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Search found 5 results on 1 pages for 'eig'.

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  • fit a ellipse in Python given a set of points xi=(xi,yi)

    - by Gianni
    I am computing a series of index from a 2D points (x,y). One index is the ratio between minor and major axis. To fit the ellipse i am using the following post when i run these function the final results looks strange because the center and the axis length are not in scale with the 2D points center = [ 560415.53298363+0.j 6368878.84576771+0.j] angle of rotation = (-0.0528033467597-5.55111512313e-17j) axes = [0.00000000-557.21553487j 6817.76933256 +0.j] thanks in advance for help import numpy as np from numpy.linalg import eig, inv def fitEllipse(x,y): x = x[:,np.newaxis] y = y[:,np.newaxis] D = np.hstack((x*x, x*y, y*y, x, y, np.ones_like(x))) S = np.dot(D.T,D) C = np.zeros([6,6]) C[0,2] = C[2,0] = 2; C[1,1] = -1 E, V = eig(np.dot(inv(S), C)) n = np.argmax(np.abs(E)) a = V[:,n] return a def ellipse_center(a): b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0] num = b*b-a*c x0=(c*d-b*f)/num y0=(a*f-b*d)/num return np.array([x0,y0]) def ellipse_angle_of_rotation( a ): b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0] return 0.5*np.arctan(2*b/(a-c)) def ellipse_axis_length( a ): b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0] up = 2*(a*f*f+c*d*d+g*b*b-2*b*d*f-a*c*g) down1=(b*b-a*c)*( (c-a)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a)) down2=(b*b-a*c)*( (a-c)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a)) res1=np.sqrt(up/down1) res2=np.sqrt(up/down2) return np.array([res1, res2]) if __name__ == '__main__': points = [(560036.4495758876, 6362071.890493258), (560036.4495758876, 6362070.890493258), (560036.9495758876, 6362070.890493258), (560036.9495758876, 6362070.390493258), (560037.4495758876, 6362070.390493258), (560037.4495758876, 6362064.890493258), (560036.4495758876, 6362064.890493258), (560036.4495758876, 6362063.390493258), (560035.4495758876, 6362063.390493258), (560035.4495758876, 6362062.390493258), (560034.9495758876, 6362062.390493258), (560034.9495758876, 6362061.390493258), (560032.9495758876, 6362061.390493258), (560032.9495758876, 6362061.890493258), (560030.4495758876, 6362061.890493258), (560030.4495758876, 6362061.390493258), (560029.9495758876, 6362061.390493258), (560029.9495758876, 6362060.390493258), (560029.4495758876, 6362060.390493258), (560029.4495758876, 6362059.890493258), (560028.9495758876, 6362059.890493258), (560028.9495758876, 6362059.390493258), (560028.4495758876, 6362059.390493258), (560028.4495758876, 6362058.890493258), (560027.4495758876, 6362058.890493258), (560027.4495758876, 6362058.390493258), (560026.9495758876, 6362058.390493258), (560026.9495758876, 6362057.890493258), (560025.4495758876, 6362057.890493258), (560025.4495758876, 6362057.390493258), (560023.4495758876, 6362057.390493258), (560023.4495758876, 6362060.390493258), (560023.9495758876, 6362060.390493258), (560023.9495758876, 6362061.890493258), (560024.4495758876, 6362061.890493258), (560024.4495758876, 6362063.390493258), (560024.9495758876, 6362063.390493258), (560024.9495758876, 6362064.390493258), (560025.4495758876, 6362064.390493258), (560025.4495758876, 6362065.390493258), (560025.9495758876, 6362065.390493258), (560025.9495758876, 6362065.890493258), (560026.4495758876, 6362065.890493258), (560026.4495758876, 6362066.890493258), (560026.9495758876, 6362066.890493258), (560026.9495758876, 6362068.390493258), (560027.4495758876, 6362068.390493258), (560027.4495758876, 6362068.890493258), (560027.9495758876, 6362068.890493258), (560027.9495758876, 6362069.390493258), (560028.4495758876, 6362069.390493258), (560028.4495758876, 6362069.890493258), (560033.4495758876, 6362069.890493258), (560033.4495758876, 6362070.390493258), (560033.9495758876, 6362070.390493258), (560033.9495758876, 6362070.890493258), (560034.4495758876, 6362070.890493258), (560034.4495758876, 6362071.390493258), (560034.9495758876, 6362071.390493258), (560034.9495758876, 6362071.890493258), (560036.4495758876, 6362071.890493258)] a_points = np.array(points) x = a_points[:, 0] y = a_points[:, 1] from pylab import * plot(x,y) show() a = fitEllipse(x,y) center = ellipse_center(a) phi = ellipse_angle_of_rotation(a) axes = ellipse_axis_length(a) print "center = ", center print "angle of rotation = ", phi print "axes = ", axes from pylab import * plot(x,y) plot(center[0:1],center[1:], color = 'red') show() each vertex is a xi,y,i point plot of 2D point and center of fit ellipse

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  • Tool to diagonalize large matrices

    - by Xodarap
    I want to compute a diffusion kernel, which involves taking exp(b*A) where A is a large matrix. In order to play with values of b, I'd like to diagonalize A (so that exp(A) runs quickly). My matrix is about 25k x 25k, but is very sparse - only about 60k values are non-zero. Matlab's "eigs" function runs of out memory, as does octave's "eig" and R's "eigen." Is there a tool to find the decomposition of large, sparse matrices? Dunno if this is relevant, but A is an adjacency matrix, so it's symmetric, and it is full rank.

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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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