | time_optimization = toc(t_opti); 364 | end -------------------------------------------------------------------------------- /RunHARA_usingNumberOfInlierMatches.m: -------------------------------------------------------------------------------- 1 | function [R_est, time_initialization, time_optimization] = ... 2 | RunHARA_usingNumberOfInlierMatches(... 3 | nViews,... 4 | edge_IDs,... 5 | RR,... 6 | nInliers_for_all_pairs,... 7 | nSamples,... 8 | s_init,... 9 | thrs_proportion,... 10 | triplet_thr,... 11 | median_thr,... 12 | err_sq_thr,... 13 | nInliers_thrs) 14 | 15 | 16 | %% Definitions: 17 | % Input: 18 | % - nViews = Number of absolute rotations (views) we want to estimate. 19 | % - edge_IDs = Edges between views. 20 | % If an i-th edge is established between view j and k, 21 | % edge_IDs(:,i) = [j;k]. 22 | % - RR = Relative rotations for all edges. 23 | % If an i-th edge is established between view j and k, 24 | % RR(:,:,i) = Estimate of (R_j)*(R_k)^T. 25 | % - nInliers_for_all_pairs = Number of valid 2D-2D correspondences 26 | % (i.e., inlier feature matches) between a 27 | % pair of views. 28 | % The number of inliers between view i and j 29 | % is given by nInliers_for_all_pairs(i,j). 30 | % - nSamples = Number of triplets we sample per edge (default = 10). 31 | % - s_init = Initial support threshold (default = 10). 32 | % - thrs_proportion = Related to the percentiles of the sampled loop 33 | % errors. We use it to set the loop thresholds. 34 | % If thrs_proportion = [0.1 0.2 0.3], it means that 35 | % we set the loop thresholds (thrs) to the 10th, 36 | % 20th, and 30th percentile of the collected 37 | % errors. 38 | % (default = [0.1, 0.2, 0.3]) 39 | % - triplet_thr = When compute the loop thresholds from the sampled 40 | % loop errors, we ignore the errors above this 41 | % threshiold. This is because we assume that any loop 42 | % error above this level is likely to be caused by one 43 | % or more outliers in the triplet. 44 | % (default = 1.0) 45 | % - median_thr = If the median of all sampled loop errors is greater 46 | % than this threshold, we skip edge filtering. 47 | % (default = 1.0) 48 | % - err_sq_thr = Corresponds to tau^2 (tau is explained in the paper). 49 | % If the edge does not conform to our initial solution, 50 | % we filter this edge. This is the threshold we use for 51 | % this check. 52 | % (default = 1.0) 53 | % - nInliers_thrs = Corresponds to d_1, d_2, ... in the paper. 54 | % If the number of inlier matches for a given edge is 55 | % below this threshold, we ignore it during the 56 | % initialization. 57 | % (default = [5, 0]) 58 | % 59 | % Output: 60 | % - R_est = Estimated absolute rotations. 61 | % - time_initialization = Time taken to obtain the initial solution. 62 | % - time_optimization = Time taken to filter edges and perform the 63 | % local refinement. 