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  • Eigenvector computation using OpenCV

    - by Andriyev
    Hi I have this matrix A, representing similarities of pixel intensities of an image. For example: Consider a 10 x 10 image. Matrix A in this case would be of dimension 100 x 100, and element A(i,j) would have a value in the range 0 to 1, representing the similarity of pixel i to j in terms of intensity. I am using OpenCV for image processing and the development environment is C on Linux. Objective is to compute the Eigenvectors of matrix A and I have used the following approach: static CvMat mat, *eigenVec, *eigenVal; static double A[100][100]={}, Ain1D[10000]={}; int cnt=0; //Converting matrix A into a one dimensional array //Reason: That is how cvMat requires it for(i = 0;i < affnDim;i++){ for(j = 0;j < affnDim;j++){ Ain1D[cnt++] = A[i][j]; } } mat = cvMat(100, 100, CV_32FC1, Ain1D); cvEigenVV(&mat, eigenVec, eigenVal, 1e-300); for(i=0;i < 100;i++){ val1 = cvmGet(eigenVal,i,0); //Fetching Eigen Value for(j=0;j < 100;j++){ matX[i][j] = cvmGet(eigenVec,i,j); //Fetching each component of Eigenvector i } } Problem: After execution I get nearly all components of all the Eigenvectors to be zero. I tried different images and also tried populating A with random values between 0 and 1, but the same result. Few of the top eigenvalues returned look like the following: 9805401476911479666115491135488.000000 -9805401476911479666115491135488.000000 -89222871725331592641813413888.000000 89222862280598626902522986496.000000 5255391142666987110400.000000 I am now thinking on the lines of using cvSVD() which performs singular value decomposition of real floating-point matrix and might yield me the eigenvectors. But before that I thought of asking it here. Is there anything absurd in my current approach? Am I using the right API i.e. cvEigenVV() for the right input matrix (my matrix A is a floating point matrix)? cheers

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  • Sorting eigenvectors by their eigenvalues (associated sorting)

    - by fbrereto
    I have an unsorted vector of eigenvalues and a related matrix of eigenvectors. I'd like to sort the columns of the matrix with respect to the sorted set of eigenvalues. (e.g., if eigenvalue[3] moves to eigenvalue[2], I want column 3 of the eigenvector matrix to move over to column 2.) I know I can sort the eigenvalues in O(N log N) via std::sort. Without rolling my own sorting algorithm, how do I make sure the matrix's columns (the associated eigenvectors) follow along with their eigenvalues as the latter are sorted?

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  • How to store generated eigen faces for future face recognition?

