added PCA solution

projects/project_pca_natural_images/solution/ConeResponse.m

@@ -0,0 +1,31 @@
+function Y = ConeResponse(X)
+
+wl_r = 700;
+wl_g = 510;
+wl_b = 440;
+wl = [wl_r; wl_g; wl_b];
+
+mu_s = 445;
+mu_m = 545;
+mu_l = 575;
+
+sig_s = 20;
+sig_m = 40;
+sig_l = 45;
+
+s = gauss(wl,mu_s,sig_s)/gauss(mu_s,mu_s,sig_s);
+m = gauss(wl,mu_m,sig_m)/gauss(mu_m,mu_m,sig_m);
+l = gauss(wl,mu_l,sig_l)/gauss(mu_l,mu_l,sig_l);
+
+S = X'*s;
+M = X'*m;
+L = X'*l;
+
+Y = [L, M, S]';
+% 
+% close all
+% hold on
+% plot(lam,s,'b')
+% plot(lam,m,'g')
+% plot(lam,l,'r')
+% hold off

projects/project_pca_natural_images/solution/gauss.m

@@ -0,0 +1,3 @@
+function Y = gauss(X,mu,sigma)
+Y = exp(-0.5*((X-mu)/sigma).^2)./sqrt(2*pi*sigma^2);
+% Y = Y/exp(-0.5*(mu/sigma).^2)./sqrt(2*pi*sigma^2);

projects/project_pca_natural_images/solution/main.m

@@ -0,0 +1,65 @@
+clear all
+close all
+pic = imread('D:\Dokumente\MATLAB\Matlabkurs2018\pca\natimg.jpg');
+pic = pic(end:-1:1,:,:);
+
+red   = double(pic(:,:,1));
+green = double(pic(:,:,2));
+blue  = double(pic(:,:,3));
+% mat = [red(:),green(:),blue(:)];
+
+mat = reshape(double(pic),size(pic,1)*size(pic,2),size(pic,3))';
+cones = ConeResponse(mat);
+% [coeff, score, latent] = pca(mat,'Centered',false);
+% [coeff, score, latent] = pca(cones,'Centered',false);
+
+% n = 10000;
+% cones = cones(:,randi([1,size(cones,2)],1,n));
+cones = mat;
+cv = cov(cones');
+[ev, ew] = eig(cv);
+[ew, ew_idx] = sort(diag(ew), 'descend');
+coeff = cones'*ev(:,ew_idx);
+% coeff = [coeff'; zeros(size(pic,1)*size(pic,2)-size(coeff,2),3)];
+
+
+c1 = reshape(coeff(:,1),size(pic,1),size(pic,2));
+c2 = reshape(coeff(:,2),size(pic,1),size(pic,2));
+c3 = reshape(coeff(:,3),size(pic,1),size(pic,2));
+
+% score
+
+figure
+subplot(221)
+contourf(red)
+axis('square')
+
+subplot(222)
+contourf(green)
+axis('square')
+
+subplot(223)
+contourf(blue)
+axis('square')
+colormap('gray')
+
+subplot(224)
+imshow('D:\Dokumente\MATLAB\Matlabkurs2018\pca\natimg.jpg')
+axis('square')
+
+figure
+subplot(221)
+contourf(c1)
+axis('square')
+
+subplot(222)
+contourf(c2)
+axis('square')
+colormap('gray')
+
+subplot(223)
+contourf(c3)
+axis('square')
+colormap('gray')
+
+% score