Matlab Environment Contents Continued Desktop tools matrices - - PowerPoint PPT Presentation

MATLAB

Tutorial Course

A.H. Taherinia

Matlab Environment

Contents

Continued Desktop tools matrices

Logical &Mathematical operations Handle Graphics

1

MATLAB Desktop Tools

Command Window Command History Help Browser Workspace Browser Editor/Debugger

2

3

Calculations at the Command Line

» a = 2; » b = 5; » a^b ans = 32 » x = 5/2*pi; » y = sin(x) y = 1 » z = asin(y) z = 1.5708 » a = 2; » b = 5; » a^b ans = 32 » x = 5/2*pi; » y = sin(x) y = 1 » z = asin(y) z = 1.5708 Results assigned to “ans” if name not specified () parentheses for function inputs Semicolon suppresses screen output

MATLAB as a calculator Assigning Variables A Note about Workspace: Numbers stored in double-precision floating point format

» -5/(4.8+5.32)^2

ans =

• 0.0488

» (3+4i)*(3-4i)

ans = 25

» cos(pi/2)

ans = 6.1230e-017

» exp(acos(0.3))

ans = 3.5470

» -5/(4.8+5.32)^2

ans =

• 0.0488

» (3+4i)*(3-4i)

ans = 25

» cos(pi/2)

ans = 6.1230e-017

» exp(acos(0.3))

ans = 3.5470

4

General Functions

whos: List current variables clear: Clear variables and functions from memory Close: Closes last figures cd: Change current working directory dir: List files in directory echo: Echo commands in M-files format: Set output format

5

Matlab Help

6

Getting help

help command

(>>help)

lookfor command

(>>lookfor)

Help Browser

(>>doc)

helpwin command (>>helpwin) Search Engine Printable Documents

“Matlabroot\help\pdf_doc\”

Link to The MathWorks

7

Matrices

Entering and Generating Matrices Concatenation Deleting Rows and Columns Array Extraction Matrix and Array Multiplication

8

» a=[1 2;3 4] a = 1 2 3 4 » b=[-2.8, sqrt(-7), (3+5+6)*3/4] b =

• 2.8000 0 + 2.6458i 10.5000

» b(2,5) = 23 b =

• 2.8000 0 + 2.6458i 10.5000 0 0

0 0 0 0 23.0000 » a=[1 2;3 4] a = 1 2 3 4 » b=[-2.8, sqrt(-7), (3+5+6)*3/4] b =

• 2.8000 0 + 2.6458i 10.5000

» b(2,5) = 23 b =

• 2.8000 0 + 2.6458i 10.5000 0 0

0 0 0 0 23.0000

• Any MATLAB expression can be entered as a matrix element
• Matrices must be rectangular. (Set undefined elements to zero)

Entering Numeric Arrays

Row separator semicolon (;) Column separator space / comma (,)

Use square brackets [ ]

9

The Matrix in MATLAB

4 10 1 6 2 8 1.2 9 4 25 7.2 5 7 1 11 0.5 4 5 56 23 83 13 10

1 2 Rows (m) 3 4 5 Columns (n) 1 2 3 4 5

1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25

A = A (2,4) A (17)

Rectangular Matrix: Scalar: 1-by-1 array Vector: m-by-1 array 1-by-n array Matrix: m-by-n array

10

» w=[1 2;3 4] + 5 w = 6 7 8 9 » x = 1:5 x = 1 2 3 4 5 » y = 2:-0.5:0 y = 2.0000 1.5000 1.0000 0.5000 0 » z = rand(2,4) z = 0.9501 0.6068 0.8913 0.4565 0.2311 0.4860 0.7621 0.0185 » w=[1 2;3 4] + 5 w = 6 7 8 9 » x = 1:5 x = 1 2 3 4 5 » y = 2:-0.5:0 y = 2.0000 1.5000 1.0000 0.5000 0 » z = rand(2,4) z = 0.9501 0.6068 0.8913 0.4565 0.2311 0.4860 0.7621 0.0185

Scalar expansion Creating sequences: colon operator (:) Utility functions for creating matrices.

