1

2

Introduction to MatLab: Image Processing

-Most of the programming operations have as input or output a matrix or a vector.

-Images are often represented a matrices.

- MatLab is a powerful tool to manipulate graphics and images.

Robot Vision Development in Practice

1. Build your robot (you are done)

2. Install a camera on it. Learn software that comes with camera, understand formats. JPG

3. Install Matlab on your laptop – student version, much software for free on WWW – Octave

4. Be able to display image from camera in one window so that you will see it and Matlab code or processing in other windows.

5. Guide your robot through stage or labyrinth and see with your own eyes what robot sees.

6. Think what is a good processing method for the image that you see.

7. Protytype this in Matlab using existing functions.

8. If necessary, use parallel Matlab on CUDA

9. If necessary, rewrite to C++ or Python or Java.3

MATLAB

This introduction will give

• a brief overview, it’s not a MATLAB tutorial !

• Some basic ideas

• Main advantages and drawbacks compared to other languages

MATLAB

• high-performance language for technical computing• computation, visualization, and programming in an easy-

to-use environment

Typical uses include:

• Math and computation• Algorithm development• Modelling, simulation, and prototyping• Data analysis, exploration, and visualization• Scientific and engineering graphics• Application development, including Graphical User

Interface building

Why MATLAB

A good choice for vision program development because:

• Easy to do very rapid prototyping• Quick to learn, and good documentation• A good library of image processing functions• Excellent display capabilities• Widely used for teaching and research in

universities and industry• Another language to impress your boss with !

Why not MATLAB

Has some drawbacks:

• Slow for some kinds of processes• Not geared to the web• Not designed for large-scale system

development

MATLAB Components

MATLAB consists of:

• The MATLAB language• a high-level matrix/array language with control flow statements, functions,

data structures, input/output, and object-oriented programming features.

• The MATLAB working environment• the set of tools and facilities that you work with as the MATLAB user or

programmer, including tools for developing, managing, debugging, and profiling

• Handle Graphics• the MATLAB graphics system. It includes high-level commands for two-

dimensional and three-dimensional data visualization, image processing, animation, and presentation graphics.

• …(cont’d)

MATLAB Components…

• The MATLAB function library. • a vast collection of computational algorithms ranging from elementary

functions like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms as well as special image processing related functions

• The MATLAB Application Program Interface (API)• a library that allows you to write C and Fortran programs that interact with

MATLAB. It include facilities for calling routines from MATLAB (dynamic linking), calling MATLAB as a computational engine, and for reading and writing MAT-files.

MATLAB

Some facts for a first impression

• Everything in MATLAB is a matrix !

• MATLAB is an interpreted language, no compilation needed (but possible)

• MATLAB does not need any variable declarations, no dimension statements, has no packaging, no storage allocation, no pointers

• Programs can be run step by step, with full access to all variables, functions etc.

What does Matlab code look like?A simple example:

a = 1while length(a) < 10a = [0 a] + [a 0]end which prints out Pascal’s triangle:

11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 7 11 8 28 56 70 56 28 8 11 9 36 84 126 126 84 36 9 1

(with “a=” before each line).

What does Matlab code look like?What does Matlab code look like?

Another simple example:

t = 0:pi/100:2*pi;y = sin(t);plot(t,y)

What does Matlab code look like?What does Matlab code look like?Another simple example:

t = 0:pi/100:2*pi;y = sin(t);plot(t,y)

Remember:

EVERYTHING IN MATLAB IS A MATRIX !

creates 1 x 200 Matrix

Argument and result: 1 x 200 Matrix

14

jpgjpg

bmpbmp

Formats of Images in MATLABFormats of Images in MATLAB

• MATLAB can import/export several image formats

– BMP BMP (Microsoft Windows Bitmap)– GIFGIF (Graphics Interchange Files)– HDF (Hierarchical Data Format)– JPEGJPEG (Joint Photographic Experts

Group)– PCX (Paintbrush)– PNG (Portable Network Graphics)– TIFF (Tagged Image File Format)– XWD (X Window Dump)– MATLAB can also load raw-dataraw-data or

other types of image data

• Data types in MATLAB– Double (64-bit double-precision

floating point)– Single (32-bit single-precision

floating point)– Int32 (32-bit signed integer)– Int16 (16-bit signed integer)– Int8 (8-bit signed integer)– Uint32 (32-bit unsigned integer)– Uint16 (16-bit unsigned integer)– Uint8Uint8 (8-bit unsigned integer)

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 exportImage 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 MatricesImages 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)

MatricesMatrices

Matrices

•Rows and columns are always numbered starting at 1

•Matlab matrices are of various types to hold different kinds of data (usually floats or integers)

• A single number is really a 1 x 1 matrix in Matlab!

