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Introduction to Image Processing

Introduction to Image Processing

This numerical tour explores some basic image processing tasks.


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.


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.

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.

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
imageplot(M, 'Image', 1,2,1);
imageplot(Mh, 'Blurred', 1,2,2);

Several differential and convolution operators are implemented.

G = grad(M);
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 ));
imageplot(M, 'Image', 1,2,1);
imageplot(Lf, 'Fourier transform', 1,2,2);

Exercice 1: (check the solution) 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 ?


Exercice 2: (check the solution) Perform low pass filtering by removing the high frequencies of the spectrum. What do you oberve ?


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));
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);
imageplot( crop(Mpad), 'Fourier (sinc)', 1,2,1);
imageplot( crop(Mspline), 'Spline', 1,2,2);