Entering Numeric Arrays

11

Numerical Array Concatenation

» a=[1 2;3 4] a = 1 2 3 4 » cat_a=[a, 2*a; 3*a, 4*a; 5*a, 6*a] cat_a = 1 2 2 4 3 4 6 8 3 6 4 8 9 12 12 16 5 10 6 12 15 20 18 24 » a=[1 2;3 4] a = 1 2 3 4 » cat_a=[a, 2*a; 3*a, 4*a; 5*a, 6*a] cat_a = 1 2 2 4 3 4 6 8 3 6 4 8 9 12 12 16 5 10 6 12 15 20 18 24

Use [ ] to combine existing arrays as matrix “elements” Row separator: semicolon (;) Column separator: space / comma (,)

Use square brackets [ ]

Note: The resulting matrix must be rectangular

4*a

12

Deleting Rows and Columns

» A=[1 5 9;4 3 2.5; 0.1 10 3i+1] A = 1.0000 5.0000 9.0000 4.0000 3.0000 2.5000 0.1000 10.0000 1.0000+3.0000i » A(:,2)=[] A = 1.0000 9.0000 4.0000 2.5000 0.1000 1.0000 + 3.0000i » A(2,2)=[] ??? Indexed empty matrix assignment is not allowed. » A=[1 5 9;4 3 2.5; 0.1 10 3i+1] A = 1.0000 5.0000 9.0000 4.0000 3.0000 2.5000 0.1000 10.0000 1.0000+3.0000i » A(:,2)=[] A = 1.0000 9.0000 4.0000 2.5000 0.1000 1.0000 + 3.0000i » A(2,2)=[] ??? Indexed empty matrix assignment is not allowed.

13

Array Subscripting / Indexing

4 10 1 6 2 8 1.2 9 4 25 7.2 5 7 1 11 0.5 4 5 56 23 83 13 10

1 2 3 4 5 1 2 3 4 5

1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25

A =

A(3,1) A(3) A(1:5,5) A(:,5) A(21:25) A(4:5,2:3) A([9 14;10 15]) A(1:end,end) A(:,end) A(21:end)’

14

Matrix Multiplication

» a = [1 2 3 4; 5 6 7 8]; » b = ones(4,3); » c = a*b c = 10 10 10 26 26 26 » a = [1 2 3 4; 5 6 7 8]; » b = ones(4,3); » c = a*b c = 10 10 10 26 26 26 [2x4] [4x3] [2x4]*[4x3] [2x3] a(2nd row).b(3rd column) » a = [1 2 3 4; 5 6 7 8]; » b = [1:4; 1:4]; » c = a.*b c = 1 4 9 16 5 12 21 32 » a = [1 2 3 4; 5 6 7 8]; » b = [1:4; 1:4]; » c = a.*b c = 1 4 9 16 5 12 21 32 c(2,4) = a(2,4)*b(2,4)

Array Multiplication 15

Matrix Manipulation Functions

• zeros: Create an array of all zeros
• ones: Create an array of all ones
• eye: Identity Matrix
• rand: Uniformly distributed random numbers
• diag: Diagonal matrices and diagonal of a matrix
• size: Return array dimensions

16

Matrix Manipulation Functions

• transpose (’): Transpose matrix
• rot90: rotate matrix 90
• tril: Lower triangular part of a matrix
• triu: Upper triangular part of a matrix
• cross: Vector cross product
• dot: Vector dot product
• det: Matrix determinant
• inv: Matrix inverse
• rank: Rank of matrix

17

Elementary Math

Logical Operators Math Functions

18

Logical Operations

» Mass = [-2 10 NaN 30 -11 Inf 31]; » each_pos = Mass>=0

each_pos = 0 1 0 1 0 1 1

» all_pos = all(Mass>=0)

all_pos =

» all_pos = any(Mass>=0)

all_pos = 1

» pos_fin = (Mass>=0)&(isfinite(Mass))

pos_fin = 0 1 0 1 0 0 1

» Mass = [-2 10 NaN 30 -11 Inf 31]; » each_pos = Mass>=0

each_pos = 0 1 0 1 0 1 1

» all_pos = all(Mass>=0)

all_pos =

» all_pos = any(Mass>=0)

all_pos = 1

» pos_fin = (Mass>=0)&(isfinite(Mass))

pos_fin = 0 1 0 1 0 0 1

= = equal to > greater than < less than >= Greater or equal <= less or equal ~ not & and | or isfinite(),etc. . . . all(), any() find

Note:

• 1 = TRUE
• 0 = FALSE

19

Elementary Math Function

• abs, sign: Absolute value and Signum Function
• sin, cos, asin, acos…: Triangular functions
• exp, log, log10: Exponential, Natural and

Common (base 10) logarithm

• ceil, floor: Round toward infinities
• fix: Round toward zero

20

Elementary Math Function

round: Round to the nearest integer gcd: Greatest common devisor lcm: Least common multiple sqrt: Square root function real, imag: Real and Image part of complex rem: Remainder after division