• Matlab variables are not given a type, and do not need to be declared

• Any matrix can be assigned to any variable

Matrices

Building matrices with [ ]:

A = [2 7 4]

A = [2; 7; 4]

A = [2 7 4; 3 8 9]

B = [ A A ]

2 7 4

2

7

4

2 7 4

3 8 9

?

Matrices

Building matrices with [ ]:

A = [2 7 4]

A = [2; 7; 4]

A = [2 7 4; 3 8 9]

B = [ A A ]

2 7 4

2

7

4

2 7 4

3 8 9

2 7 4

3 8 9

2 7 4

3 8 9

Matrices

Matrices

Some operators must be handled with care:

A = [1 2 ; 4 5]

B = A * A prints 9 12 24 33

B = A .* A prints 1 4 16 25

Element by element multiplication

Submatrices

A matrix can be indexed using another matrix, to produce a subset of its elements:

a = [100 200 300 400 500 600 700] b = [3 5 6]

c = a(b):

300 500 600

Submatrices

To get a subsection of a matrix, we can produce the index matrix with the colon operator:

a(2:5)printsans = 200 300 400 500

•This works in 2-D as well, e.g. c(2:3, 1:2) produces a 2 x 2 submatrix.

•The rows and columns of the submatrix are renumbered.

loops

‘for’ loops in MATLAB iterate over matrix elements:

b = 0for i = [ 3 9 17]

b = b + i;end

Result: 29

Note:The MATLAB way to write that program would have been:b = sum([ 3 9 17]);

Avoid loops if possible !

loops

The typical ‘for’ loop looks like:

for i = 1:6…

end

Which is the same as:

for i = [1 2 3 4 5 6]…

end

loops

Once again:

AVOID LOOPS

Images

So why MATLAB and IMAGE PROCESSING ?

Images

Images can be treated as matrices !

Matrix

>> A=[1 2 3;3 2 1]

A =

1 2 3

3 2 1

>>b=A(1,:)

b =

1 2 3

>> B=A'

B =

1 3

2 2

3 1

Images and Matrices

• Accesing image elements (row, column)>> A(2,1)ans = 4

• : can be used to extract a whole column or row>> A(:,2)ans =2

5 8• or a part of a column or row

>> A(1:2,2)ans =2

5

X

Y

A = 12 345 67 8 9

Image ArithmeticImage Arithmetic• Arithmetic operations such as addition, subtraction, multiplication and

division can be applied to images in MATLAB– +, -, *, / performs matrix operations

>> A+Aans = 2 4 6

8 10 12 14 16 18

>> A*Aans = 30 36 42

66 81 96 102 126 150

• To perform an elementwise operation use . (.*, ./, .*, .^ etc)>> A.*Aans = 1 4 9

16 25 36 49 64 81

A = 12 345 67 8 9

Logical ConditionsLogical 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)

row = 3

col = 1

>> [row col]=find(A>7)

row = 3

3

col = 2

3

>> Indx=find(A<5)

Indx = 1

2

4

7

A = 12 345 67 8 9

Flow ControlFlow 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;

else

A(row, col)=0;

endA =

1 2 0 2 1 2 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(row, col)=2;

else

A(row, col)=0;

end

end

end

A =

1 2 0 2 1 2 0 2 1

Flow Control

• while, expression, statements, end

Indx=1;

while A(Indx)<6

A(Indx)=0;

Indx=Indx+1;

end

A = 12 345 67 8 9

A =

0 2 3 0 5 6 7 8 9

Working with M-FilesWorking 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

endend

B=A;

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Examples

Try these MATRIX AND VECTOR OPERATIONS

This is how we can define a vector>> v=[1, 2, 3]

