Lab 1: Matlab primer for Image Processing

Stéphane Marchand-Maillet
Stephane.Marchand-Maillet@cui.unige.ch
Sviatoslav Voloshynovskiy
Sviatoslav.Voloshynovskyy@cui.unige.ch
 
 

March 13, 2002

Abstract:

This tutorial aims at getting you to a level in Matlab programming so that you will be able to follow subsequent exercises in the ``Advanced Image Processing'' course given at University of Geneva. This tutorial does not aim at being complete and is surely not the best you may find (on the Web for example).

Contents

• Getting started
• Online calculation and multidimensional variables
• Online calculation
• Multidimensional variables
• Specific commands
• Accessing variable elements
• 3D arrays
• Matlab programs
• Creating programs
• Example:
• Programming instructions
• if test
• for loop
• while loop
• switch test
• Some useful commands and tips
• Commands
• Tips
• Exercises

Getting started

The first thing to do is to call the Matlab environment. Depending on which platform you are using, this can be clicking on an icon (Windows) or typing the matlab command in a shell (Unix, Linux, DOS). Whatever this is, you should end up with a prompt that resembles:

                              < M A T L A B >
                  Copyright 1984-1999 The MathWorks, Inc.
                        Version 5.3.1.29215a (R11.1)
                                Oct  6 1999
  To get started, type one of these: helpwin, helpdesk, or demo.
  For product information, type tour or visit www.mathworks.com.
>>

You just entered the Matlab interpreter. You may now type commands and the result will be displayed as a response, just as in any shell.

Some useful general commands are:

• quit exits the environment.
•  help <command> where <command> is a Matlab command. By itself, help gives the list of toolboxes (packages) that are installed on your system.
•  lookfor <something> where <something> is what you are looking for in plain English. Actually, lookfor searches the expression <something> in the help pages. Try lookfor Fourier for example.
•  pwd and cd allow you to navigate in the directory structure (Unix-like notation).
•  who gives you the list of variables currently defined. whos gives you the same list with their size.
•  clear all clears all variables. clear <var1 var2> clears only the variables <var1 var2>.
•  close all close all figures. close closes the current figure.
•  help general extends this list of generic commands.

Online calculation and multidimensional variables

The matlab interpreter will respond to commands you will input at the prompt. These commands can either be ``system commands'' (eg cd) or ``calculation commands'' (eg 1+1).

Online calculation

Type

>> 1+1

the system responds and prompts for the next command:

ans =
     2
>>

(which makes worthy a CHF 1000.- investment!).

By default the result is set into a variable called ans. Therefore, typing whos gives you something like

>> whos
  Name      Size         Bytes  Class 
  ans       1x1              8  double array
Grand total is 1 elements using 8 bytes

which is fairly explicit. If you would like the result to be stored in some other variable a, say, type

>> a=1+1
a =
     2

This therefore declares and sets the variable a to 2. From now on, a may be used for its value

>> b=a+2
b =
     4

and so on. You may declare any variable, provided its name follows some simple rules (eg, starts with a letter, no +,-,/-* signs, etc).

Anytime you type a command, Matlab outputs the result. This may be avoided with terminating the command by a semi-colon (;). Therefore:

>> a=1;
>> b=2;
>> c=a+b
c =
     3

or

>> a=1;b=2;c=a+b
c =
     3

Note the difference with

>> a=1,b=2,c=a+b
a =
     1
b =
     2
c =
     3

You now know how to create (and delete - clear) variables. All generic operations are available in Matlab, use help elfun (elementary functions) for a list (see also help ops and help specfun).

Multidimensional variables

Typing a=1 creates a scalar variable a. Matlab generalises this principle to vector and matrices (a vector being a matrix with one dimension set to 1). Therefore,

>> u=[1 2 3]
u =
     1     2     3
>> v=[1;2;3]
v =
     1
     2
     3

create a row (u) and a column (v) vector. More generally,

>> m=[1 2 3 4; 5 6 7 8; 8 9 10 11]
m =
     1     2     3     4
     5     6     7     8
     8     9    10    11

creates a  matrix.

Provided their sizes correspond, most operations are available for matrices. A lot of specific operations related to linear algebra are also available and can be listed using help matfun. Note that some operations operate on the term level (cos, log, etc).

Matlab offers two other types of operations on matrices. Firstly, one may add (or multiply) a constant value to all the matrix elements

>> m+1
ans =
     2     3     4     5
     6     7     8     9
     9    10    11    12

Secondly, one may combine matrices globally

>> m=[1 2;3 4];
>> n=[1 0;0 1];
>> m*n
ans =
     1     2
     3     4

(classical matrix multiplication). Or locally

>> m.*n
ans =
     1     0
     0     4

(term per term multiplication). The fact of adding the ``.'' in front of * and / operators makes them operate locally.

Specific commands

Matlab offers several matrix manipulation commands (see help elmat for a list (these include commands for creating some specific matrices). The most basic command being the transpose command given by '

>> m=[1 2;3 4]
m =
     1 y    2
     3     4
>> m'
ans =
     1     3
     2     4

See also help sparfun for a list of commands operating on sparse matrices.

