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% Introducing Matlab (adapted from http://www.cns.nyu.edu/~eero and
% http://www.cs.dartmouth.edu/~farid/teaching/cs88/matlab.intro.html)
% via http://www-cse.ucsd.edu/%7Esjb/classes/matlab/matlab.intro.html
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% (1) Help and basics
% The symbol "%" is used in front of a comment.
% To get help type "help" (will give list of help topics) or "help topic"
% If you don't know the exact name of the topic or command you are looking for,
% type "lookfor keyword" (e.g., "lookfor regression")
% When writing a long matlab statement that exceeds a single row use ...
% to continue statement to next row.
% When using the command line, a ";" at the end means matlab will not
% display the result. If ";" is omitted then matlab will display result.
% Use the up-arrow to recall commands without retyping them (and down
% arrow to go forward in commands).
% Other commands borrowed from emacs and/or tcsh:
% C-a moves to beginning of line (C-e for end), C-f moves forward a
% character (C-b moves back), C-d deletes a character, C-k deletes
% the line to the right of the cursor, C-p goes back through the
% command history and C-n goes forward (equivalent to up and down arrows),
% tab command completion.
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% (2) Objects in matlab -- the basic objects in matlab are scalars,
% vectors, and matrices...
N = 5 % a scalar
v = [1 0 0] % a row vector
v = [1;2;3] % a column vector
v = v' % transpose a vector
(row to column or column to row)
v = [1:.5:3] % a vector in a specified range:
v = pi*[-4:4]/4 % [start:end] or [start:stepsize:end]
v = [] % empty vector
m = [1 2 3; 4 5 6] % a matrix: 1ST parameter is ROWS
% 2ND parameter is COLS
m = zeros(2,3) % a matrix of zeros
v = ones(1,3) % a matrix of ones
m = eye(3) % identity matrix
v = rand(3,1) % random matrix with values in [0,1] (see also randn)
load matrix_data % read data from a file:
% create a file 'matrix_data' containing:
% 2 3 4
% 5 6 7
% 1 2 3
matrix_data
v = [1 2 3]; % access a vector element
v(3) % vector(number)
% Index starts from 1
m = [1 2 3; 4 5 6]
m(1,3) % access a matrix element
% matrix(rownumber, columnnumber)
m(2,:) % access a matrix row (2nd row)
m(:,1) % access a matrix column (1st row)
size(m) % size of a matrix
size(m,1) % number rows
size(m,2) % number of columns
m1 = zeros(size(m)) % create a new matrix with size of m
who % list of variables
whos % list/size/type of variables
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% (3) Simple operations on vectors and matrices
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% (A) Pointwise (element by element) Operations:
% addition of vectors/matrices and multiplication by a scalar
% are done "element by element"
a = [1 2 3 4]; % vector
2 * a % scalar multiplication
a / 4 % scalar multiplication
b = [5 6 7 8]; % vector
a + b % pointwise vector addition
a - b % pointwise vector addition
a .^ 2 % pointise vector squaring (note .)
a .* b % pointwise vector multiply (note .)
a ./ b % pointwise vector divide (note .)
log( [1 2 3 4] ) % pointwise arithmetic operation
round( [1.5 2; 2.2 3.1] ) % pointwise arithmetic operation
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% (B) Vector Operations (no for loops needed)
% Built-in matlab functions operate on vectors, if a matrix is given,
% then the function operates on each column of the matrix
a = [1 4 6 3] % vector
sum(a) % sum of vector elements
mean(a) % mean of vector elements
var(a) % variance
std(a) % standard deviation
max(a) % maximum
a = [1 2 3; 4 5 6] % matrix
a(:) % vectorized version of the matrix
mean(a) % mean of each column
max(a) % max of each column
max(max(a)) % to obtain max of matrix
max(a(:)) % or...