Matlab prints out the followingv =    

1     2     3

Similarly we can define a matrix>> M= [ 1 2 3; 4 5 6; 7 8 9]The result is:M =    

1     2     3     4     5     6     7     8     9

If you want to suppress the MatLab output then you need to finish the line with semicolon as follows.>>M= [ 1 2 3; 4 5 6; 7 8 9];

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ProjectionProjectionSay you want to extract some rows and columns of a matrix. This is called a

projection. We simply give the subset of rows and columns as parameters, as follows

>> M11=M(2:3 , 2:3)

M11 =     5     6     8     9

To specify all elements in a given dimension one can use ':‘ So to get all rows but just columns 1 and 2, we type

>> A= M( :, 1:2)A =     1     2     4     5     7     8

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Let’s talk about image files and their formats…..Color vs GrayScale

Basic Image Processing functions:

Reading in an image:>> img1=imread('Water lilies.jpg');

Displaying an image:

>> imshow(img1);

Finding out size of an image:>> size(img1);>> size(img1)

ans =

600 800 3

WORKING WITH IMAGES in MatLabWORKING WITH IMAGES in MatLab

imread

imshow

size

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Cropping an image:

>> imgsmall=img1(200:300,300:400,1:3);>> imshow(imgsmall)>> imgsmall=img1(150:250,350:450,1:3);>> imshow(imgsmall)>> size(imgsmall)

ans =

101 101 3

Exercise: 1. Find 2 images online 2. Crop them to the same size 3. Add the two images together.

4. Display resulting image

Advanced Exercise:1. Rescale images to same size then add them2. See next slide to see HOWTO rescale

WORKING WITH IMAGES in MatLab

variable imgsmall

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ReScalingReScalingWe can rescale by changing the number of rows and columns, yet preserve the

information in the image

>> [rows, cols, colors]= size(img1)

rows = 600 cols = 800 colors = 3

% Increase the number of rows>> stretchfactor = 1.5>> rowVec= linspace(1,rows,stretchfactor*rows);>> newrows=round(rowVec);>> newimag=img1(newrows,:,:)>> imshow(newimg);

% Decrease number of columns>> stretchfactor = 0.75;>> colVec= linspace(1,cols,stretchfactor*cols);>> newcols=round(colVec);>> newimag=newimg(:,newcols,:)>>imshow(newimg)

linspace

round

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Example Program: Inverting an imageExample Program: Inverting an imageTo invert invert or to add two images we need to convert to double and then

rescale the result back so that it looks like an image

InvImg= 1 - double(IMG1)/255;

NewImg = uint8(round(InvImg*255)))

Imshow(NewImg);uint8

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Color Masking

Sometimes we want to replace pixels of an image of one or more colors with pixels from another image. It is useful to use a “blue or green screen” in some instances.

Find an image with a big plot of one color. First we will replace that color. And then we will find another image for pixel replacement.

Let us plot the color values of one chosen row…This will tell us the pixel values of the color we want to replace.

1. v = imread(‘myimg.jpg’)2. image(v)3. row= input(‘which row?’);4. red = v(row,:,1);5. green = v(row,:,2);6. blue = v(row,:,3);7. plot(red,’r’);8. hold on9. plot(green,’g’);10. plot(blue,’b’);

WORKING WITH IMAGES in MatLab

input

49

Suppose we want to replace those values whose intensities exceed a threshold value of 160 in each color.

• v= imread(‘myimg.jpg’);• thresh= 160• layer = (v(:,:,1) > thresh) & (v(:,:,2) > thresh) (v(:,:,2) > thresh) • mask(:,:,1) = layer;• mask(:,:,2) = layer;• mask(:,:,3) = layer;

If you want to only mask a portion of the image you can use something like…>> mask(700:end,:,:)= false;Which sets the mask so that we do not affect rows 700 and above

To reset the color to red>>newv = v;>>newv(mask)(1) = 255

Or to replace pixels from a different image w use…>> newv(mask) = w(mask);

Let us try to do this with a blue screen…..

