Matching features of images using PCA-SIFT - computer-vision

Question

I want to match features in two images to detect copy-move forgery. I used the PCA-SIFT code to detect image features. But, I am having trouble in matching the PCA-SIFT features. According to several papers, similar matching process is used for PCA-SIFT as is used in SIFT. I have used the following code snippet to match features.
%des1 and des2 are the PCA-SIFT descriptors obtained from two images
% Precompute matrix transpose
des2t = des2';
matchTable = zeros(1,size(des1,1));
cnt=0; %no. of matches
%ration of ditances
distRatio = 0.5;
%normalising features
m1=max(max(des1));
m2=max(max(des2));
m=max(m1,m2);
des1=des1./m;
des2=des2./m;
for i = 1 : size(des1,1)
%finding eucledian distance of a vector in one image to all features in second image
A=des1(i,:);
D = des2-repmat(A,size(des2,1),1);
[vals,indx] = sort((sum(D.^2,2)).^(1/2)); %sort distances
% Check if nearest neighbor has angle less than distRatio times 2nd.
if (vals(1) < distRatio * vals(2))
matchTable(i) = indx(1);
cnt=cnt+1;
else
matchTable(i) = 0;
end
end
cnt
The above code works fine for SIFT features. But I am not able to get correct results for PCA-SIFT features even after trying several values of distRatio(0-1). I'm also not sure if the matlab central code for PCA-SIFT(mentioned above) does the exact process as mentioned in this paper
If somebody has any idea about the above problem then please comment.

Answer 1

The problem is, PCA does not preserve euclidean distance between 2 vectors. Take a simple example where your data is along the line y = x. The distance between 2 points along the line will depend on both co-ordinates, even if all your data is 1 dimensional, i.e. lying along the line. When you apply PCA, the new euclidean distance will only take the principle component into account, which would be the line y=x, so distance between (1,1), (2,2) would just be 1 instead of sqrt(2).
However, if you normalize the features by their euclidean norm, nearest neighbor using euclidean distance is equivalent to computing cosine-similarity (dot-product) between features.
https://en.wikipedia.org/wiki/Cosine_similarity
Therefore I would first recommend you to test if matching for sift features works if you normalize them by their L2 norm. If yes, you could apply PCA on those features, again normalize the PCA features by their L2 norm and then compute euclidean distance. As far as I remember, L2 norm of a sift vector is 1. So, you only need normalize your PCA-SIFT features by their L2 norm and compute euclidean distance.