im doing face recognition project.please explain the above coding in a step by step manner in how it works

%% illumination normalization

[x y] = ndgrid(1:size(I,1),1:size(I,2)); z = double(I); [Gx Gy] = gradient(z); mag = sqrt(Gx.^2+Gy.^2); h = fspecial('average',3); smooth = imfilter(z,h); norm_x = Gx./smooth; norm_y = Gy./smooth; niter = 10; kappa = 10; lambda = 0.25; im = double(norm_x+norm_y); figure,imshow(im),title('Smoothed image'); [rows,cols] = size(im); diff = im; var = 2;

for i = 1:niter diffl = zeros(rows+2,cols+2); diffl(2:rows+1,2:cols+1) = diff; %differences deltaN = diffl(1:rows,2:cols+1) - diff; deltaS = diffl(3:rows+2,2:cols+1) - diff; deltaE = diffl(2:rows+1,3:cols+2) - diff; deltaW = diffl(2:rows+1,1:cols) - diff;

    %conduction
    cN = exp(-(deltaN/kappa).^2);
    cS = exp(-(deltaS/kappa).^2);
    cE = exp(-(deltaE/kappa).^2);
    cW = exp(-(deltaW/kappa).^2);

    diff = diff+lambda*(cN.*deltaN+cS.*deltaS+cE.*deltaE+cW.*deltaW);

end

R = mat2gray(diff); bgImg = z;%Background Image fgImg = R;%Foreground Image

%Define Alpha Factor alphaFactor = 0.2;% 0 <= alphaFactor =< 1

%Size Validation bg_size = size(bgImg); fg_size = size(fgImg); sizeErr = isequal(bg_size, fg_size); if(sizeErr == 0) disp('Error: Images to be fused should be of same dimensions'); return; end

%Fuse Images fusedImg = FuseImages(bgImg, fgImg, alphaFactor); fusedImg = 25+uint8(fusedImg);

%Display Images figure; imshow(fusedImg);title('Illumination Normalized');

%% PCA feature extraction fusedImg=im2double(fusedImg); [Evalues, Evectors, x_mean]=PCA(fusedImg); figure,imshow(Evectors,[]);title('PCA');

features=entropy(x_mean)

Answer 1

[Hari]

Hi,

The provide scirpt is mainly used for illumination normalization and PCA feature extraction.

Here is the some explanation for the same:

Illumination Normalization:

The code starts by computing the gradients of the image I using "gradient", which helps in identifying intensity changes. It then smooths the image using an averaging filter ("fspecial" and "imfilter") and normalizes the gradients.

[Gx, Gy] = gradient(double(I)); % Compute gradients
h = fspecial('average', 3); % Create averaging filter
smooth = imfilter(double(I), h); % Smooth the image
norm_x = Gx ./ smooth; % Normalize gradients

Anisotropic Diffusion:

This step performs anisotropic diffusion to enhance the image. It iteratively updates the image using conduction coefficients (cN, cS, cE, cW) to preserve edges.

for i = 1:niter
    % Compute differences and conduction coefficients
    % Update the image using the diffusion equation
end

Image Fusion:

The background and foreground images are fused using an alpha blending technique. This ensures that both images have the same dimensions before blending.

alphaFactor = 0.2;
fusedImg = FuseImages(bgImg, fgImg, alphaFactor); % Fuse images

PCA Feature Extraction:

The fused image is converted to double precision, and PCA is performed to extract features. The eigenvectors and mean are computed, and the entropy of the mean is used as a feature.

fusedImg = im2double(fusedImg);
[Evalues, Evectors, x_mean] = PCA(fusedImg); % Perform PCA
features = entropy(x_mean); % Compute entropy of the mean

Display Results:

The code displays the smoothed image, the fused image, and the PCA eigenvectors, helping visualize the effects of each processing step.

figure, imshow(im), title('Smoothed image');
figure, imshow(fusedImg), title('Illumination Normalized');
figure, imshow(Evectors, []), title('PCA');

Refer to the documentation of "gradient": https://www.mathworks.com/help/matlab/ref/gradient.html and "fspecial": https://www.mathworks.com/help/images/ref/fspecial.html for more details on these functions.

Hope this helps!