    - by user3237134
    My code works in the following manner: 1.First, it obtains several images from the training set 2.After loading these images, we find the normalized faces,mean face and perform several calculation. 3.Next, we ask for the name of an image we want to recognize 4.We then project the input image into the eigenspace, and based on the difference from the eigenfaces we make a decision. 5.Depending on eigen weight vector for each input image we make clusters using kmeans command. Source code i tried: clear all close all clc % number of images on your training set. M=1200; %Chosen std and mean. %It can be any number that it is close to the std and mean of most of the images. um=60; ustd=32; %read and show images(bmp); S=[]; %img matrix for i=1:M str=strcat(int2str(i),'.jpg'); %concatenates two strings that form the name of the image eval('img=imread(str);'); [irow icol d]=size(img); % get the number of rows (N1) and columns (N2) temp=reshape(permute(img,[2,1,3]),[irow*icol,d]); %creates a (N1*N2)x1 matrix S=[S temp]; %X is a N1*N2xM matrix after finishing the sequence %this is our S end %Here we change the mean and std of all images. We normalize all images. %This is done to reduce the error due to lighting conditions. for i=1:size(S,2) temp=double(S(:,i)); m=mean(temp); st=std(temp); S(:,i)=(temp-m)*ustd/st+um; end %show normalized images for i=1:M str=strcat(int2str(i),'.jpg'); img=reshape(S(:,i),icol,irow); img=img'; end %mean image; m=mean(S,2); %obtains the mean of each row instead of each column tmimg=uint8(m); %converts to unsigned 8-bit integer. Values range from 0 to 255 img=reshape(tmimg,icol,irow); %takes the N1*N2x1 vector and creates a N2xN1 matrix img=img'; %creates a N1xN2 matrix by transposing the image. % Change image for manipulation dbx=[]; % A matrix for i=1:M temp=double(S(:,i)); dbx=[dbx temp]; end %Covariance matrix C=A'A, L=AA' A=dbx'; L=A*A'; % vv are the eigenvector for L % dd are the eigenvalue for both L=dbx'*dbx and C=dbx*dbx'; [vv dd]=eig(L); % Sort and eliminate those whose eigenvalue is zero v=[]; d=[]; for i=1:size(vv,2) if(dd(i,i)>1e-4) v=[v vv(:,i)]; d=[d dd(i,i)]; end end %sort, will return an ascending sequence [B index]=sort(d); ind=zeros(size(index)); dtemp=zeros(size(index)); vtemp=zeros(size(v)); len=length(index); for i=1:len dtemp(i)=B(len+1-i); ind(i)=len+1-index(i); vtemp(:,ind(i))=v(:,i); end d=dtemp; v=vtemp; %Normalization of eigenvectors for i=1:size(v,2) %access each column kk=v(:,i); temp=sqrt(sum(kk.^2)); v(:,i)=v(:,i)./temp; end %Eigenvectors of C matrix u=[]; for i=1:size(v,2) temp=sqrt(d(i)); u=[u (dbx*v(:,i))./temp]; end %Normalization of eigenvectors for i=1:size(u,2) kk=u(:,i); temp=sqrt(sum(kk.^2)); u(:,i)=u(:,i)./temp; end % show eigenfaces; for i=1:size(u,2) img=reshape(u(:,i),icol,irow); img=img'; img=histeq(img,255); end % Find the weight of each face in the training set. omega = []; for h=1:size(dbx,2) WW=[]; for i=1:size(u,2) t = u(:,i)'; WeightOfImage = dot(t,dbx(:,h)'); WW = [WW; WeightOfImage]; end omega = [omega WW]; end % Acquire new image % Note: the input image must have a bmp or jpg extension. % It should have the same size as the ones in your training set. % It should be placed on your desktop ed_min=[]; srcFiles = dir('G:\newdatabase\*.jpg'); % the folder in which ur images exists for b = 1 : length(srcFiles) filename = strcat('G:\newdatabase\',srcFiles(b).name); Imgdata = imread(filename); InputImage=Imgdata; InImage=reshape(permute((double(InputImage)),[2,1,3]),[irow*icol,1]); temp=InImage; me=mean(temp); st=std(temp); temp=(temp-me)*ustd/st+um; NormImage = temp; Difference = temp-m; p = []; aa=size(u,2); for i = 1:aa pare = dot(NormImage,u(:,i)); p = [p; pare]; end InImWeight = []; for i=1:size(u,2) t = u(:,i)'; WeightOfInputImage = dot(t,Difference'); InImWeight = [InImWeight; WeightOfInputImage]; end noe=numel(InImWeight); % Find Euclidean distance e=[]; for i=1:size(omega,2) q = omega(:,i); DiffWeight = InImWeight-q; mag = norm(DiffWeight); e = [e mag]; end ed_min=[ed_min MinimumValue]; theta=6.0e+03; %disp(e) z(b,:)=InImWeight; end IDX = kmeans(z,5); clustercount=accumarray(IDX, ones(size(IDX))); disp(clustercount); QUESTIONS: 1.It is working fine for M=50(i.e Training set contains 50 images) but not for M=1200(i.e Training set contains 1200 images).It is not showing any error.There is no output.I waited for 10 min still there is no output. I think it is going infinite loop.What is the problem?Where i was wrong? 2.Instead of running the training set everytime how eigen faces generated are stored so that stored eigen faces are used for future face recoginition for a new input image.So it reduces wastage of time.

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  • Vectorization of matlab code for faster execution

