Added filtering matlab file

filtering/main.m

@@ -0,0 +1,117 @@
+clear
+close all
+clc
+format compact
+
+%loading an image
+im = im2double(imread('dog.jpg'));
+
+%making image spectrum for graphics
+imf_r = mat2gray(log(abs(fftshift(fft2(im(:,:,1))))+1));
+imf_g = mat2gray(log(abs(fftshift(fft2(im(:,:,2))))+1));
+imf_b = mat2gray(log(abs(fftshift(fft2(im(:,:,3))))+1));
+imf = cat(3, imf_r, imf_g, imf_b);
+
+%graphics
+figure
+subplot(1,2,1); imshow(im)
+title('Original image')
+subplot(1,2,2); imshow(imf,[])
+title('Image spectrum (log)')
+
+%dimensions of the image
+[r,c,colors] = size(im);
+
+%making gaussian low-pass filter mask
+s = 0.1; %sigma in 1/pix
+sigma = 0.1*min([r c]);
+
+h = fspecial('gaussian',[r c],sigma); %gaussian mask
+f = linspace(-0.5,0.5,c); %frequency grid
+
+%graphics
+figure
+norm = max(max(h(r/2,:)))^-1; %normalizing coefficient
+plot(f,norm*h(r/2,:),'b')
+line([s s], [0 1], 'Color', 'r', 'LineWidth', 1)
+line(-[s s], [0 1], 'Color', 'r', 'LineWidth', 1)
+grid
+title(['Gaussian filter with \sigma = ',num2str(s),' pix^{-1}'])
+xlabel('frequency, pix^{-1}')
+
+%graphics
+figure
+imshow(log(abs(h)+1),[])
+title('Gaussian mask in frequency domain')
+
+%applying LP filter to channels spectra
+im1f_r = fftshift(fft2(im(:,:,1))).*h;
+im1f_g = fftshift(fft2(im(:,:,2))).*h;
+im1f_b = fftshift(fft2(im(:,:,3))).*h;
+
+%getting image from spectra
+im1_r = mat2gray(abs(ifft2(ifftshift(im1f_r))));
+im1_g = mat2gray(abs(ifft2(ifftshift(im1f_g))));
+im1_b = mat2gray(abs(ifft2(ifftshift(im1f_b))));
+im1 = cat(3,im1_r,im1_g,im1_b);
+
+%making image spectrum for graphics
+imf1_r = mat2gray(log(abs(fftshift(fft2(im1(:,:,1))))+1));
+imf1_g = mat2gray(log(abs(fftshift(fft2(im1(:,:,2))))+1));
+imf1_b = mat2gray(log(abs(fftshift(fft2(im1(:,:,3))))+1));
+imf1 = cat(3, imf1_r, imf1_g, imf1_b);
+
+%graphics
+figure
+subplot(1,2,1); imshow(im1,[])
+title('Filtered image')
+subplot(1,2,2); imshow(imf1,[])
+title('Filtered image spectrum (log)')
+
+%Fourier transform of gaussian mask
+hs = ifftshift(ifft2(h));
+
+%graphics
+figure
+imshow(log(abs(hs)+1),[])
+title('Gaussian mask in spatial domain')
+
+uncut = 11; %size of spatial domain mask
+cut = floor(11/2); %half-size of spatial domain mask
+
+hs_cut = hs((r/2-cut+1):(r/2+cut+1),(c/2-cut+1):(c/2+cut+1)); %cut mask
+H = sum(sum(abs(hs_cut)))^-1*abs(hs_cut); %normalized mask
+
+%grapahics
+figure
+plot(H(cut+1,:))
+grid
+title({['Cut Gaussian mask of size ', num2str(uncut) ,'x'...
+    num2str(uncut)],[' in spatial domain']})
+
+%applying mask to image
+im2 = imfilter(im, H); 
+
+%making image spectrum for graphics
+imf2_r = mat2gray(log(abs(fftshift(fft2(im2(:,:,1))))+1));
+imf2_g = mat2gray(log(abs(fftshift(fft2(im2(:,:,2))))+1));
+imf2_b = mat2gray(log(abs(fftshift(fft2(im2(:,:,3))))+1));
+imf2 = cat(3, imf2_r, imf2_g, imf2_b);
+
+%graphics
+figurep
+subplot(1,2,1); imshow(im2,[])
+title('Filtered image')
+subplot(1,2,2); imshow(imf2,[])
+title('Filtered image spectrum (log)')
+
+im3 = imfilter(im, H, 'circular'); % periodic boundary option
+
+%graphics
+figure
+subplot(1,3,1); imshow(im1(1:50,1:50,:),[])
+title('Frequency processed image')
+subplot(1,3,2); imshow(im2(1:50,1:50,:),[])
+title({['Spatially processed image'],['Zero boundary option']})
+subplot(1,3,3); imshow(im3(1:50,1:50,:),[])
+title({['Spatially processed image'],['Periodic boundary option']})