Question

I want to create an image compression program with matlab use PCA. I have the code listed below. But this code is fail, the image is colorless, but still gray. Can you help me to fix my code.

clc
clear all

picture = im2double(imread('picture1.jpg'));

Red = picture(:,:,1);

premean = mean(Red(:));
premax = max(Red(:));
premin = min(Red(:));
x = size(Red,1);
y = size(Red,2);
Z = ones(x,y)*premean;
A = (Red - Z)*(1/premax - premin);

B = cov(A);
[veceig,eig,C] = pcacov(B);

NewRed = A*veceig(:,1:50);
ReturnRed = NewRed*veceig(:,1:50);
Return2Red = ((premax - premin)*ReturnRed)+ Z;

Green = picture(:,:,2);

premean_2 = mean(Green(:));
premax_2 = max(Green(:));
premin_2 = min(Green(:));
x2 = size(Green,1);
y2 = size(Green,2);
Z2 = ones(x2,y2)*premean_2;
A2 = (Green - Z2)*(1/premax_2 - premin_2);

D = cov(A2);
[veceig2,eig,E] = pcacov(D);

NewGreen = A2*veceig2(:,1:50);
ReturnGreen = NewGreen*veceig2(:,1:50);
Return2Green = ((premax_2 - Premin_2)*ReturnGreen)+ Z2;

Blue = picture(:,:,3);

premean_3 = mean(Blue(:));
premax_3 = max(Blue(:));
premin_3 = min(Blue(:));
x3 = size(Blue,1);
y3 = size(Blue,2);
Z3 = ones(x3,y3)*premean_3;
A3 = (Blue - Z3)*(1/premax_3 - premin_3);

F = cov(A3);
[veceig3,eig,G] = pcacov(F);

NewBlue = A3*veceig3(:,1:50);
ReturnBlue = NewBlue*veceig3(:,1:50);
Return2Blue = ((premax_3 - Premin_3)*Return2Blue)+ Z3;

figure,plot(cumsum(C)),cumsum(E),cumsum(G);

figure,imshow(A:A2:A2);
title('Original Image Normalization');

figure,imshow(ReturnRed:ReturnBlue:ReturnGreen);
title('Original Result of Decompression Normalization');

figure,imshow(Red:Green:Blue);

imshow(Red:Green:Blue);

Answer 1

Here I introduce a Matlab code for image compression using the very easy algorithm of PCA, in my code, I haven't used predefined functions for PCA but wrote the algorithm myself for a better understanding of PCA

clear;
	clc;
	% Start of PCA code,
	Data = imread('/home/ammar/Desktop/PCA/Ammar3.png');
	Data_gray = rgb2gray(Data);
	Data_grayD = im2double(Data_gray);
	figure,
	set(gcf,'numbertitle','off','name','Grayscale Image'),
	imshow(Data_grayD)
	Data_mean = mean(Data_grayD);
	[a b] = size(Data_gray);
	Data_meanNew = repmat(Data_mean,a,1);
	DataAdjust = Data_grayD – Data_meanNew;
	cov_data = cov(DataAdjust);
	[V, D] = eig(cov_data);
	V_trans = transpose(V);
	DataAdjust_trans = transpose(DataAdjust);
	FinalData = V_trans * DataAdjust_trans;
	% End of PCA code
	% Start of Inverse PCA code,
	OriginalData_trans = inv(V_trans) * FinalData;
	OriginalData = transpose(OriginalData_trans) + Data_meanNew;
	figure,
	set(gcf,'numbertitle','off','name','RecoveredImage'),
	imshow(OriginalData)
	% End of Inverse PCA code
	% Image compression
	PCs=input('Enter number of PC colomuns needed? ');
	PCs = b - PCs;
	Reduced_V = V;
	for i = 1:PCs,
	Reduced_V(:,1) =[];
	end
	Y=Reduced_V'* DataAdjust_trans;
	Compressed_Data=Reduced_V*Y;
	Compressed_Data = Compressed_Data' + Data_meanNew;
	figure,
	set(gcf,'numbertitle','off','name','Compressed Image'),
	imshow(Compressed_Data)
	% End of image compression

Results:

Original image

After keeping only 5 eigenvectors

After keeping only 10 eigenvectors

After keeping only 20 eigenvectors