Intro matlab and convolution islam

Introduction to MATLAB and
image processing
Amin Allalou
amin@cb.uu.se

Centre for Image Analysis
Uppsala University

Computer Assisted Image Analysis
April 4 2008

MATLAB and images
• The help in MATLAB is very good, use it!
• An image in MATLAB is treated as a matrix
• Every pixel is a matrix element
• All the operators in MATLAB defined on
matrices can be used on images: +, -, *, /, ^, sqrt, sin, cos etc.

Images in MATLAB
• MATLAB can import/export • Data types in MATLAB
several image formats – Double (64-bit double-precision
– BMP (Microsoft Windows Bitmap) floating point)
– GIF (Graphics Interchange Files) – Single (32-bit single-precision
– floating point)
HDF (Hierarchical Data Format)
– Int32 (32-bit signed integer)
– JPEG (Joint Photographic Experts
Group) – Int16 (16-bit signed integer)
– PCX (Paintbrush) – Int8 (8-bit signed integer)
– PNG (Portable Network Graphics) – Uint32 (32-bit unsigned integer)
– TIFF (Tagged Image File Format) – Uint16 (16-bit unsigned integer)
– XWD (X Window Dump) – Uint8 (8-bit unsigned integer)
– MATLAB can also load raw-data or
other types of image data

Images in MATLAB
• Binary images : {0,1}
• Intensity images : [0,1] or uint8, double etc.
• RGB images : m-by-n-by-3
• Indexed images : m-by-3 color map
• Multidimensional images m-by-n-by-p (p is the number of layers)

Image import and export
• Read and write images in Matlab
>> I=imread('cells.jpg');
>> imshow(I)
>> size(I)
ans = 479 600 3 (RGB image)
>> Igrey=rgb2gray(I);
>> imshow(Igrey)
>> imwrite(lgrey, 'cell_gray.tif', 'tiff')

Alternatives to imshow
>>imagesc(I)
>>imtool(I)
>>image(I)

Images and Matrices
• How to build a matrix (or image)?
>> A = [ 1 2 3; 4 5 6; 7 8 9 ];
A= 1 2 3
4 5 6
7 8 9
>> B = zeros(3,3)
B= 0 0 0
0 0 0
0 0 0
>> C = ones(3,3)
C= 1 1 1
1 1 1
1 1 1

>>imshow(A) (imshow(A,[]) to get automatic pixel range)

Images and Matrices
• Accesing image elements (row, column) X
>> A(2,1)
ans = 4
• : can be used to extract a whole column or
row Y
>> A(:,2)
ans =
2
5
8
• or a part of a column or row A=
>> A(1:2,2) 22 3
ans = 35 6
2 7 8 9
5

Image Arithmetic
• Arithmetic operations such as addition, subtraction, multiplication and
division can be applied to images in MATLAB
– +, -, *, / performs matrix operations
>> A+A
ans = 2 4 6
8 10 12 A=
14 16 18
22 3
>> A*A
35 6
ans = 30 36 42
7 8 9
66 81 96
102 126 150

• To perform an elementwise operation use . (.*, ./, .*, .^ etc)
>> A.*A
ans = 1 4 9
16 25 36
49 64 81

Logical Conditions
• equal (==) , less than and greater than (< and >), not equal (~=) and not (~)
• find(‘condition’) - Returns indexes of A’s elements that satisfies the
condition.
>> [row col]=find(A==7)
A=
row = 3
22 3
col = 1
35 6
>> [row col]=find(A>7)
7 8 9
row = 3
3
col = 2
3
>> Indx=find(A<5)
Indx = 1
2
4
7

Flow Control
• Flow control in MATLAB
- if, else and elseif statements
(row=1,2,3 col=1,2,3)
if row==col
A(row, col)=1;
elseif abs(row-col)==1
A(row, col)=2; A=
else
1 2 0
A(row, col)=0; 2 1 2
end 0 2 1

Flow Control
• Flow control in MATLAB
- for loops

for row=1:3
for col=1:3
if row==col
A(row, col)=1;
elseif abs(row-col)==1 A=
A(row, col)=2;
else 1 2 0
2 1 2
A(row, col)=0; 0 2 1
end
end
end

Flow Control
• while, expression, statements, end A=
22 3
Indx=1; 35 6
7 8 9
while A(Indx)<6
A(Indx)=0;
Indx=Indx+1;
end

A=

0 2 3
0 5 6
7 8 9

Working with M-Files
• M-files can be scripts that simply execute a series of MATLAB statements,
or they can be functions that also accept input arguments and produce
output.
• MATLAB functions:
– Are useful for extending the MATLAB language for your application.
– Can accept input arguments and return output arguments.
– Store variables in a workspace internal to the function.

Working with M-Files
• Create a new empty m-file

function B=test(I)
[row col]=size(I)
for r=1:row
for c=1:col
if r==c
A(r, c)=1;
elseif abs(r-c)==1
A(r, c)=2;
else
A(r, c)=0;
end
end
end
B=A;

Intro matlab and convolution islam

Superposition theorem

• The superposition theorem for electrical circuits states that for a linear system the response (
Voltage or Current) in any branch of a bilateral linear circuit having more than one independent
source equals the algebraic sum of the responses caused by each independent source acting alone,
while all other independent sources are replaced by their internal impedances.

Requirements for Linearity
• A system is called linear if it has two
mathematical properties:
2.Homogeneity
3.Additivity
4.Shift invariance
(where “Shift invariance” is not a strict
requirement for linearity, but it is a
mandatory property for most DSP
techniques.)

Superposition: the Foundation of DSP

Decomposition & Convolution
• While many different decompositions are
possible, two form the backbone of signal
processing:
2.Impulse decomposition
3.Fourier decomposition.
• When impulse decomposition is used, the
procedure can be described by a
mathematical operation called convolution.

Definition of delta function (unit
impulse) and impulse response

Shifted & Scaled Delta function

Convolution

If the system being considered is a filter, the impulse
response is called the filter kernel, the
convolution kernel, or simply, the kernel. In
image processing, the impulse response is called
the point spread function.

Correlation
Correlation is a mathematical operation that is
very similar to convolution.
Just as with convolution, correlation uses two
signals to produce a third signal.
This third signal is called the cross-correlation of
the two input signals.
If a signal is correlated with itself, the resulting
signal is instead called the autocorrelation.

Correlation

The formula essentially slides the function along
the x-axis, calculating the integral of their
product at each position. When the functions
match, the value of is maximized. This is because
when peaks (positive areas) are aligned, they
make a large contribution to the integral.
Similarly, when troughs (negative areas) align,
they also make a positive contribution to the
integral because the product of two negative
numbers is positive

Convolution In MATLAB
• Linear filtering of an image is accomplished
through an operation called convolution.
Convolution is a neighborhood operation in
which each output pixel is the weighted sum
of neighboring input pixels. The matrix of
weights is called the convolution kernel, also
known as the filter. A convolution kernel is a
correlation kernel that has been rotated 180
degrees.

Intro matlab and convolution islam

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