Matlab introduction

Image processing
in Matlab
TBMI02
Medical Image Analysis
Division of Medical Informatics
Department of Biomedical Engineering
Linköping University

Agenda
Matlab basics
How are images represented in Matlab?
How do we read images into Matlab?
How do we write images from Matlab?
How do we look at images?
How do we perform operations on images?
How do we perform convolution?
Information, then laboration with exercises

Matlab basics
Matlab = matrix laboratory
All variables are matrices, a vector is a N x 1
or a 1 x N matrix, a scalar is a 1 x 1 matrix
Interpreting language, no compiler
For-loops are slow
Vectorized code is fast
Type help and the function name to know
how the function works
Code is either a function or a script
Every line that is not terminated with a
semicolon prints the result

Matlab basics
Create a matrix
a = ones(10,20), all the values are 1
a = zeros(40,42), all values are 0
a = randn(100,100), random values from a normal
distribution with mean 0 and variance 1
a = rand(100,100), random values from a uniform
distribution on the interval (0,1)
Warning, if you don’t create a matrix before your
operations, your program can be slow due to that Matlab
has to allocate memory and copy data each time you
change the matrix

Matlab basics
my_vector = ones(100,1)
my_vector(10) gives the 10th value
my_image = ones(100,100)
my_image(20,30) gives the pixel value at
x = 30, y = 20
my_volumes = ones(100,100,100,100)
my_volumes(5,2,3,4) gives the voxel value at
x = 2, y = 5, z = 3, t = 4

Matlab basics
Indirect indexing
my_image(my_image > 10) = 100
my_image(isnan(my_image)) = 0

Matlab basics
Pointwise operations use a dot before the
operator, for example .* ./ , otherwise the
operator is interpreted as a matrix operation
Addition, subtraction
C = A + B, C = A – B
Pointwise multiplication and matrix
multiplication
C = A .* B, C = A * B
Pointwise division and matrix division
C = A ./ B, C = A / B
A = B^2, matrix square, A = B.^2, pointwise
square

Matlab basics
Transpose a matrix with ’
Row vector, a = ones(1,10)
Column vector, b = ones(10,1)
Scalar product, c = b’*b
Matrix product, c = b*b’

for-loops
for a = 1:5
a
end
for a = 1:2:100
a
end
for a = 100:-1:1
a
end

if-statements
if (a == b)
c = d;
elseif (a == f)
c = t;
else
c = e;
end

Functions and scripts
A function takes a number of parameters and
returns a number of parameters
Can’t access variables inside the function,
without setting them as out parameters
A script simply runs the code in a m-file
Use scripts for the laborations in this course
Scripts and functions can be launched from
the Matlab terminal, i.e. if the filename is
mylab1.m, simply type mylab1 and enter
Scripts can also be launched with the runbutton
in the editor

Image representation
An image in Matlab is stored as a matrix
The size of the matrix is height * width
my_image = ones(height,width)
The data is stored as row major, i.e. y first
(column major is normally used in other
languages)
Pixel value at (x,y) = my_image(y,x)
Origo is at the top left corner of the image
y is positive downwards, x is positive to the
right
[height width] = size(my_image)

Casting between types
Matlab variables are normally doubles, i.e.
floating point numbers with 64 bit precision
When an image is read into Matlab, it is
normally NOT a double, necessary to convert
to a double
my_image = double(my_image);
Other types are single (32 bit float),
uint16 (16 bit unsigned integers) etc
my_image = single(my_image);

Reading and writing images
Read an image into a Matlab matrix
my_image =
double(imread(’my_image.jpg’,’jpg’));
Write a matrix to file
imwrite(uint8(image1),’image1.jpg’,’jpg’);
For medical images
dicomread, dicomwrite

Looking at images
imagesc(my_image), autoscaled
(WARNING, autoscaling can fool you)
image(my_image), not autoscaled
colormap gray to look at grayscale images
colorbar to see the scale
gopimage, to look at complex valued images
(in this course only, not Matlab standard)
figure, create a new figure
figure(number), create a figure with a number
surf(my_image), simple surface rendering

The colon operator
Colour images have 3 channels
(for example RGB or YCbCr), i.e.
my_image = zeros(sy,sx,3)
To get one channel, use the colon operator
my_red_image = my_image(:,:,1);
To get one vertical line from an image,
my_line = my_image(:,5)
To get one horizontal line from an image,
my_line = my_image(5,:)
Downsample an image a factor 2
my_image = my_image(1:2:end,1:2:end);

The colon operator
Useful for max, min, sum etc
my_image(:) returns a column vector with all
the pixel values
max(my_image) gives the maximum for each
column
max(my_image(:)) gives the maximum value
of the image, equivalent to
max(max(my_image))
The same principle for min, sum

Convolution
conv2 performs 2D convolution
’same’, the filter response has the same size as the
image
filter_response = conv2(my_image,my_filter,’same’)
’valid’, the filter response is smaller than the image
filter_response = conv2(my_image,my_filter,’valid’)
’full’ (default), the filter response is bigger than the
image
filter_response = conv2(my_image,my_filter)
For higher dimensions, convn (slow)

Fast Fourier Transform
MY_IMAGE = fft2(my_image);
my_image = ifft2(MY_IMAGE);
fftshift, ifftshift to move the DC component
Can be used for convolution
For higher dimensions, fftn, ifftn

Interpolation
interp2 can be used for 2D interpolation,
supports nearest, linear, cubic and sinc
interpolation
For higher dimensions, interp3, interpn
(both are slow)

Help functions
clc, removes all text in the terminal
close all, close all the figures
clear all, removes all the variables
save, save Matlab data to a *.mat file
load, load data from a *.mat file

Mex-files
To get faster programs (for example forloops),
it is possible to combine C
programming with Matlab through mex-files
A mex-file is a C-file with some extra code for
communication with Matlab
The mex-file is compiled through Matlab
The compiled mex-file acts as a normal
Matlab function
Not used in this course but can be good to
know that it exists

Exercises
Read an image into Matlab
Look at the image
Create a simple filter, for example with fspecial
(use randn to see fun results)
Look at the filter with surf
Perform 2D convolution with ’same’, ’valid’ and ’full’
and compare the results at the edge
Try different filter sizes
Perform a 2D FFT and look at the logarithm of the
magnitude, with and without fftshift
Compare pointwise multiplication and matrix
multiplication when multiplying two small matrices

Exercises
Loop through all the pixels in an image and
multiply the pixel value by 2 if the pixel value
is bigger than a threshold that you set
Do the same operation as above, but without
for-loops
Take an image and interpolate it to double the
size, using different interpolation techniques,
and compare the results
Add random noise to an image, with different
variance of the noise, look at the results
Flip every second line in an image from left to
right, using fliplr