21

Elementary Math Function

• max, min: Maximum and Minimum of arrays
• mean, median: Average and Median of arrays
• std, var: Standard deviation and variance
• sort: Sort elements in ascending order
• sum, prod: Summation & Product of Elements

22

Graphics Fundamentals

23

Graphics

Basic Plotting

plot, title, xlabel, grid,legend, hold, axis

Editing Plots

Property Editor

24

2-D Plotting

Syntax: Example:

plot(x1, y1, 'clm1', x2, y2, 'clm2', ...) plot(x1, y1, 'clm1', x2, y2, 'clm2', ...) x=[0:0.1:2*pi]; y=sin(x); z=cos(x); plot(x,y,x,z,'fontsize',14); legend('Y data','Z data ,'linewidth',2) title('Sample Plot','fontsize',14); xlabel('X values','fontsize',14); ylabel('Y values','fontsize',14); grid on x=[0:0.1:2*pi]; y=sin(x); z=cos(x); plot(x,y,x,z,'fontsize',14); legend('Y data','Z data ,'linewidth',2) title('Sample Plot','fontsize',14); xlabel('X values','fontsize',14); ylabel('Y values','fontsize',14); grid on

25

Sample Plot

Title Ylabel Xlabel Grid Legend 26

Subplot

subplot(m,n,p)

income = [3.2 4.1 5.0 5.6];

• utgo = [2.5 4.0 3.35 4.9];

subplot(2,1,1); plot(income); subplot(2,1,2); plot(outgo); income = [3.2 4.1 5.0 5.6];

• utgo = [2.5 4.0 3.35 4.9];

subplot(2,1,1); plot(income); subplot(2,1,2); plot(outgo); 27

Subplot

28

Subplot

subplot(m,n,p) income = [3.2 4.1 5.0 5.6];

• utgo = [2.5 4.0 3.35 4.9];

subplot(2,2,[1 3]); plot(income); subplot(2,2,2); plot(outgo); subplot(2,2,4); plot(income+outgo); income = [3.2 4.1 5.0 5.6];

• utgo = [2.5 4.0 3.35 4.9];

subplot(2,2,[1 3]); plot(income); subplot(2,2,2); plot(outgo); subplot(2,2,4); plot(income+outgo);

29

Subplot

30

Subplots

Syntax:

»subplot(2,2,1); » … »subplot(2,2,2) » ... »subplot(2,2,3) » ... »subplot(2,2,4) » ... »subplot(2,2,1); » … »subplot(2,2,2) » ... »subplot(2,2,3) » ... »subplot(2,2,4) » ... subplot(rows,cols,index) subplot(rows,cols,index)

31

Programming and Application Development

32

Script and Function Files

• Script Files
• Work as though you typed commands into

MATLAB prompt

• Variable are stored in MATLAB workspace
• Function Files
• Let you make your own MATLAB Functions
• All variables within a function are local
• All information must be passed to functions as

parameters

• Sub functions are supported

33

Basic Parts of a Function M-File

function y = mean (x) % MEAN Average or mean value. % For vectors, MEAN(x) returns the mean value. % For matrices, MEAN(x) is a row vector % containing the mean value of each column. [m,n] = size(x); if m == 1 m = n; end y = sum(x)/m;

Output Arguments Input Arguments Function Name Online Help Function Code

34

eps = 1; while (1+eps) > 1 eps = eps/2; end eps = eps*2 eps = 1; while (1+eps) > 1 eps = eps/2; end eps = eps*2

while Loops

Flow Control Statements 35

a = zeros(k,k) % Preallocate matrix for m = 1:k for n = 1:k a(m,n) = 1/(m+n -1); end end a = zeros(k,k) % Preallocate matrix for m = 1:k for n = 1:k a(m,n) = 1/(m+n -1); end end

for Loop

method = 'Bilinear'; switch lower(method) case {'linear','bilinear'} disp('Method is linear') case 'cubic' disp('Method is cubic')

• therwise

disp('Unknown method.') end Method is linear method = 'Bilinear'; switch lower(method) case {'linear','bilinear'} disp('Method is linear') case 'cubic' disp('Method is cubic')

