Introduction to Image Processing
This numerical tour explores some basic image processing tasks.
Contents
Installing toolboxes and setting up the path.
You need to download the following files: signal toolbox and general toolbox.
You need to unzip these toolboxes in your working directory, so that you have toolbox_signal and toolbox_general in your directory.
For Scilab user: you must replace the Matlab comment '%' by its Scilab counterpart '//'.
Recommandation: You should create a text file named for instance numericaltour.sce (in Scilab) or numericaltour.m (in Matlab) to write all the Scilab/Matlab command you want to execute. Then, simply run exec('numericaltour.sce'); (in Scilab) or numericaltour; (in Matlab) to run the commands.
Execute this line only if you are using Matlab.
getd = @(p)path(p,path); % scilab users must *not* execute this
Then you can add the toolboxes to the path.
getd('toolbox_signal/'); getd('toolbox_general/');
Image Loading and Displaying
Several functions are implemented to load and display images.
First we load an image.
% path to the images name = 'lena'; n = 256; M = load_image(name, []); M = rescale(crop(M,n));
We can display it. It is possible to zoom on it, extract pixels, etc.
clf; imageplot(M, 'Original', 1,2,1); imageplot(crop(M,50), 'Zoom', 1,2,2);
Image Modification
An image is a 2D array, that can be modified as a matrix.
clf; imageplot(-M, '-M', 1,2,1); imageplot(M(n:-1:1,:), 'Flipped', 1,2,2);
Blurring is achieved by computing a convolution with a kernel.
% compute the low pass kernel k = 9; h = ones(k,k); h = h/sum(h(:)); % compute the convolution Mh = perform_convolution(M,h); % display clf; imageplot(M, 'Image', 1,2,1); imageplot(Mh, 'Blurred', 1,2,2);
Several differential and convolution operators are implemented.
G = grad(M); clf; imageplot(G(:,:,1), 'd/dx', 1,2,1); imageplot(G(:,:,2), 'd/dy', 1,2,2);
Fourier Transform
The 2D Fourier transform can be used to perform low pass approximation and interpolation (by zero padding).
Compute and display the Fourier transform (display over a log scale). The function fftshift is useful to put the 0 low frequency in the middle. After fftshift, the zero frequency is located at position (n/2+1,n/2+1).
Mf = fft2(M); Lf = fftshift(log( abs(Mf)+1e-1 )); clf; imageplot(M, 'Image', 1,2,1); imageplot(Lf, 'Fourier transform', 1,2,2);
Exercice 1: (the solution is exo1.m) To avoid boundary artifacts and estimate really the frequency content of the image (and not of the artifacts!), one needs to multiply M by a smooth windowing function h and compute fft2(M.*h). Use a sine windowing function. Can you interpret the resulting filter ?
exo1;
Exercice 2: (the solution is exo2.m) Perform low pass filtering by removing the high frequencies of the spectrum. What do you oberve ?
exo2;
It is possible to do image interpolating by adding high frequencies
p = 64; n = p*4; M = load_image('boat', 2*p); M = crop(M,p); Mf = fftshift(fft2(M)); MF = zeros(n,n); sel = n/2-p/2+1:n/2+p/2; sel = sel; MF(sel, sel) = Mf; MF = fftshift(MF); Mpad = real(ifft2(MF)); clf; imageplot( crop(M), 'Image', 1,2,1); imageplot( crop(Mpad), 'Interpolated', 1,2,2);
A better way to do interpolation is to use cubic-splines. It avoid ringing artifact because the spline kernel has a smaller support with less oscillations.
Mspline = image_resize(M,n,n); clf; imageplot( crop(Mpad), 'Fourier (sinc)', 1,2,1); imageplot( crop(Mspline), 'Spline', 1,2,2);