WORKING WITH IMAGES in MatLab

50

HistogramsHistograms

51

imread

imshow

Images in MATLABImages in MATLAB

52

imhist

53

histeq

HistogramHistogram EqualizationEqualization

54

55

NoiseNoise

56

imnoise

medfilt2

1.1.Adding NoiseAdding Noise2.2.Filtering NoiseFiltering Noise

57

Add Image to noiseAdd Image to noise

58

Median Filtering removes noiseMedian Filtering removes noise

59

imnoise fspecial

imfliter

Median Filtering removes Gaussian noiseMedian Filtering removes Gaussian noise

60

FSPECIAL creates FSPECIAL creates special 2D filtersspecial 2D filters

61

Imfilter – multidimensional filteringImfilter – multidimensional filtering

62

ThresholdingThresholding

63

64

IM2BW – converting to binary by IM2BW – converting to binary by thresholdingthresholding

65

Repeated thresholdingRepeated thresholding

66

Separating background by Separating background by thresholdingthresholding

67

Extracting features:Extracting features:1.1.CornerCorner2.2.Center pointCenter point

68

Edge Edge DetectionDetection

69

edge

Example of kernel-based Example of kernel-based filtering - Sobelfiltering - Sobel

70

Edge, Sobel and PrewittEdge, Sobel and Prewitt

71

Roberts, Laplacian, Zero-cross, Roberts, Laplacian, Zero-cross, Canny edge detection methodsCanny edge detection methods

72

Use of threshold in Use of threshold in Sobel affects what is Sobel affects what is

foundfound

73

““Laplacian of Gaussian” Laplacian of Gaussian” filtering is often betterfiltering is often better

74

1.1. Canny Filter is even better Canny Filter is even better – this is a major invention – this is a major invention with many applications in with many applications in robotics. robotics.

2.2. Can one invent a better Can one invent a better one?one?

75

Many variants of Many variants of combining combining

thresholding and thresholding and edge detection existedge detection exist

76

Hough Hough TransformTransform

77

1.1. Hough Transform has links to Fourier, Hough Transform has links to Fourier, Radon and Neural Nets. Radon and Neural Nets.

2.2. A deep conceptA deep concept

78

Camera Camera CalibrationCalibration

79

Matrix/vector multiplicationMatrix/vector multiplication

Calibration of CamerasCalibration of Cameras

80

Sequences of operationsSequences of operations

81

Noise, filtering and histogrammingNoise, filtering and histogramming

Matlab versus other languages

Help

Help command

Help svd

C++ vs. Matlab

int j;

.

for (j=1;j<23;j=j+2)

{

A[4][j]=3*j;

}

for i = 1:2:N

for J = 1:N

A(I,J) =(I+J-1);

end

end

C++ vs. Matlab (cont.)

int j;

while (j<28)

{

…….;

}

while N> 0,

E = E + F;

F = A*F/N;

N = N + 1;

end

C++ vs. Matlab (cont.)

If (i==j)

{ A[i][j]=2;

}

else if (abs(i-j)!=1)

{

…….;

}

if i == j

A(i,j) = 2;

elseif abs(i-j) ~= 1

A(i,j) = -1;

else

A(i,j) = 0;

end

C++ vs. Matlab (cont.)

• Index to an array can be zero.

• double, float , int…

• “;” is very important

• Index into matrix can’t be negative or zero.

• Don’t need to worry about the data type

• “;” not so important

Functions

double* stat(double *x)

{

…….;

return stdev;

}

function [mean,stdev] = stat(x)

n = length(x);

mean = avg(x,n);

stdev =…

function mean = avg(x,n)

mean = sum(x)/n;

Functions(cont.)

function Matrix2VectorAv=A(1,:);for i=2:x Av=[Av A(i,:)];endAv=Av';

void Matrix2Vector( )

{

……;

……;

}

Functions(cont.)

A function declaration cannot appear within a script M-file

void AddF(int i);

int main()

{ ……addF(i);

}

void AddF(int i)

{

i=i+1;

}

File name testFunR.m

function testFun

i=2;

AddF(i);

i

function AddF(i)

i=i+1;

Graphing

In file PlotTest.m

t = 0:.3:10;

y = sin(t);

plot(t,y,’r’) ;

To make a graph of y = sin(t) on the interval t = 0 to t = 10

Graphing(cont.)

graphing the fuction z(x,y) = x exp( - x^2 - y^2)

In file MeshTest.m

[x,y] = meshgrid (-2:.2:2, -2:.2:2);

z = x .* exp(-x.^2 - y.^2);

mesh(z)

Graphing(cont.)

