1. Matlab Tutorial

2. Matrices

3. Matrices

4. 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

5. Images and Matrices How to build a matrix (or image)?
>> B = zeros(3,3)
B =
>> C = ones(3,3)
C =
>>imshow(A) (imshow(A,[]) to get automatic pixel range)

6. Building Matrices Building matrices with [ ]: A = [2 7 4]
B = [ A A ] 2 7 4 2 7 4 2 7 4 3 8 9 ? 2 7 4 2 7 4 3 8 9 3 8 9

7. Operating on whole Matrices

8. Special matrix operators
Some operators must be handled with care:
A = [1 2 ; 4 5]
B = A * A prints
B = A .* A prints
Element by element multiplication

9. Submatrices
A matrix can be indexed using another matrix, to produce a subset of its elements:
a = [ ] b = [3 5 6]
c = a(b):

10. Submatrices
To get a subsection of a matrix, we can produce the index matrix with the colon operator:
a(2:5)
prints
ans =
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.
a = [ ]

11. loops ‘for’ loops in MATLAB iterate over matrix elements: b = 0
for i = [ ]
b = b + i;
end
Result: 29
Note:
The MATLAB way to write that program would have been:
b = sum([ ]);
Avoid loops if possible !

12. loops The typical ‘for’ loop looks like: for i = 1:6 … end
Which is the same as:
for i = [ ]

13. Famous Matrix Manipulation Algorithms
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)
Linear systems: A\b solves A*x = b

14. Constructing Matrices
Basic built-ins:
All zeroes, ones: zeros, ones
Identity: eye
Random: rand (uniform), randn (unit normal)
Ranges: m:n, m:i:n (i is step size)
Composing big matrices out of small matrix blocks
repmat(A, m, n): “Tile” a big matrix with m x n copies of A

15. Manipulations & Calculations on matrices
Transpose (‘), inverse (inv)
Matrix arithmetic: +, -, *, /, ^
Elementwise arithmetic: .*, ./, .^
Functions
Vectorized
sin, cos, etc.

16. Deconstructing Matrices
Indexing individual entries by row, col: A(1, 1) is upper-left entry
Ranges: e.g., A(1:10, 3), A(:, 1)
Matrix to vector and vice versa by column:
B = A(:),
A(:) = B
Transpose to use row order
find: Indices of non-zero elements

17. Control Structures

18. Control Structures
Expressions, relations (==, >, |, &, functions, etc.)
if/while expression statements end
Use comma to separate expression from statements if on same line
if a == b & isprime(n), M = inv(K); else M = K; end
for variable = expression statements end
for i=1:2:100, s = s / 10; end

19. function [c,d,e]= pyt(a,b) % returns the hypotenuse in a right angle % triangle according to Pythagoras theorem. % c is the hypotenuse, % d and e are the two sharp angles c=sqrt(a.^2+b.^2); d=atan(b./a); e=pi/2-d;

20. if: if (A > B), statement; if i==1, elseif (A< B), statement;
elseif ~A, statement;
else,
end
if i==1,
statement;
end
if res(n,2) ~= 0,
else,

21. switch
switch (rem(n,3) ==0) & (rem(n,2)==0) case 0 disp('n is not dividable by 6') case 1 disp('n is dividable by 6') otherwise error('This is impossible.') end

22. for
for n=1:1:4, subplot(2,2,n) plot(a(:,1),a(:,n+1)) title(num2str(n)) end

23. while
a = 4; fa = sin(a); b = 2; fb = sin(b); while a - b > 5 * eps, x = (a+b)/2; fx = sin(x); if sign(fx) == sign(fa), a = x; fa=fx; break; else b = x; fb = fx; end

24. Plotting 2-D vectors: plot(x, y) 3-D: plot3(x, y, z)(space curve)
plot(0:0.01:2*pi, sin(0:0.01:2*pi))
3-D: plot3(x, y, z)(space curve)
Surfaces
meshgrid makes surface from axes, mesh plots it
[X,Y] = meshgrid(-2:.2:2, -2:.2:2);
Z = X .* exp(-X.^2 - Y.^2);
mesh(Z)
surf: Solid version of mesh
Saving figures, plots: print –depsc2 filename