• therwise

disp('Unknown method.') end Method is linear

Switch Statement

Flow Control Statements 36

if ((attendance >= 0.90) & (grade_average >= 60)) pass = 1; end; if ((attendance >= 0.90) & (grade_average >= 60)) pass = 1; end;

if Statement

Function M-file

function r = ourrank(X,tol) % rank of a matrix s = svd(X); if (nargin == 1) tol = max(size(X)) * s(1)* eps; end r = sum(s > tol); function r = ourrank(X,tol) % rank of a matrix s = svd(X); if (nargin == 1) tol = max(size(X)) * s(1)* eps; end r = sum(s > tol); function [mean,stdev] = ourstat(x) [m,n] = size(x); if m == 1 m = n; end mean = sum(x)/m; stdev = sqrt(sum(x.^2)/m – mean.^2); function [mean,stdev] = ourstat(x) [m,n] = size(x); if m == 1 m = n; end mean = sum(x)/m; stdev = sqrt(sum(x.^2)/m – mean.^2);

Multiple Input Arguments use ( ) Multiple Output Arguments, use [ ] »r=ourrank(rand(5),.1); »[m std]=ourstat(1:9);

37

38

Image Processing Toolbox

Introduction

Collection of functions (MATLAB files) that supports a wide range of image processing operations

Image Coordinate

Read an Image

Read in an image Validates the graphic format

(bmp, hdf, jpeg, pcx, png, tiff, xwd)

Store it in an array

clear, close all; I = imread(‘pout.tif`); [X, map] = imread(‘pout.tif’);

Display an Image

imshow(I)

Check the Image in Memory

< Name, Size, Bytes, Class >

whos

Name Size Bytes Class ans 291x240 69840 uint8 array Grand total is 69840 elements using 69840 bytes

[0, 1] double [0, 65535] uint16 [0, 255] uint8

Data Classes

Convert between image Classes

Histogram Equalization

Histogram: distribution of intensities

figure, imhist(I)

Equalize Image (contrast)

I2 = histeq(I); figure, imshow(I2) figure, imhist(I2)

Histogram Equalization (cont.)

Histogram Equalization (cont.)

Write the Image

Validates the extension Writes the image to disk

imwrite(I2, ’pout2.png’); imwrite(I2, ‘pout2.png’, ‘BitDepth’, 4);

Filtering Using imfilter

Filtering of images, either by correlation

• r convolution, can be performed using

the toolbox function imfilter. This example filters an image with a 5- by-5 filter containing equal weights. Such a filter is often called an averaging averaging filter filter. .

Filtering Using imfilter

I = imread('coins.png'); h = ones(5,5) / 25; I2 = imfilter(I,h); imshow(I), title('Original Image'); figure, imshow(I2), title('Filtered Image')

Create special 2-D filters

h = fspecial(type) creates a two- dimensional filter h of the specified type. Syntax h = fspecial(type) h = fspecial(type,parameters)

Create special 2-D filters

Using Median Filtering

Median filtering is similar to using an averaging filter, in that each output pixel is set to an average of the pixel values in the neighborhood of the corresponding input pixel. B = medfilt2(A,[m n]) B = medfilt2(A) B = medfilt2(A,'indexed',...)

Using Median Filtering

I = imread('eight.tif'); subplot(2,2,1), imshow(I), title('Original image'); J = imnoise(I,'salt & pepper',0.02); subplot(2,2,2), imshow(J), title('Salt & pepper noise add'); K = imfilter(J, fspecial('average',3)); subplot(2,2,3), imshow(K), title('averaging filter'); L = medfilt2(J,[3 3]); subplot(2,2,4), imshow(L), title('median filter');

Median Filtering

Image Arithmetic

imabsdiff imadd imcomplement imdivide imlincomb immultiply imsubtract

Adding Images

X = uint8([ 255 0 75; 44 225 100]); Y = uint8([ 50 50 50; 50 50 50 ]); Z = imadd(X,Y) Z = 255 50 125 94 255 150

Adding Images (cont.)

I = imread(‘rice.tif’); J = imread(‘cameraman.tif’); K = imadd(I, J); imshow(K)

Adding Images (cont.)

Brighten an image results saturation RGB = imread(‘flowers.tif’); RGB2 = imadd(RGB, 50); subplot(1, 2, 1); imshow(RGB); subplot(1, 2, 2); imshow(RGB2);

Subtracting Images

Background of a scene

rice = imread(‘rice.tif’); background = imopen(rice, strel(‘disk’, 15)); rice2 = imsubtract(rice, background); imshow(rice), figure, imshow(rice2);

Negative values

imabsdiff

Subtracting Images (cont.)

