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);