64 | 65 | %% Step 0: Preprocessing 66 | 67 | t_init = tic; 68 | 69 | nEdges = size(edge_IDs,2); 70 | 71 | edge_info = cell(1, nViews); % Lists the views connected to each view. 72 | for i = 1:nEdges 73 | j = edge_IDs(1,i); 74 | k = edge_IDs(2,i); 75 | edge_info{j} = [edge_info{j}, k]; 76 | edge_info{k} = [edge_info{k}, j]; 77 | end 78 | 79 | nEdgesForEachView = zeros(1, nViews); 80 | for i = 1:nViews 81 | nEdgesForEachView(i) = length(edge_info{i}); 82 | end 83 | 84 | A = zeros(nViews,nViews); 85 | G = eye(3*nViews); 86 | for i = 1:nEdges 87 | j = edge_IDs(1,i); 88 | k = edge_IDs(2,i); 89 | R_jk = RR(:,:,i); 90 | G(3*j-2:3*j, 3*k-2:3*k) = R_jk; 91 | G(3*k-2:3*k, 3*j-2:3*j) = R_jk'; 92 | A(j,k) = 1; 93 | A(k,j) = 1; 94 | end 95 | 96 | % Sample loop errors: 97 | errs = []; 98 | errs_total = []; 99 | for i = 1:nEdges 100 | j = edge_IDs(1,i); 101 | k = edge_IDs(2,i); 102 | R_jk = G(3*j-2:3*j, 3*k-2:3*k); 103 | 104 | ls = intersect(edge_info{j}, edge_info{k}); 105 | ls = UniformSampling(ls, nSamples); 106 | 107 | for l = ls 108 | R_jl = G(3*j-2:3*j, 3*l-2:3*l); 109 | R_kl = G(3*k-2:3*k, 3*l-2:3*l); 110 | 111 | delta_R = R_jk - (R_jl*R_kl'); 112 | err_sq = sum(sum(delta_R.^2)); 113 | 114 | errs_total(end+1) = err_sq; 115 | 116 | if (err_sq < triplet_thr) 117 | errs(end+1) = err_sq; 118 | end 119 | end 120 | end 121 | 122 | med_err = median(errs_total); 123 | 124 | errs = sort(errs); 125 | nErrs = length(errs); 126 | thrs = errs(round(nErrs*thrs_proportion)); 127 | 128 | 129 | %% Step 1: Initialization 130 | 131 | thr_idx = 1; 132 | s = s_init; 133 | 134 | inlier_idx = 1; 135 | nInliers_thr = nInliers_thrs(inlier_idx); 136 | 137 | isFamily = zeros(1, nViews); 138 | R_init = cell(1,nViews); 139 | 140 | % Find the most connected node: 141 | [~, id_to_check] = max(nEdgesForEachView); 142 | 143 | % Add it to family. 144 | newFamily = id_to_check; 145 | newFamily_nEdges = nEdgesForEachView(id_to_check); 146 | 147 | isFamily(id_to_check) = 1; 148 | R_init{id_to_check} = eye(3); 149 | 150 | 151 | supportedNeighborsTable = zeros(nViews, length(thrs), s_init); 152 | % Example: For each view, it's the transpose of the following table: 153 | % 154 | % | thr1 | thr2 | thr3 | ... 155 | % #nbors supported by 1 other neighbor | 12 | 14 | 10 | ... 156 | % #nbors supported by 2 other neighbors | 20 | 31 | 24 | ... 157 | % ... 158 | % #nbors supported by s_init neighbors | 50 | 100 | 80 | ... 159 | 160 | votes = zeros(1,nViews); 161 | has_voted = zeros(1,nViews); 162 | 163 | while(min(isFamily)==0) 164 | 165 | % If the neighbors of the first one in newFamily are consistent 166 | % with each other, add them to the family. 167 | 168 | while(~isempty(newFamily)) 169 | id_to_check = newFamily(1); 170 | newFamily(1) = []; 171 | newFamily_nEdges(1) = []; 172 | 173 | % Set the non-family neighbors' rotations: 174 | 175 | neighbors_ = edge_info{id_to_check}; 176 | neighbors = []; 177 | for j = neighbors_ 178 | if (nInliers_for_all_pairs(j, id_to_check) >= nInliers_thr) 179 | neighbors(end+1) = j; 180 | end 181 | end 182 | 183 | all_neighbors_are_family = true; 184 | for j = neighbors 185 | if (~isFamily(j)) 186 | all_neighbors_are_family = false; 187 | R_ji = G(3*j-2:3*j, 3*id_to_check-2:3*id_to_check); 188 | R_init{j} = R_ji*R_init{id_to_check}; 189 | end 190 | end 191 | 192 | if (all_neighbors_are_family) 193 | supportedNeighborsTable(id_to_check, :, :) = zeros(length(thrs), s_init); 194 | continue; 195 | end 196 | 197 | consistent_neighbors = cell(1, length(thrs)); 198 | % Example: 199 | % If (1, 2), (1, 3), (2, 3) have error less than thrs(1), 200 | % and (1, 2), (1, 3), (2, 3), (2, 4), (3, 4) have error less 201 | % than thrs(2), then we have 202 | % consistent_neighbors{1} = [1, 2, 1, 3, 2, 3] 203 | % consistent_neighbors{2} = [1, 2, 1, 3, 2, 3, 2, 4, 3, 4] 204 | 205 | 206 | % Check consistency between them: 207 | for jj = 1:length(neighbors)-1 208 | j = neighbors(jj); 209 | for kk = jj + 1:length(neighbors) 210 | k = neighbors(kk); 211 | if (A(j,k)==0 || nInliers_for_all_pairs(j, k) < nInliers_thr) 212 | continue; 213 | end 214 | if (isFamily(j) && isFamily(k)) 215 | continue; 216 | end 217 | 218 | R_jk = G(3*j-2:3*j, 3*k-2:3*k); 219 | delta_R = R_init{j}*R_init{k}'-R_jk; 220 | err_sq = sum(sum(delta_R.^2)); 221 | 222 | for ii = 1:length(thrs) 223 | if (err_sq < thrs(ii)) 224 | consistent_neighbors{ii} = [consistent_neighbors{ii}, j, k]; 225 | end 226 | end 227 | end 228 | end 229 | 230 | % Next, we find out how many times each neighbor appears in 231 | % consistent_neighbors at the current loop threshold. 232 | % If a neighbor appears s or more times, we add it to family. 233 | 234 | [consistent_neighbors_sorted, freqs_sorted] = SortNonFamilyNeighbors(consistent_neighbors{thr_idx}, isFamily); 235 | 236 | 237 | family_candidates = []; 238 | for i = 1:length(consistent_neighbors_sorted) 239 | if (freqs_sorted(i) >= s) 240 | if (~isFamily(consistent_neighbors_sorted(i))) 241 | family_candidates(end+1) = consistent_neighbors_sorted(i); 242 | end 243 | else 244 | break; 245 | end 246 | end 247 | 248 | 249 | for i = 1:length(family_candidates) 250 | j = family_candidates(i); 251 | 252 | isFamily(j) = 1; 253 | [newFamily, newFamily_nEdges] = AddToNewFamily(... 254 | j, ... 255 | nEdgesForEachView(j), ... 256 | newFamily, ... 257 | newFamily_nEdges); 258 | 259 | % Reset thr and s (since new family member is added). 260 | s = s_init; 261 | thr_idx = 1; 262 | end 263 | 264 | 265 | % Now that consistent_neighbors have been updted, update 266 | % supportedNeighborsTable too: 267 | 268 | for ii = 1:length(thrs) 269 | [~, freq_sorted] = SortNonFamilyNeighbors(consistent_neighbors{ii}, isFamily); 270 | 271 | for i = 1:s_init 272 | supportedNeighborsTable(id_to_check, ii, i) = sum(freq_sorted >= i); 273 | end 274 | end 275 | 276 | end 277 | % newFamily is now empty. 278 | 279 | 280 | % Either (1) move on to the next base node, (2) increase the loop 281 | % threshold, or (3) decrease the support threshold, s: 282 | 283 | [max_support, id_min] = max(supportedNeighborsTable(:, thr_idx, s)); 284 | 285 | if (max_support > 0) 286 | newFamily = id_min; 287 | newFamily_nEdges = nEdgesForEachView(id_min); 288 | else 289 | if (thr_idx < length(thrs)) 290 | thr_idx = thr_idx + 1; 291 | else 292 | s = s-1; 293 | thr_idx = 1; 294 | end 295 | end 296 | 297 | if (s > 0) 298 | continue; 299 | end 300 | 301 | % Here, s = 0. Do SRA (single rotation averaging)! 302 | % Let every family member vote for nonfamily neighbors. 303 | % The one with the most votes gets added to family through SRA. 304 | votes(isFamily==1) = 0; 305 | voters = 1:nViews; 306 | voters = voters(~has_voted & isFamily); 307 | for i = voters 308 | for j = edge_info{i} 309 | if (~isFamily(j) && nInliers_for_all_pairs(j, i) >= nInliers_thr) 310 | votes(j) = votes(j) + 1; 311 | end 312 | end 313 | end 314 | has_voted(voters) = 1; 315 | 316 | 317 | % Add the one with the most votes to the family. 