Why is my Hotelling Transform implementation producing garbage?

I have to implement a Karhunen-Loeve / Hotelling Transform and i seemingly get garbage output. I have no errors and seemed to have respected the algorithm taught in class. I tested it using the b&w Lena image and the output is just a black and white mess. Code and testing steps provided below.

function [B] = TKL2D(image)
[numberOfLines, numberOfColumns] = size(image);

% mean value computation
imageMean = mean2(image);
stationaryImg = image - imageMean;

% autoCorr Matrix
autoCorrMat = (transpose(stationaryImg) * stationaryImg ) / size(stationaryImg, 1);

% spectral component 
[V, D] = eig(autoCorrMat);
% sorting the eigenvalues from largest to smallest, rearranging the indices
% of the V matrix and searching for the critical point between the primary
% and secondary components (using findCriticalPoint)
diagValues = diag(D);
[sortedD, indices] = sort(diagValues, 'descend');
V = V(:, indices);

% bar(sortedD)
criticalPoint = findCriticalPoint(sortedD, 0.1); % 10% error
fprintf('%i\n', criticalPoint);
slicedV = V(:, 1: criticalPoint);

% TKL2D => transformed matrix
processedImage = transpose(slicedV) * transpose(stationaryImg);

% reconstructed original matrix
B = slicedV * processedImage + imageMean;

end

function [i] = findCriticalPoint(sortedArray, baseError)
    error = baseError * sortedArray(1);
    % error is a percentage of the largest value in the ordered array of
    % eigenvalues

    for i = 1 : ( length(sortedArray) - 1)
        if (sortedArray(i) - sortedArray(i + 1)) > error
            break; 
            % stop when the diff between 2 consecutive values is larger
            % than the previously computed error (i always get 1 or 2
            % primary components)
        end
    end
end

Testing script attached below

>> image = imread('lena.png');
>> greyImg = im2double(rgb2grey(image));
>> greyImg = im2double(rgb2gray(image));
>> restored = TKL2D(greyImg);
1
>> imshow(restored)
>> 

As almost always, it seems that there's only 1 critical point.

Can any obvious flaw be identified? Thanks.

Answer 1

[yanqi liu]

yes，sir，please check

criticalPoint = findCriticalPoint(sortedD, 0.1);

it is 1，if modify it to

criticalPoint = max(20,findCriticalPoint(sortedD, 0.1));

you can get different result

[Adre Vold]

Thanks, it seems to work better now. How can i improve the overall restored quality? It seems that even if i hardcode large values i still get quite the pixelated image.

[yanqi liu]

yes，sir，may be increase error threshold