%?Karhunen-Loeve?for?face?recognition?
%?By?Alex?Chirokov?Alex.Chirokov@gmail.com
clear?all;

%?Load?the?ATT?image?set
k?=?0;
for?i=1:1:40
????for?j=1:1:10
????????filename??=?sprintf（‘C:\\MATLAB\\att_faces\\s%d\\%d.pgm‘ij）;
????????image_data?=?imread（filename）;
????????k?=?k?+?1;
????????x（:k）?=?image_data（:）;?
????????anot_name（k:）?=?sprintf（‘%2d:%2d‘ij）;???%?for?plot?annotations
?????end;
end;
nImages?=?k;?????????????????????%total?number?of?images
imsize?=?size（image_data）;???????%size?of?image?（they?all?should?have?the?same?size）?
nPixels?=?imsize（1）*imsize（2）;???%number?of?pixels?in?image
x?=?double（x）/255;???????????????%convert?to?double?and?normalize
%Calculate?the?average
avrgx?=?mean（x‘）‘;
for?i=1:1:nImages
????x（:i）?=?x（:i）?-?avrgx;?%?substruct?the?average
end;
subplot（221）;?imshow（reshape（avrgx?imsize））;?title（‘mean?face‘）
%compute?covariance?matrix
cov_mat?=?x‘*x;
[VD]?=?eig（cov_mat）;?????????%eigen?values?of?cov?matrix
V?=?x*V*（abs（D））^-0.5;???????????????
subplot（222）;?imshow（ScaleImage（reshape（V（:nImages??）imsize）））;?title（‘1st?eigen?face‘）;
subplot（223）;?imshow（ScaleImage（reshape（V（:nImages-1）imsize）））;?title（‘2st?eigen?face‘）;
subplot（224）;?plot（diag（D））;?title（‘Eigen?values‘）;

%image?decomposition?coefficients
KLCoef?=??x‘*V;?

%reconstruction?of?Image
%KLCoef（:1:1:1）=?0;??%?filtration
image_index?=?12;??%index?of?face?to?be?reconstructed
reconst?=?V*KLCoef‘;
diff?=?abs（reconst（:image_index）?-?x（:image_index））;
strdiff_sum?=?sprintf（‘delta?per?pixel:?%e‘sum（sum（diff））/nPixels）;
figure;
subplot（221）;?imshow（（reshape（avrgx+reconst（:image_index）?imsize）））;?title（‘Reconstructed‘）;
subplot（222）;?imshow（（reshape（avrgx+x（:image_index）?imsize）））;title（‘original‘）;
subplot（223）;?imshow（ScaleImage（reshape（diff?imsize）））;?title（strdiff_sum）;

for?i=1:1:nImages
????dist（i）?=?sqrt（dot（KLCoef（1:）-KLCoef（i:）?KLCoef（1:）-KLCoef（i:）））;?%euclidean
end;
subplot（224）;?plot（dist‘.-‘）;?title（‘euclidean?distance?from?the?first?face‘）;

%2D?plot?of?first?2?decomposition?coefficients?with?annotatons
%?annotations?have?format?Face:Extression?i.e?5:6?means?image?was?taken
%?from?s5/6.pgm?expression?6?of?the?person?in?the?set?s5.
figure;
show_faces?=?1:1:nImages/2;
plot（KLCoef（show_facesnImages）?KLCoef（show_facesnImages-1）‘.‘）;?title（‘Desomposition:?Numbers?indicate?（Face:expression）‘）;
for?i=show_faces
????name?=?anot_name（i:）;
????text（KLCoef（inImages）?KLCoef（inImages-1）name‘FontSize‘8）;
end;

%?Find?similar?faces??variable?‘image_index‘?defines?face?used?in?comparison?
image_index?=?78;
for?i=1:1:nImages
????dist_comp（i）?=?sqrt（dot（KLCoef（image_index:）-KLCoef（i:）?KLCoef（image_index:）-KLCoef（i:）））;?%euclidean
????strDist（i）?=?cellstr（sprintf（‘%2.2f\n‘dist_comp（i）））;
end;
[sorted?sorted_index]?=?sort（dist_comp）;?%?sort?distances
figure;?%?open?new?figure
for?i=1:1:9
????subplot（33i）;?imshow（（reshape（avrgx+x（:so

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????3071??2005-02-24?15:03??Karhunen-Loeve?Decomposition?for?Face?Recognition\KarhunenLoeve.m

?????文件????????114??2005-02-20?19:54??Karhunen-Loeve?Decomposition?for?Face?Recognition\ScaleImage.m

?????目錄??????????0??2006-04-13?22:55??Karhunen-Loeve?Decomposition?for?Face?Recognition

-----------?---------??----------?-----??----

?????????????????3185????????????????????3