Whenever it comes to creating a list, Matlab uses matrices. Matlab offers a simple mechanism for creating some specific lists For example, the integers between 1 and 5 are given by

>> a=1:5
a =
     1     2     3     4     5

The syntax actually generalises with a step from:step:to

>> a=1:0.5:4
a =
    1.0000    1.5000    2.0000    2.5000    3.0000    3.5000    4.0000

Accessing variable elements

Matlab uses parenthesis for accessing matrix (or vector) elements

>> a=2*(1:10);
>> a(5)
ans =
    10         
>> m=[1 2 3 4; 5 6 7 8; 8 9 10 11]; 
>> m(1,2)
ans =
     2

(note that for matrices we have M(row,column)). The previous mechanism gives us a technique for extracting parts of vectors and matrices:

>> m=[1 2 3 4; 5 6 7 8; 8 9 10 11];
>> u=m(3,2:4)
u =
     9    10    11
>> b=2:4;
>> x=m(3,b)
x =
     9    10    11
>> v=m(:,4)
v =
     4
     8
    11

3D arrays

Since version 5, Matlab offers the management of 3D arrays.

>> d(:,:,1)=[1 2 3;3 4 5];
>> d(:,:,2)=[2 3 4;5 2 4];
>> d(:,:,3)=[3 4 6;7 9 3];
>> d(:,:,4)=[3 6 7;2 3 5];                                                                                    
>> whos d
  Name      Size         Bytes  Class
  d         2x3x4          192  double array

Provided sizes are consistent, matrices operations may apply on these 3D arrays.

This is one form under which a RGB images will be stored.

Matlab programs

Matlab goes beyond this simple interaction. It offers a complete set of programming commands that can be used to create loops, tests and other structure any other programming language can offer (see help lang for a list).

Creating programs

Up to now, commands were typed one after each other within the interpretor. Matlab offers the possibility to create batch programs (and functions) that can be called from the interpretor (and from other batch programs). Actually most of high-level commands of matlab correspond to batch programs. The technique is simple:

• create a file mycommand.m in the current directory
•  type commands in this file
•  execute these commands by typing mycommand in the interpretor.

Example:

Write these lines in the mycommand.m file:

% this is my first Matlab program
a=1;
b=3;
c=a+b;
fprintf(1,'c is now %d\n',c);

and type mycommand

>> mycommand
c is now 4

The detail of commands in the mycommand.m file can be found via the help facility. One thing to note is that anything after a percent (%) is a comment.

One may also create functions in a similar way. Type this in the myfunction.m file

function [result]=myfunction(a)
% [result]=addtwo(a)
% adds 2 to the input
% this is my first Matlab function
result=a+2;

and try

>> b=myfunction(3)
b =
     5

Here, it is important that the function has the same name as its file. One nice feature is that this permits online help, created by the first comments in the function file.

>> help myfunction 
  [result]=addtwo(a)
  adds 2 to the input
  this is my first Matlab function

From then on, one can build a complete library (toolbox) of functions with the appropriate documentation. Simply put all function files in a directory dir, add its path on the search path (with addpath('dir')). help dir will then display the first comments of each M-file. Any toolbox is done like this (try which logm) to see the file corresponding to the logm command.

Programming instructions

On top of calculations commands, Matlab proposes generic programming instruction for creating loops, test and so on.

if test

if I == J
  A(I,J) = 2;
elseif abs(I-J) == 1
  A(I,J) = -1;
else
  A(I,J) = 0;
end

Note: The NOT condition is given by the tilde (~=, not equal).

for loop

for I = 1:N,
 for J = 1:N,
  A(I,J) = 1/(I+J-1);
 end
end

Note that instead of 1:N we could have any integer row vector.

while loop

E = 0*A; F = E + eye(size(E)); N = 1;
while norm(E+F-E,1) > 0,
 E = E + F;
 F = A*F/N;
 N = N + 1;
end

switch test

switch lower(METHOD)
 case {'linear','bilinear'}
  disp('Method is linear')
 case 'cubic'
  disp('Method is cubic')
 case 'nearest'
  disp('Method is nearest')
 otherwise
  disp('Unknown method.')
end

See help lang for further instructions.

Some useful commands and tips

Commands

When manipulating matrices and images, the following commands are often very useful (see their respective help).

• length returns the largest dimension of an array.
•  size returns the dimension of an array
•  sum sums the element of an array along its first non-singleton dimension (columns for a matrix)
•  max returns the largest element of an array along its first non-singleton dimension (columns for a matrix)
•  min returns the smallest element of an array along its first non-singleton dimension (columns for a matrix)
•  rand generates random numbers
•  sort sorts numbers
•  conv2 operates a 2D convolution between a matrix and a mask
•  imread reads an image in a given format as a matrix
•  imwrite write a matrix as an image
•  fft2, dct2 2D- Fourier and DCT transform of an array.

Tips

• Have explicit names for variables
•  When creating a matrix, declare it first as a complete array rather than element by element. Compare:

clear m;
for i=1:500
 for j=1:500
  m(i,j)=i+j;
 end
end

and

clear m;
m=zeros(500);
for i=1:500
 for j=1:500
  m(i,j)=i+j;
 end
end

• Use global operations rather than local, ie

u=1:500;
v=u.*(u>500);

rather than

u=1:500;
for i=1:500
 if u(i)>500
  v(i)=u(i);
 else
  v(i)=0;
 end
end

• use [value index]=sort(rand(1,n)) to generate a random selection within the set of the first n integers.

Exercises

• Test whether a given matrix is symmetric, orthogonal, singular or otherwise.
•  Load an image and save it after a rotation of 90 degrees.
•  Load an image and calculate its RGB histograms (in at least two different ways).
•  Imagine what you can do with Matlab :o)

Mon Mar 12 12:10:06 MET 2001