特征子空间 matlab,使用张量子空间分析进行图像特征值提取

*人脸识别中TesorLDAA算法Matlab程序

clc;clear;

cd E:人脸识别ORL人脸图库样本：测试集5_5train

fdir=dir('*.bmp');

fnum1=size(fdir,1);

nbcol=255;

class=15;

% M_Xtran=0;

for i=1:fnum1

imgname=fdir(i,1).name;

d=imread(imgname);

a=double(d);

[m,n]=size(a);

Xtran(:,:,i)=a;

% Xtran(:,i)=reshape(a,m*n,1);

% M_Xtran=M_Xtran+a;

end

M_Xtran=sum(Xtran(:,:,:),3);

M_X_mean=M_Xtran/fnum1;%求均值矩阵M(X)

%计算类内均值矩阵M(X)

for i=1:class

Xtran_class_mean(:,:,i)=sum(Xtran(:,:,5*(i-1)+1:5*(i-1)+5),3)/5;

end

%计算Sw,Sv

Sw_U=0;

Sb_U=0;

Sw_V=0;

Sb_V=0;

for i=1:class

d=Xtran_class_mean(:,:,i);

for j=5*(i-1)+1:5*(i-1)+5

h=Xtran(:,:,j);

Sw_U=Sw_U+(h-d)'*(h-d);

Sw_V=Sw_V+(h-d)*(h-d)';

end

end

C_k=fnum1/class;

for i=1:class

d= Xtran_class_mean(:,:,i);

Sb_U=Sb_U+C_k*(d-M_X_mean)'*(d-M_X_mean);

Sb_V=Sb_V+C_k*(d-M_X_mean)*(d-M_X_mean)';

end

%计算投影矩阵U，V

SS_V=inv(Sw_V)*(Sb_V);

SS_U=inv(Sw_U)*(Sb_U);

[U11,D11]=eig(SS_V);

[V11,E11]=eig(SS_U);

u1=U11(:,1);

v1=V11(:,1);

d1=D11(:,1);

e1=E11(:,1);

U=u1;

V=v1;

D=d1;

E=e1;

Au=eye(m);

Av=eye(n);

for i=2:m

Bv=U'*inv(Sw_V)*U;

Mv=(Au-inv(Sw_V)*U*inv(Bv)*U')*SS_V;

[UKK,DKK]=eig(Mv);

uk=UKK(:,1);

dk=DKK(:,1);

U=[U uk];

D=[D dk];

end

for i=2:n

Bu=V'*inv(Sw_U)*V;

Mu=(Av-inv(Sw_U)*V*inv(Bu)*V')*SS_U;

[VKK,EKK]=eig(Mu);

vk=VKK(:,1);

ek=EKK(:,1);

V=[V vk];

E=[E ek];

end

%降维

Tr_D=sum(D(1,:));

for i=1:m

Tr_d=sum(D(1,1:i));

Per_d_D=Tr_d/Tr_D;

if Per_d_D>=0.90

k=i;

break,end

end

Tr_E=sum(E(1,:));

for i=1:n

Tr_e=sum(E(1,1:i));

Per_e_E=Tr_e/Tr_E;

if Per_e_E>=0.90

l=i;

break,end

end

u=U(:,1:k);

v=V(:,1:l);

% % %查看矩阵U，V的正交性

S_U_1=U*U';

S_V_1=V*V';

% %还原图像检测投影矩阵的可行性

% figure(1)

% t1=Xtran(:,:,1);

% imshow(uint8(t1));

% grid on

% figure(2)

% t2=U*U'*t1*V*V';

% imshow(uint8(t2));

% grid on

% figure(3)

% t3=u*u'*t1*v*v';

% imshow(uint8(t3));

% grid on

% %叠代

% %计算Sw,Sv

Sw_U=0;

Sb_U=0;

Sw_V=0;

Sb_V=0;

for i=1:class

d= Xtran_class_mean(:,:,i);

for j=5*(i-1)+1:5*(i-1)+5

h=Xtran(:,:,j);

Sw_U=Sw_U+(h-d)'*u*u'*(h-d);

Sw_V=Sw_V+(h-d)*v*v'*(h-d)';

end

end

C_k=fnum1/class;

for i=1:class

d= Xtran_class_mean(:,:,i);

Sb_U=Sb_U+C_k*(d-M_X_mean)'*u*u'*(d-M_X_mean);