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% (C) Matrix Operations:
[1 2 3] * [4 5 6]' % row vector 1x3 times column vector 3x1
% results in single number, also
% known as dot product or inner product
[1 2 3]' * [4 5 6] % column vector 3x1 times row vector 1x3
% results in 3x3 matrix, also
% known as outer product
a = rand(3,2) % 3x2 matrix
b = rand(2,4) % 2x4 matrix
c = a * b % 3x4 matrix
a = [1 2; 3 4; 5 6] % 3 x 2 matrix
b = [5 6 7]; % 1 x 3 vector
b * a % matrix multiply
a' * b' % matrix multiply
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%(4) Saving your work
save mysession % creates mysession.mat with all variables
save mysession a b % save only variables a and b
clear all % clear all variables
clear a b % clear variables a and b
load mysession % load session
a
b
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%(5) Relations and control statements
% Example: given a vector v, create a new vector with values equal to
% v if they are greater than 0, and equal to 0 if they less than or
% equal to 0.
v = [3 5 -2 5 -1 0] % 1: FOR LOOPS
u = zeros( size(v) ); % initialize
for i = 1:size(v,2) % size(v,2) is the number of columns
if( v(i) > 0 )
u(i) = v(i);
end
end
u
v = [3 5 -2 5 -1 0] % 2: NO FOR LOOPS
u2 = zeros( size(v) ); % initialize
ind = find( v>0 ) % index into >0 elements
u2(ind) = v( ind )
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%(6) Creating functions using m-files:
% Functions in matlab are written in m-files. Create a file called
% 'thres.m' In this file put the following 4 lines:
function res = thres( v )
u = zeros( size(v) ); % initialize
ind = find( v>0 ) % index into >0 elements
u(ind) = v( ind )
v = [3 5 -2 5 -1 0]
thres( v ) % call from command line
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%(7) Plotting
x = [0 1 2 3 4]; % basic plotting
plot( x );
plot( x, 2*x );
axis( [0 8 0 8] );
x = pi*[-24:24]/24;
plot( x, sin(x) );
xlabel( 'radians' );
ylabel( 'sin value' );
title( 'dummy' );
gtext( 'put cursor where you want text and press mouse' );
figure; % multiple functions in separate graphs
subplot( 1,2,1 );
plot( x, sin(x) );
axis square;
subplot( 1,2,2 );
plot( x, 2.*cos(x) );
axis square;
figure; % multiple functions in single graph
plot( x,sin(x) );
hold on; % hold on tells matlab to write on top
plot (x, 2.*cos(x), '--' ); % of the current plot
legend( 'sin', 'cos' );
hold off;
figure; % matrices as images
m = rand(64,64);
imagesc(m)
colormap gray;
axis image
axis off;
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%(8) Working with the Images and the Matlab Image Processing Toolbox
[I,map]=imread('lena.png'); % use as it is, Matlab has pre-stored images
I = imread('lena.png'); % or
figure
imshow(I) % display it as indexed image w/colormap
I2=ind2gray(I,map); % convert it to indexed mage
figure
imagesc(I2,[0 1]) % scale data to use full colormap
% for values between 0 and 1
colormap('gray') % use gray colormap
axis('image') % make displayed aspect ratio proportional
% to image dimensions
figure
imshow(I)
rect=getrect; % select rectangle
I2=imcrop(I,rect); % crop
I2=rgb2gray(I2); % convert cropped image to grayscale
imagesc(I2) % scale data to use full colormap
% between min and max values in I2
colormap('gray')
colorbar % turn on color bar
impixelinfo % display pixel values interactively
truesize % display at resolution of one screen pixel
% per image pixel
truesize(2*size(I2)) % display at resolution of two screen pixels
% per image pixel
I3=imresize(I2,0.5,'bil'); % resize by 50% using bilinear
% interpolation
I3=imrotate(I2,45,'bil','crop'); % rotate 45 degrees and crop to
% original size
I3=double(I2); % convert from uint8 to double, to allow
% math operations
imagesc(I3.^2) % display squared image (pixel-wise)
imagesc(log(I3)) % display log of image
% ----------------------------------------------------------------------------------
im = imread( 'lady.gif' );
>> size( im )
>> ans =
256 256
- When loaded into the matlab workspace, an image is simply a 2-D