25. Miscellaneous Diary: Recording a session
diary filename
diary off
tic, toc bracketing code to measure execution time

26. Once again:
AVOID LOOPS

27. 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)
row = 3
col = 1
>> [row col]=find(A>7) 3
col = 2
>> Indx=find(A<5)
Indx = 1 2 4 7
A =

28. Flow Control A = 1 2 0 2 1 2 0 2 1 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;
end
A =

29. Flow Control A = 1 2 0 2 1 2 0 2 1 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
A =

30. Flow Control
while, expression, statements, end
Indx=1;
while A(Indx)<6
A(Indx)=0;
Indx=Indx+1;
end
A =
A =

31. M-Files Any text file ending in “.m”
Use path or addpath to tell Matlab where code is (non-persistent?)
Script: Collection of command line statements
Function: Take argument(s), return value(s). First line defines:
function y = foo(A)
function [x, y] = foo2(a, M, N)
Comment: Start line with %

32. 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.

33. 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
B=A;

34. Composition of MATLAB

35. Examples
Try these MATRIX AND VECTOR OPERATIONS
This is how we can define a vector
>> v=[1, 2, 3]
Matlab prints out the following
v =    
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];

36. Projection
Say 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 = 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 =

37. WORKING WITH IMAGES in MatLab
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 =
imread
imshow
size

38. variable imgsmall WORKING WITH IMAGES in MatLab
Cropping an image:
>> imgsmall=img1(200:300,300:400,1:3);
>> imshow(imgsmall)
>> imgsmall=img1(150:250,350:450,1:3);
>> size(imgsmall)
ans =
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:
Rescale images to same size then add them
See next slide to see HOWTO rescale
variable imgsmall

39. ReScaling linspace round
We can rescale by changing the number of rows and columns, yet preserve the information in the image
>> [rows, cols, colors]= size(img1)
rows = 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

40. Example Program: Inverting an image
To 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

41. input WORKING WITH IMAGES in MatLab 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.
v = imread(‘myimg.jpg’)
image(v)
row= input(‘which row?’);
red = v(row,:,1);
green = v(row,:,2);
blue = v(row,:,3);
plot(red,’r’);
hold on
plot(green,’g’);
plot(blue,’b’);
input

42. WORKING WITH IMAGES in MatLab
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…..

43. Histograms

44. Image reading and showing
imread
imshow

45. Image Histogram
imhist

46. Histogram Equalization
histeq

48. Noise

49. Adding Noise
Filtering Noise
imnoise
medfilt2

50. Add Image to noise

51. Median Filtering removes noise

52. Median Filtering removes Gaussian noise
imnoise
fspecial
imfliter

53. FSPECIAL creates special 2D filters

54. Imfilter – multidimensional filtering

55. Thresholding

56. Thresholding

57. IM2BW – converting to binary by thresholding

58. Repeated thresholding

59. Separating background by thresholding

60. Feature Extraction
Extracting features:
Corner
Center point

61. Edge Detection

62. Example of kernel-based filtering - Sobel
Edge Detection
edge
Example of kernel-based filtering - Sobel

63. Edge, Sobel and Prewitt

64. Roberts, Laplacian, Zero-cross, Canny edge detection methods

65. Use of threshold in Sobel affects what is found

66. “Laplacian of Gaussian” filtering is often better

67. Canny Filter is even better – this is a major invention with many applications in robotics.
Can one invent a better one?

68. Edge Detection with gray and binary images
Many variants of combining thresholding and edge detection exist

69. EDGE DETECTION IN MATLAB

70. Hough Transform

71. Hough Transform
Hough Transform has links to Fourier, Radon and Neural Nets.
A deep concept

72. Camera Calibration

73. Calibration of Cameras Matrix/vector multiplication

74. Sequences of operations

75. Noise, filtering and histogramming

76. Fourier Transform in MATLAB

77. Other data
MATLAB can also handle
Movies
3D objects …

78. Sources Rolf Lakaemper Fred Annexstein Jason Rife Hyunki Lee
Amin Allalou