318 | [maxVotes, id_to_check] = max(votes); 319 | if (maxVotes == 0) 320 | if (inlier_idx == length(nInliers_thrs)) 321 | break; 322 | end 323 | 324 | % Switch to a smaller nInliers_thr: 325 | inlier_idx = inlier_idx + 1; 326 | nInliers_thr = nInliers_thrs(inlier_idx); 327 | 328 | thr_idx = 1; 329 | s = s_init; 330 | 331 | supportedNeighborsTable = zeros(nViews, length(thrs), s_init); 332 | votes = zeros(1,nViews); 333 | has_voted = zeros(1,nViews); 334 | 335 | continue; 336 | end 337 | isFamily(id_to_check) = 1; 338 | newFamily = id_to_check; 339 | newFamily_nEdges = nEdgesForEachView(id_to_check); 340 | 341 | 342 | % Determine the rotation of the new family member. 343 | c = 0; 344 | R_i = cell(1,1); 345 | for j = edge_info{id_to_check} 346 | if (isFamily(j) && nInliers_for_all_pairs(j, id_to_check) >= nInliers_thr) 347 | c = c + 1; 348 | R_ij = G(3*id_to_check-2:3*id_to_check, 3*j-2:3*j); 349 | R_i{c} = R_ij*R_init{j}; 350 | end 351 | end 352 | R_init{id_to_check} = ClosestToChordalL1Mean(R_i, true, 10, 0.001); 353 | 354 | % Reset thr and s (since new family member is added). 355 | s = s_init; 356 | thr_idx = 1; 357 | end 358 | 359 | 360 | time_initialization = toc(t_init); 361 | 362 | 363 | %% Step 2: Edge filtering 364 | 365 | t_opti = tic; 366 | 367 | if (med_err > median_thr) 368 | edge_IDs_ = edge_IDs; 369 | RR_ = RR; 370 | else 371 | RR_ = zeros(3,3); 372 | edge_IDs_ = zeros(2,1); 373 | 374 | cc = 0; 375 | for i = 1:nEdges 376 | j = edge_IDs(1,i); 377 | k = edge_IDs(2,i); 378 | 379 | R_jk = RR(:,:,i); 380 | R_jk_est = R_init{j}*R_init{k}'; 381 | 382 | delta_R = R_jk_est-R_jk; 383 | err_sq = sum(sum(delta_R.^2)); 384 | 385 | if (err_sq < err_sq_thr) 386 | cc = cc + 1; 387 | RR_(:,:,cc) = RR(:,:,i); 388 | edge_IDs_(:,cc) = [j;k]; 389 | end 390 | end 391 | %disp(['Edges removed = ', num2str((nEdges-cc)/nEdges*100), '%']) 392 | end 393 | 394 | %% Step 3: Local optimization 395 | 396 | nIterations = 250; 397 | [R_est, ~, ~] = LocalOptimization(R_init, edge_IDs_, RR_, 'L0.5', nIterations); 398 | 399 | time_optimization = toc(t_opti); 400 | end -------------------------------------------------------------------------------- /SkewSymmetricMatrix.m: -------------------------------------------------------------------------------- 1 | function out = SkewSymmetricMatrix(in) 2 | out=[0 -in(3) in(2) ; in(3) 0 -in(1) ; -in(2) in(1) 0 ]; 3 | end -------------------------------------------------------------------------------- /SortNonFamilyNeighbors.m: -------------------------------------------------------------------------------- 1 | function [val_sorted, freq_sorted] = SortNonFamilyNeighbors(x, isFamily) 2 | 3 | % Sort the (non-family) nodes in the order of descending frequency. 4 | 5 | if (isempty(x)) 6 | val_sorted = []; 7 | freq_sorted = []; 8 | return; 9 | end 10 | 11 | 12 | val = []; 13 | freq = []; 14 | for i = 1:length(x) 15 | xi = x(i); 16 | if (isFamily(xi)) 17 | continue; 18 | end 19 | 20 | idx = find(val==xi); 21 | if (isempty(idx)) 22 | val(end+1) = xi; 23 | freq(end+1) = 1; 24 | else 25 | freq(idx) = freq(idx) + 1; 26 | end 27 | end 28 | 29 | if (isempty(freq)) 30 | val_sorted = []; 31 | freq_sorted = []; 32 | return; 33 | end 34 | 35 | [freq_sorted, sort_idx] = sort(freq, 'descend'); 36 | val_sorted = val(sort_idx); 37 | 38 | end -------------------------------------------------------------------------------- /Test_HARA.m: -------------------------------------------------------------------------------- 1 | clear all; close all; clc; 2 | folder = fileparts(which(mfilename)); 3 | addpath(genpath(folder)); 4 | 5 | %% Create a synthetic dataset: 6 | % (This is an example without the number of valid 2D-2D correspondences): 7 | 8 | nViews = 100; 9 | connectivity = 0.2; 10 | outlier_ratio = 0.5; 11 | inlier_noise_deg = 10; 12 | 13 | [R_gt, edge_IDs, RR] = CreateSyntheticData(nViews, connectivity, outlier_ratio, inlier_noise_deg); 14 | 15 | 16 | 17 | %% Run HARA: 18 | 19 | % Set parameters: 20 | median_thr = 1; 21 | triplet_thr = 1; 22 | err_sq_thr = 1; 23 | nSamples = 10; 24 | s_init = 10; 25 | thrs_proportion = [0.1 0.2 0.3]; 26 | % nInliers_thrs = [5 0]; 27 | 28 | [R_est, time_initialization, time_optimization] = RunHARA(nViews, edge_IDs, RR, nSamples, s_init, thrs_proportion, triplet_thr, median_thr, err_sq_thr); 29 | % [R_est, time_initialization, time_optimization] = RunHARA_usingNumberOfInlierMatches(nViews, edge_IDs, RR, nInliers_for_all_pairs, nSamples, s_init, thrs_proportion, triplet_thr, median_thr, err_sq_thr, nInliers_thrs) 30 | 31 | disp(['Initialization took ', num2str(time_initialization), 's, Optimization took ', num2str(time_optimization), 's.']) 32 | 33 | 34 | %% Evaluate results: 35 | 36 | [~,~, mean_error_L1_alignment, ~] = AlignRotationL1(R_gt, R_est); 37 | [~, ~, rms_error_L2_alignment] = AlignRotationL2(R_gt, R_est); 38 | 39 | disp(['Resulting errors (deg): theta_1 = ', num2str(mean_error_L1_alignment),... 40 | ', theta_2 = ', num2str(rms_error_L2_alignment)]) 41 | 42 | 43 | 44 | 45 | 46 | -------------------------------------------------------------------------------- /UniformSampling.m: -------------------------------------------------------------------------------- 1 | function out = UniformSampling(data, r) 2 | 3 | % Sample r numbers from data uniformly and deterministically. 4 | 5 | n = length(data); 6 | if (r >= n) 7 | out = data; 8 | return; 9 | end 10 | quotient = floor(n/r); 11 | remainder = n-r*quotient; 12 | if (remainder==0) 13 | out = data(quotient:quotient:n); 14 | return; 15 | end 16 | out = nan(1, r); 17 | i = 0; 18 | c = 0; 19 | out_idx = 0; 20 | while (out_idx < r) 21 | i = i + 1; 22 | if (i > length(data)) 23 | i = 1; 24 | quotient = floor(length(data)/(r-out_idx)); 25 | end 26 | if (c == 0) 27 | out_idx = out_idx + 1; 28 | out(out_idx) = data(i); 29 | data(i) = []; 30 | i = i-1; 31 | end 32 | c = c + 1; 33 | if (c == quotient+1) 34 | c = 0; 35 | end 36 | end 37 | end -------------------------------------------------------------------------------- /q2R.m: -------------------------------------------------------------------------------- 1 | function R = q2R(q) 2 | qw = q(1); qx = q(2); qy = q(3); qz = q(4); 3 | R = zeros(3,3); 4 | R(1,1) = 1 - 2*qy^2 - 2*qz^2; 5 | R(1,2) = 2*qx*qy - 2*qz*qw; 6 | R(1,3) = 2*qx*qz + 2*qy*qw; 7 | R(2,1) = 2*qx*qy + 2*qz*qw; 8 | R(2,2) = 1 - 2*qx^2 - 2*qz^2; 9 | R(2,3) = 2*qy*qz - 2*qx*qw; 10 | R(3,1) = 2*qx*qz - 2*qy*qw; 11 | R(3,2) = 2*qy*qz + 2*qx*qw; 12 | R(3,3) = 1 - 2*qx^2 - 2*qy^2; 13 | end --------------------------------------------------------------------------------