Multiplying Images

Scaling: multiply by a constant

(brightens >1, darkens <1)

Preserves relative contrast

I = imread(‘moon.tif’); J = immultiply(I, 1.2); imshow(I); figure, imshow(J)

Multiplying Images (cont.)

Dividing Images (Ratioing)

I = imread('rice.png'); J = imdivide(I,2); subplot(1,2,1), imshow(I) subplot(1,2,2), imshow(J)

Spatial Transformations

Map pixel locations in an input image to new locations in an output image

Resizing Rotation Cropping

Resizing Images

Change the size of an image

I = imread(‘ic.tif’); J = imresize(I, 1.25); K = imresize(I, [100 150]); figure, imshow(J) figure, imshow(K)

Resizing Images (cont.)

Rotating Images

Rotate an image by an angle in degrees

I = imread(‘ic.tif’); J = imrotate(I, 35, ‘bilinear’); imshow(I) figure, imshow(J)

Rotating Images (cont.)

Cropping Images

Extract a rectangular portion of an image

imshow ic.tif I = imcrop;

GUIDE

GUIDE:

Graphical User Interface Design Environment

GUIDE

Morphological Opening

Remove objects that cannot completely contain a structuring element Estimate background illumination

clear, close all I = imread(‘rice.png’); imshow(I) background = imopen(I, strel(‘disk’, 15)); imshow(background)

Morphological Opening (cont.)

Subtract Images

Create a more uniform background

I2 = imsubtract(I, background); figure, imshow(I2)

Adjust the Image Contrast

stretchlim computes [low hight] to be mapped into [bottom top]

I3 = imadjust(I2, stretchlim(I2), [0 1]); figure, imshow(I3)

Apply Thresholding to the Image

Create a binary thresholded image

• 1. Compute a threshold to convert the intensity

image to binary

• 2. Perform thresholding creating a logical matrix

(binary image) level = graythresh(I3); bw = im2bw(I3, level); figure, imshow(bw)

Apply Thresholding to the Image (cont.)

Labeling Connected Components Determine the number of objects in the image Accuracy

(size of objects, approximated background, connectivity parameter, touching objects) [labeled, numObjects] = bwlabel(bw, 4); numObjects

{= 80}

max(labeled(:))

Select and Display Pixels in a Region Interactive selection

grain = imcrop(labeled)

Colormap creation function

RGB_label = label2rgb(labeled, @spring, ‘c’, ‘shuffle’); imshow(RGB_label); rect = [15 25 10 10]; roi = imcrop(labeled, rect)

Object Properties

Measure object or region properties

graindata = regionprops(labeled, ‘basic’) graindata(51).Area {296} graindata(51).BoundingBox {142.5 89.5 24.0 26.0} graindata(51).Centroid {155.3953 102.1791}

Create a vector which holds just one property for each object

allgrains = [graindata.Area]; whos

Statistical Properties of Objects

max(allgrains)

{ 695 }

Return the component label of a grain size

biggrain = find(allgrains == 695) { 68 }

Mean grain size

mean(allgrains)

{ 249 }

Histogram (#bins)

hist(allgrains, 20)

Statistical Properties of Objects (cont.)

Storage Classes

double (64-bit), uint8 (8-bit), and uint16 (16-bit)

Converting (rescale or offset)

double im2double (automatic rescale and offsetting) RGB2 = im2uint8(RGB1); im2uint16 imapprox (reduce number of colors: indexed images)

Image Types

Index

Data matrix (uint8, uint16, double) Colormap matrix (m x 3 array of double [0 1])

Intensity (black = 0, white = ∞) Binary (0, 1)

B = logical(uint8(round(A))); (logical flag on) B = +A; (logical flag off)

RGB (m x n x 3 of truecolor)

Converting Image Types

dither gray2ind grayslice im2bw ind2gray ind2rgb mat2gray rgb2gray rgb2ind

Multiframe Image Arrays

Same size, #planes, colormap Store separate images into one multiframe array

A = cat(4, A1, A2, A3, A4, A5)

Extract frames from a multiframe array

FRM3 = MULTI(:, :, :, 3)

Display a frame

imshow(MULTI(:, :, :, 7))

Coordinate Systems

Pixel Coordinates

Discrete unit

(integer)

(r, c) ⎡ = (1, 1)

Spatial Coordinates

Continuous unit (x, y) ⎡= (0.5, 0.5)

123

Non-default Spatial Coordinate System

A = magic(5); x = [19.5 23.5]; y = [8.0 12.0]; image(A, ‘xData’, x, ‘yData’, y), axis image, colormap(jet(25))