matrix (3-D for color). At load time, the matrix is of type uint8,
which should be converted to type double, particularly if you are
going to perform any floating point operations on the image:
>> im = double( im );
- There are two basic functions for displaying an image: image and
imagesc:
>> image( im );
- Notice that things look pretty strange -- for an 8-bit grayscale
image, there are a few things that you need to do to display the
image properly. First, for grayscale images, the values of the
image matrix are passed through a lookup table. The lookup table is
given by the function colormap. The default colormap is something
that you don't want for grayscale images. For an 8-bit grayscale,
you want the colormap to be:
>> colormap ( gray(256) ); % type gray(256) to see that this is simply a
% linear grayscale lookup table
- The proportions of the image are now funny. You need to set the
axis appropriately:
>> axis image;
>> axis off; % if you don't care about the labels
- The image is not being drawn at a 1:1 ratio. If you have the image
processing toolbox, then you can use 'truesize' to display the image
at the correct scale. If not, this little bit of code will do the
trick:
>> [ydim,xdim] = size( im );
>> p = get( gcf, 'Position' );
>> set( gcf, 'Position', [p(1) p(2) xdim, ydim] ); % set size of figure
>> set( gca, 'Position', [0 0 1 1] ); % set size of axis
- I suggest creating a function called, for example, im_show, that
bundles all of these steps, so that you can just simply call that
function.
- The command imagesc is the same as image, excpet that the image
values are auto-scaled to fill the full range. For example:
>> im = double( imread( 'feynman.pgm' ) );
>> im = 0.5*im + 64;
>> disp( [min(im(:)) max(im(:))] )
>> image( im );
>> colormap ( gray(256) );
>> axis image off;
% notice that the image is low contrast...
>> imagesc( im ); % while this image looks like the original
- The command imagesc is very dangerous, because it can be deceiving.
I suggest only using imagesc as follows:
>> imagesc( im, [0 255] );
which forces the intensity value 0 to be the first entry in the
colormap, and the entry 255 to be the last entry in the colormap,
effectively turning auto-scaling off.
- Color images are handled a little different than grayscale images.
>> im = double( imread( 'mandrill.tif' ) );
>> size(im)
ans =
256 256 3
>> image( im );
??? Error using ==> image
Error using ==> image
TrueColor CData contains element out of range 0.0 <= value <= 1.0.
- Be careful when extracting the size of a color image:
>> [xdim,ydim,zdim] = size(im) % right
xdim =
256
ydim =
256
zdim =
3
>> [xdim,ydim] = size(im) % wrong
xdim =
256
ydim =
768 % 256 x 3
- Unlike grayscale images, Matlab will only display color images if
they are of type uint8.
>> image( uint8(im) );
>> axis image off;
Note that the colormap does not need to be set -- the reason is that
for color images, the colormap is ignored, and instead, the RGB
channels are used to determine the color at each pixel.
You can get access to each color channel: the red channel is
im(:,:,1), green is im(:,:,2) and blue is im(:,:,3).
- When writing images back to disk, they must be in uint8 format:
>> imwrite( uint8(im), 'bab.tif' );
where the filename extension is used to determine the image format.
When writing jpeg, you can specifiy the quality (in a scale of
[0,100]):
>> imwrite( uint8(im), 'bab.jpg', 'quality', 90 );
- few other things you can do with image are, access rows, columns, add, multiply
>> im1 = imread('lena.png');
>> [xdim1, ydim1, z1] = size(im1);
>> im2 = imread('mandrill.tif');
>> [xdim2, ydim2, z2] = size(im2);
>> im3 = im2(1:xdim1, 1:ydim1, :);
>> im4 = im1 + im3;
>> imshow(im4)
>> im5 = (double(im1) + double(im3))/2;
>> image(uint8(im5));
>> im6 = im1 .* im3;
>> mx = max(im6(:)); mi = min(im6(:));
>> im7 = uint8(255*(double(im6)-mi)/(mx-mi));
>> image(im7);
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