Multiple windows in one figure

SubplotTest.m

t = 0:.3:10;

y = sin(t);

z= cos(t);

subplot(2,1,1);

plot(t,y) ;

subplot(2,1,2);

plot(t,z);

Graphing(cont.)

Multiple windows in one figure

SubplotTest.m

t = 0:.3:10;

y = sin(t);

z= cos(t);

subplot(1,2,1);

plot(t,y) ;

subplot(1,2,2);

plot(t,z);

Matrix Manipulation

•Singular value decomposition---[U,S,V]=svd(A)

•Eigenvalues and eigenvectors---[V,D] = eig(A)

• Orthogonal-triangular decomposition- [Q,R]=qr(A)

•LU factorization --[L,U] = lu(A)

•Matrix rank -- a=rank(A)

•Condition number -- a=cond(A)

Image Processing Toolbox

•Read an image ---- I=imread(filename)

•Display an image ---- imshow(I)

•Write an image ---- imwrite(I, filename,FMT)

Image Processing Toolbox(cont.)

ImageRWD.m

function ImageTest

Itif=imread('image1.tif');

imwrite(Itif,'image1.bmp','bmp');

Ibmp=imread('image1.bmp');

subplot(1,2,1);

imshow(Itif);

subplot(1,2,2);

imshow(Ibmp);

Image Processing Toolbox(cont.)

EdgeTest.m

function EdgeTest

Itif=imread('image1.tif');

B=edge(Itif,'canny');

subplot (1,2,1);

imshow(Itif);

subplot(1,2,2);

imshow(B);

Image Processing Toolbox(cont.)

•Pixel values and statistics --corr2,imhist…

•Image enhancement – histeq, medfilt2…

•Linear filter -- conv2, filter2…

•Image transform -- dct2, fft…

•Binary image Op. --- dilate, erode…

Neural NetworkNeural Network

•Feed-forward backpropagatoin

•Hopfield Networks

•Self-organizing maps

•Radial Basis networks

•………………

Neural Networks(cont.)•Create feed-forward NN

•Net=newff([-1 2;0 5],[31],{‘tansig’,’purelin’},’traingd’);

•Training •[net,tr]=train(net,p,t)

•net.trainParam.????; “show”, “lr”, “epochs”, “goal”

•Simulation

•A=sim(net,q);

•Neural Model – tansig, logsig, purelin.•Training method –traingd, traingdm.

MenuMenufunction MenuDemo

cell_list = {};

fig_number = 1;

title_figure = 'Menu Demo';

cell_list{1,1} = {'Plot','PlotTest;'};

cell_list{1,2} = {'Mesh','MeshTest;'};

cell_list{1,3} = {'Image','ImageRWD;'};

cell_list{1,4} = {'Image Edge','EdgeTest;'};

cell_list{2,1} = {'????','PlotTest;'};

cell_list{2,2} = {'????','PlotTest;'};

cell_list{2,3} = {'????','PlotTest;'};

cell_list{2,4} = {'Exit',['disp(''Bye. To run again, type "menu".'');

close(' num2str(fig_number) ');']};

show_window(cell_list,fig_number,title_figure,120,20,3);

Menu (cont.)

•cell_list{1,1} = {‘name',‘function;'};

•show_window(cell_list,fig_number,title_figure,x,y,z);

EDGE DETECTION IN MATLABEDGE DETECTION IN MATLAB

Fourier Transform in MATLABFourier Transform in MATLAB

By the way…

MATLAB can also handle

• Movies

• 3D objects

• …

Conclusion

MATLAB is a mighty tool to manipulate matrices

Images can be treated as matrices

MATLAB is a mighty tool to manipulate images

In my opinion…

MATLAB should be used to code software prototypes

Research is mostly about prototypes, not runtime-optimized software

MATLAB should be used in research

In my opinion…

•MATLAB prototypes must be re-coded (e.g. in C++) if there’s need for speed

•Algorithm development time is drastically shorter in MATLAB

110

end

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

112

Prepared by Fred AnnexsteinUniversity of CincinnatiSome Rights Reserved

CIS 350 – 1

Introduction to MATLAB

Dr. Rolf Lakaemper