NMF 非负矩阵分解 图像重构

%% 图像数据提取 clc,clear I1=imread('att_faces/s1/1.pgm'); I2 = imread('att_faces/s1/2.pgm'); I3 = imread('att_faces/s1/3.pgm'); I4 = imread('att_faces/s1/4.pgm'); I5 = imread('att_faces/s1/5.pgm'); I6 = imread('att_faces/s1/6.pgm'); I7 = imread('att_faces/s1/7.pgm'); I8 = imread('att_faces/s1/8.pgm'); I9 = imread('att_faces/s1/9.pgm'); I10 = imread('att_faces/s1/10.pgm'); [Sn Sm]=size(I1); Scal=0.75; %图像缩放比例 Wid=round(Sm*Scal); Hei=round(Sn*Scal); Person1=[I1;I2;I3;I4;I5;I6;I7;I8;I9;I10]; Person1=imresize(Person1,[Hei*10 Wid]); %resize为每幅图像的宽度的10倍 figure(1) imshow(Person1,'border', 'loose') I1=imread('att_faces/s2/1.pgm'); I2 = imread('att_faces/s2/2.pgm'); I3 = imread('att_faces/s2/3.pgm'); I4 = imread('att_faces/s2/4.pgm'); I5 = imread('att_faces/s2/5.pgm'); I6 = imread('att_faces/s2/6.pgm'); I7 = imread('att_faces/s2/7.pgm'); I8 = imread('att_faces/s2/8.pgm'); I9 = imread('att_faces/s2/9.pgm'); I10 = imread('att_faces/s2/10.pgm'); Person2=[I1;I2;I3;I4;I5;I6;I7;I8;I9;I10]; Person2=imresize(Person2,[round(Sn*10*Scal) round(Sm*Scal)]); % figure(2) % imshow(Person2,'border', 'loose') I1=imread('att_faces/s3/1.pgm'); I2 = imread('att_faces/s3/2.pgm'); I3 = imread('att_faces/s3/3.pgm'); I4 = imread('att_faces/s3/4.pgm'); I5 = imread('att_faces/s3/5.pgm'); I6 = imread('att_faces/s3/6.pgm'); I7 = imread('att_faces/s3/7.pgm'); I8 = imread('att_faces/s3/8.pgm'); I9 = imread('att_faces/s3/9.pgm'); I10 = imread('att_faces/s3/10.pgm'); Person3=[I1;I2;I3;I4;I5;I6;I7;I8;I9;I10]; Person3=imresize(Person3,[round(Sn*10*Scal) round(Sm*Scal)]); % figure(3) % imshow(Person3,'border', 'loose') I1=imread('att_faces/s4/1.pgm'); I2 = imread('att_faces/s4/2.pgm'); I3 = imread('att_faces/s4/3.pgm'); I4 = imread('att_faces/s4/4.pgm'); I5 = imread('att_faces/s4/5.pgm'); I6 = imread('att_faces/s4/6.pgm'); I7 = imread('att_faces/s4/7.pgm'); I8 = imread('att_faces/s4/8.pgm'); I9 = imread('att_faces/s4/9.pgm'); I10 = imread('att_faces/s4/10.pgm'); Person4=[I1;I2;I3;I4;I5;I6;I7;I8;I9;I10]; Person4=imresize(Person4,[round(Sn*10*Scal) round(Sm*Scal)]); % figure(4) % imshow(Person4,'border', 'loose') AllPerson=zeros(Hei*Wid,40); %40个人，40列 for i=1:1:Hei*10 for j=1:1:Wid rows=mod((i-1)*69+j,84*69); %行 if rows==0 rows=84*69; end cols=ceil(i/Hei); %列 AllPerson(rows,cols)=Person1(i,j); end end for i=1:1:Hei*10 for j=1:1:Wid rows=mod((i-1)*69+j,84*69); %行 if rows==0 rows=84*69; end cols=ceil(i/Hei)+10; %列 AllPerson(rows,cols)=Person2(i,j); end end for i=1:1:Hei*10 for j=1:1:Wid rows=mod((i-1)*69+j,84*69); %行 if rows==0 rows=84*69; end cols=ceil(i/Hei)+20; %列 AllPerson(rows,cols)=Person3(i,j); end end for i=1:1:Hei*10 for j=1:1:Wid rows=mod((i-1)*69+j,84*69); %行 if rows==0 rows=84*69; end cols=ceil(i/Hei)+30; %列 AllPerson(rows,cols)=Person4(i,j); end end figure(5) AllPerson=AllPerson'; AllPerson=mat2gray(AllPerson); %0-1之间的double数 84*69 40个人 %AllPerson=AllPerson'; imshow(AllPerson,'border', 'loose') AllPerson=AllPerson'; %% NMF分解 V=AllPerson; [n m]=size(V); r=30; %降维后的维数 W=double(rand(n,r)); H=double(rand(r,m)); VHT=V*H'; WHHT=W*(H*H'); WTV=W'*V; WTWH=W'*W*H; W1=zeros(n,r); H1=zeros(r,m); Temp=zeros(n,m); for k=1:500 W=W.*(VHT./WHHT); WTV=W'*V; WTWH=W'*W*H; H=H.*(WTV./WTWH); VHT=V*H'; WHHT=W*(H*H'); i(k)=k; Temp=V-W*H; Temp=Temp.*Temp; e(k)=sum(sum(Temp)); end %% 还原特征图像 figure(6) W=W'; imshow(mat2gray(W)) title('基图像') W=W'; figure(10) imshow(mat2gray(H)); imageD=W*H; %重构图像 figure(7); imshow(mat2gray(imageD)); title('重构出的图像矩阵') figure(8) plot(i,e) title('误差值变化趋势图') xlabel('迭代次数') ylabel('误差值') ReImage=zeros(r*Hei,Wid); for i=1:1:Hei*r for j=1:1:Wid rows=mod((i-1)*69+j,84*69); %行 if rows==0 rows=84*69; end cols=ceil(i/Hei); %列 ReImage(i,j)=W(rows,cols); end end ReImage=ReImage'; figure(20); imshow(mat2gray(ReImage)); title('从W中还原图像') %纯粹是为了显示图像方便 ReImage=ReImage'; Image1=zeros(840,69); Image2=zeros(840,69); Image3=zeros(840,69); for i=1:1:840 for j=1:1:69 Image1(i,j)=255-ReImage(i,j); end end for i=1:1:840 for j=1:1:69 Image2(i,j)=255-ReImage(i+840,j); end end for i=1:1:840 for j=1:1:69 Image3(i,j)=255-ReImage(i+1680,j); end end figure(21) subplot(1,3,1) imshow(mat2gray(Image1),'border', 'loose') subplot(1,3,2) imshow(mat2gray(Image2),'border', 'loose') subplot(1,3,3) imshow(mat2gray(Image3),'border', 'loose') %从ImageD中还原图像 PersonT=zeros(84,69); for i=1:1:Hei for j=1:1:Wid rows=mod((i-1)*69+j,84*69); if rows==0 rows=84*69; end cols=ceil(i/Hei); PersonT(i,j)=imageD(rows,cols); end end figure(22) imshow(mat2gray(PersonT),'border', 'loose') title('还原出的某一个脸'); % Person1=Person1'; % subplot(4,1,1) % imshow(Person1,'border', 'loose') % Person2=Person2'; % subplot(4,1,2) % imshow(Person2,'border', 'loose') % Person3=Person3'; % subplot(4,1,3) % imshow(Person3,'border', 'loose') % Person4=Person4'; % subplot(4,1,4) % imshow(Person4,'border', 'loose')