Sb_V=Sb_V+C_k*(d-M_X_mean)*v*v'*(d-M_X_mean)';

end

% %二次计算投影矩阵U，V

SS_V=inv(Sw_V)*(Sb_V);

SS_U=inv(Sw_U)*(Sb_U);

[U11,D11]=eig(SS_V);

[V11,E11]=eig(SS_U);

u1=U11(:,1);

v1=V11(:,1);

d1=D11(:,1);

e1=E11(:,1);

% fprintf('d1=%dn',d1);

% fprintf('e1=%dn',e1);

U=u1;

V=v1;

D=d1;

E=e1;

Au=eye(m);

Av=eye(n);

for i=2:m

Bv=U'*inv(Sw_V)*U;

Mv=(Au-inv(Sw_V)*U*inv(Bv)*U')*SS_V;

[UKK,DKK]=eig(Mv);

uk=UKK(:,1);

dk=DKK(:,1);

U=[U uk];

D=[D dk];

end

for i=2:n

Bu=V'*inv(Sw_U)*V;

Mu=(Av-inv(Sw_U)*V*inv(Bu)*V')*SS_U;

[VKK,EKK]=eig(Mu);

vk=VKK(:,1);

ek=EKK(:,1);

V=[V vk];

E=[E ek];

end

% Tr_d1_D=trace(d1)/trace(D);

% Tr_e1_E=trace(e1)/trace(E);

% %查看矩阵U，V的正交性

S_U_2=U*U';

S_V_2=V*V';

% %

% % %还原图像检测投影矩阵的可行性

% t4=U*U'*t1*V*V';

% figure(4)

% imshow(uint8(t4));

% grid on

% % 降维

% %选取占特征值综合的X%的特征值对应的特征向量组成投影矩阵,

Tr_D=sum(D(1,:));

for i=1:m

Tr_d=sum(D(1,1:i));

Per_d_D=Tr_d/Tr_D;

if Per_d_D>=0.90

k=i;

break,end

end

Tr_E=sum(E(1,:));

for i=1:n

Tr_e=sum(E(1,1:i));

Per_e_E=Tr_e/Tr_E;

if Per_e_E>=0.90

l=i;

break,end

end

u=U(:,1:k);

v=V(:,1:l);

% % %查看矩阵u，v的正交性

% S_u=u*u';

% S_v=v*v';

%

% % %还原图像检测投影矩阵的可行性

% t5=u*u'*t4*v*v';

% figure(5)

% imshow(uint8(t5));

% grid on

% figure(5)

% z=u*u'*M_X_mean*v*v';

% imshow(uint8(z));

% grid on

%把图像矩阵影射到张量子空间中

for i=1:fnum1

d=Xtran(:,:,i);

e=u'*d*v;

Ytran(:,:,i)=e;

end

% % %查看投影到张量子空间后的图像形状

% c=Ytran(:,1);

% d=reshape(c,k,l);

% figure(6)

% imshow(uint8(d));

% grid on

%计算投影到张量子空间中的图像类内均值

% for i=1:class

% Ytran_class_mean(:,:,i)=sum(Ytran(:,:,10*(i-1)+1:10*(i-1)+10),3)/10;

% end

%人脸识别

cd E:人脸识别ORL人脸图库样本：测试集5_5test

fdir=dir('*.bmp');

fnum2=size(fdir,1);

for i=1:fnum2

imgname=fdir(i,1).name;

d=imread(imgname);

a=double(d);

[m,n]=size(a);

Xtest(:,:,i)=a;

end

for i=1:fnum2

f=Xtest(:,:,i);

g=u'*f*v;

Ytest(:,:,i)=g;

end

correct=0;

error=0;

for i=1:fnum2

h=Ytest(:,:,i);

for j=1:fnum1

f=Ytran(:,:,j);

% dis(i,j) =sqrt(sum(sum((f-h)*(f-h)')));

% r=(f-h)*(f-h)';

% [P,Q]=eig(r);

% dis(i,j)=sqrt(trace(Q*Q'));

% %识别率为X%=95%, Y=163,Z=81.5

dis(i,j) = sqrt(sum(sum((f-h).^2)));

%识别率为 X%=95%,Y=168 ,Z=84

% X%=90%,Y=168,Z=84

end

end

for i=1:fnum2

[mind,ind] = min(dis');

if ceil(ind(i)/5) == ceil(i/5)

correct = correct + 1;

else

error = error + 1;

end

end

correct_detection=correct/(correct+error);

fprintf('correct=%dn',correct);

fprintf('error=%dn',error);