pca.zip_The Image_bounding box_bounding box and pca_pca image_sh

function [res1,res2,mbbw,mbbh,mx,my]=pca(im) %im: image binaire %res1 orientation de l'objet: angle polaire dans [0,2PI] %res2 image transform�e par pca suivant ses axes naturels %mbbw=xmax-xmin mbbh=ymax-ymin dans l'space pca ou le MBB min bounding box %mx,may centroide %vari variance suivant la composante principale [h w]=size(im); res2=zeros(h,w); xmin=9999.0; xmax=-999.0; ymin=9999.0; ymax=-999.0; t=sum(im(:));%nb element v=zeros(t,2);%liste des pt � traiter c=zeros(2);%mat de covariance res=zeros(2);%matrice de transformation %on trouve la liste des pt � traiter i=1; for x=1:w for y=1:h if im(y,x) v(i,1)=x; v(i,2)=y; i=i+1; end end end %moyenne des pt mx=mean(v(:,1)); my=mean(v(:,2)); %recentrage de la liste sv=v;%save list v(:,1)=v(:,1)-mx; v(:,2)=v(:,2)-my; %matrice de covariance e1=dot(v(:,1),v(:,1)); e2=dot(v(:,1),v(:,2)); e3=dot(v(:,2),v(:,2)); c(1,1)=e1;c(1,2)=e2; c(2,1)=e2;c(2,2)=e3; c=double(c)/double(t); %resolution du polynome caracteristique tmp=c(1,1)+c(2,2); delta=tmp*tmp - 4.0*( c(1,1)*c(2,2)-c(2,1)*c(1,2) ); delta=sqrt(delta); lamda1=(tmp+delta)*0.5; lamda2=(tmp-delta)*0.5; if lamda2>lamda1 tmp=lamda1; lamda1=lamda2; lamda2=tmp; end %ker(c-lamda.I) %vect propre 1 vp1=[1.0 0.0]; cp=c; cp(1,1)=cp(1,1)-lamda1; cp(2,2)=cp(2,2)-lamda1; if cp(1,2)>0 vp1=[ 1.0 -cp(1,1)/cp(1,2) ]; else if cp(2,2)>0 vp1=[ -cp(2,1)/cp(2,2) 1.0 ]; end end %vect propre 1 vp2=[0.0 1.0]; cp=c; cp(1,1)=cp(1,1)-lamda2; cp(2,2)=cp(2,2)-lamda2; if cp(1,2)>0 vp2=[ 1.0 -cp(1,1)/cp(1,2) ]; else if cp(2,2)>0 vp2=[ -cp(2,1)/cp(2,2) 1.0 ]; end end %res vp1=vp1/sqrt(dot(vp1,vp1)); vp2=vp2/sqrt(dot(vp2,vp2)); res(1,1)=vp1(1);res(1,2)=vp2(1); res(2,1)=vp1(2);res(2,2)=vp2(2); %res1: orientation de vp1 par rapport � (ox) res1=atan2(vp1(2),vp1(1)); %transformation pca res=res'; for i=1:t pt=[sv(i,1)-mx sv(i,2)-my]'; pt=res*pt; x=pt(1)+mx; y=pt(2)+my; xmin=min(x,xmin); xmax=max(x,xmax); ymin=min(y,ymin); ymax=max(y,ymax); x=uint32( max(1,min(x,256)) ); y=uint32( max(1,min(y,256)) ); res2(y,x)=1; end mbbw=xmax-xmin; mbbh=ymax-ymin;