Bad result / high deviation using procrustes

2015 12 4
1 个回答
回答已采纳
更新时间：2015 12 11
1 次查看（30 天）

0 个投票

I try using procrustes to get the transformation between two point sets, each with 4 points. Manually I found a transformation, that aligns the two point set quite good (TFM_Ref). But the transformation calculated by procrustes (TFM_PcR) is quite bad compared to TFM_Ref.
clearvars
%%Data
S =[-52.0000 0 0;
11.5000 25.0000 0;
53.0000 0 0;
-20.0000 -42.0000 0];
T =[ 0 0 2.71;
42.4000 -23.2300 0;
104.5800 4.4400 0;
70.9000 45.1900 0];
%%Test transformation (determined manually)
TFM_Ref = [-0.9991 -0.0427 0 53.0000;
0.0427 -0.9991 0 0 ;
0 0 1.0000 0 ;
0 0 0 1.0000];
S2T_Ref = unique(transformPointsInverse(affine3d(TFM_Ref'), S),'rows');
T_Ref = unique(T,'rows');
RMSE_Ref = rms(rms(T_Ref-S2T_Ref))
%%Procrustes
[~,~,transform] = procrustes(T, S, 'scaling',0, 'reflection',0);
TFM_PrC = inv([[transform.T', transform.c(1,:)']; 0 0 0 1]);
S2T_PrC = unique(transformPointsInverse(affine3d(TFM_PrC'), S), 'rows');
RMSE_PrC = rms(rms(T_Ref-S2T_PrC))

请先登录，再回答此问题。

 采纳的回答

Fritz
Fritz 2015-12-11
编辑：Fritz 2015-12-11

0 个投票

I found a solution using procrustes with all permutations of the source points. The best transformation is the one with the minimum dissimilarity measure.
clearvars
%%Data
Source =[-52.00 0 0;
11.50 25.00 0;
53.00 0 0;
-20.00 -42.00 0];
Target =[ 0 0 2.71;
42.40 -23.23 0 ;
104.58 4.44 0 ;
70.90 45.19 0 ];
%%Procrustes
IndexPermutations = perms(1:size(Source,1)); % All permutations of the indices of Source
for i=1:length(IndexPermutations)
[D(i,1), ~, TFMs(i)] = procrustes(Target, Source(IndexPermutations(i,:),:), ...
'scaling',0, 'reflection',0); % Try procrustes with all permutations
end
[DMin, I_DMin] = min(D); % Get the index of the smallest dissimilarity measure
TFM = [[TFMs(I_DMin).T', TFMs(I_DMin).c(1,:)']; 0 0 0 1]; % Create the transformation
Source = Source(IndexPermutations(I_DMin,:),:);
Source_tfmd = transformPointsForward(affine3d(TFM'), Source);
rms(rms(Target-Source_tfmd))

更多回答（0 个）

类别

在 帮助中心 和 File Exchange 中查找有关 Dimensionality Reduction and Feature Extraction 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by