    - by user3237134
    My code works in the following manner: 1.First, it obtains several images from the training set 2.After loading these images, we find the normalized faces,mean face and perform several calculation. 3.Next, we ask for the name of an image we want to recognize 4.We then project the input image into the eigenspace, and based on the difference from the eigenfaces we make a decision. 5.Depending on eigen weight vector for each input image we make clusters using kmeans command. Source code i tried: clear all close all clc % number of images on your training set. M=1200; %Chosen std and mean. %It can be any number that it is close to the std and mean of most of the images. um=60; ustd=32; %read and show images(bmp); S=[]; %img matrix for i=1:M str=strcat(int2str(i),'.jpg'); %concatenates two strings that form the name of the image eval('img=imread(str);'); [irow icol d]=size(img); % get the number of rows (N1) and columns (N2) temp=reshape(permute(img,[2,1,3]),[irow*icol,d]); %creates a (N1*N2)x1 matrix S=[S temp]; %X is a N1*N2xM matrix after finishing the sequence %this is our S end %Here we change the mean and std of all images. We normalize all images. %This is done to reduce the error due to lighting conditions. for i=1:size(S,2) temp=double(S(:,i)); m=mean(temp); st=std(temp); S(:,i)=(temp-m)*ustd/st+um; end %show normalized images for i=1:M str=strcat(int2str(i),'.jpg'); img=reshape(S(:,i),icol,irow); img=img'; end %mean image; m=mean(S,2); %obtains the mean of each row instead of each column tmimg=uint8(m); %converts to unsigned 8-bit integer. Values range from 0 to 255 img=reshape(tmimg,icol,irow); %takes the N1*N2x1 vector and creates a N2xN1 matrix img=img'; %creates a N1xN2 matrix by transposing the image. % Change image for manipulation dbx=[]; % A matrix for i=1:M temp=double(S(:,i)); dbx=[dbx temp]; end %Covariance matrix C=A'A, L=AA' A=dbx'; L=A*A'; % vv are the eigenvector for L % dd are the eigenvalue for both L=dbx'*dbx and C=dbx*dbx'; [vv dd]=eig(L); % Sort and eliminate those whose eigenvalue is zero v=[]; d=[]; for i=1:size(vv,2) if(dd(i,i)>1e-4) v=[v vv(:,i)]; d=[d dd(i,i)]; end end %sort, will return an ascending sequence [B index]=sort(d); ind=zeros(size(index)); dtemp=zeros(size(index)); vtemp=zeros(size(v)); len=length(index); for i=1:len dtemp(i)=B(len+1-i); ind(i)=len+1-index(i); vtemp(:,ind(i))=v(:,i); end d=dtemp; v=vtemp; %Normalization of eigenvectors for i=1:size(v,2) %access each column kk=v(:,i); temp=sqrt(sum(kk.^2)); v(:,i)=v(:,i)./temp; end %Eigenvectors of C matrix u=[]; for i=1:size(v,2) temp=sqrt(d(i)); u=[u (dbx*v(:,i))./temp]; end %Normalization of eigenvectors for i=1:size(u,2) kk=u(:,i); temp=sqrt(sum(kk.^2)); u(:,i)=u(:,i)./temp; end % show eigenfaces; for i=1:size(u,2) img=reshape(u(:,i),icol,irow); img=img'; img=histeq(img,255); end % Find the weight of each face in the training set. omega = []; for h=1:size(dbx,2) WW=[]; for i=1:size(u,2) t = u(:,i)'; WeightOfImage = dot(t,dbx(:,h)'); WW = [WW; WeightOfImage]; end omega = [omega WW]; end % Acquire new image % Note: the input image must have a bmp or jpg extension. % It should have the same size as the ones in your training set. % It should be placed on your desktop ed_min=[]; srcFiles = dir('G:\newdatabase\*.jpg'); % the folder in which ur images exists for b = 1 : length(srcFiles) filename = strcat('G:\newdatabase\',srcFiles(b).name); Imgdata = imread(filename); InputImage=Imgdata; InImage=reshape(permute((double(InputImage)),[2,1,3]),[irow*icol,1]); temp=InImage; me=mean(temp); st=std(temp); temp=(temp-me)*ustd/st+um; NormImage = temp; Difference = temp-m; p = []; aa=size(u,2); for i = 1:aa pare = dot(NormImage,u(:,i)); p = [p; pare]; end InImWeight = []; for i=1:size(u,2) t = u(:,i)'; WeightOfInputImage = dot(t,Difference'); InImWeight = [InImWeight; WeightOfInputImage]; end noe=numel(InImWeight); % Find Euclidean distance e=[]; for i=1:size(omega,2) q = omega(:,i); DiffWeight = InImWeight-q; mag = norm(DiffWeight); e = [e mag]; end ed_min=[ed_min MinimumValue]; theta=6.0e+03; %disp(e) z(b,:)=InImWeight; end IDX = kmeans(z,5); clustercount=accumarray(IDX, ones(size(IDX))); disp(clustercount); Running time for 50 images:Elapsed time is 103.947573 seconds. QUESTIONS: 1.It is working fine for M=50(i.e Training set contains 50 images) but not for M=1200(i.e Training set contains 1200 images).It is not showing any error.There is no output.I waited for 10 min still there is no output. I think it is going infinite loop.What is the problem?Where i was wrong?

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