Page 102 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

90 Chapter 3

Note that CM = TM’ * CT * TM

As the pixel positions of the image are represented as positive integers,
are transformed vectors are properly biased and rounded off.

1.3 Matlab Program

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hotellinggv.m

A=imread('Binimage','bmp');
A=double(A);
[x,y]=find(A==0);
vector=[x y];
Meanvector=sum(vector)/length(vector);
CM=(vector'*vector)/length(vector);
CM=CM-Meanvector'*Meanvector;
%Covariance matrix for the original set of vectors is CM
[E,V]=eig(C);
%Transformation Matrix
TM=E';
transvector=TM*(vector'-repmat(Meanvector',1,length(vector)));
xposition=fix(transvector(1,:)+abs(min(transvector(1,:)))+1);
yposition=fix(transvector(2,:)+abs(min(transvector(2,:)))+1);
B=zeros(50,50);
for i=1:1:length(xposition)
B(xposition(i),yposition(i))=1;
end
%Covariance matrix computed for transformed vectors is computed as CT
MeanvectorT=sum(transvector')/length(transvector');
CT=(transvector*transvector')/length(transvector');
CT=CT-MeanvectorT'*MeanvectorT;
figure
subplot(2,1,1)
imshow(A)
title('ORIGINAL IMAGE')
subplot(2,1,2)
imshow(uint8(B*255))
title('TRANSFORMED IMAGE USING HOTELLING TRANSFORMATION')
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