MATLAB Tutorial Course A.H. Taherinia
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MATLAB Tutorial Course
A.H. Taherinia
Matlab Environment
Contents Continued
Desktop toolsmatricesLogical &Mathematical operationsHandle Graphics
1
MATLAB Desktop Tools
Command WindowCommand HistoryHelp BrowserWorkspace BrowserEditor/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)^2ans =
-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)^2ans =
-0.0488» (3+4i)*(3-4i)ans =
25» cos(pi/2)ans =6.1230e-017
» exp(acos(0.3))ans =
3.5470
4
General Functionswhos: List current variablesclear: Clear variables and functions from memoryClose: Closes last figurescd: Change current working directorydir: List files in directoryecho: Echo commands in M-filesformat: Set output format
5
Matlab Help
6
Getting helphelp command (>>help)
lookfor command (>>lookfor)
Help Browser (>>doc)
helpwin command (>>helpwin)
Search EnginePrintable Documents
“Matlabroot\help\pdf_doc\”Link to The MathWorks
7
Matrices
Entering and Generating MatricesConcatenationDeleting Rows and ColumnsArray ExtractionMatrix 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 separatorsemicolon (;)
Column separatorspace / 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 0.5 4 5 56
23 83 13 0 10
1
2
Rows (m) 3
4
5
Columns(n)
1 2 3 4 51 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 arrayVector: m-by-1 array
1-by-n arrayMatrix: m-by-n array
10
» w=[1 2;3 4] + 5w =
6 78 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 0.45650.2311 0.4860 0.7621 0.0185
» w=[1 2;3 4] + 5w =
6 78 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 0.45650.2311 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 43 4 6 83 6 4 89 12 12 165 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 43 4 6 83 6 4 89 12 12 165 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 0.5 4 5 56
23 83 13 0 10
1
2
3
4
5
1 2 3 4 51 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 1026 26 26
» a = [1 2 3 4; 5 6 7 8];
» b = ones(4,3);
» c = a*b
c =
10 10 1026 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 9 165 12 21 32
» a = [1 2 3 4; 5 6 7 8];
» b = [1:4; 1:4];
» c = a.*b
c =
1 4 9 165 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>=0each_pos =
0 1 0 1 0 1 1» all_pos = all(Mass>=0)all_pos =
0» 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>=0each_pos =
0 1 0 1 0 1 1» all_pos = all(Mass>=0)all_pos =
0» 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 Functionround: Round to the nearest integergcd: Greatest common devisorlcm: Least common multiplesqrt: Square root functionreal, imag: Real and Image part of
complexrem: 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
GraphicsBasic Plotting
plot, title, xlabel, grid,legend, hold, axis
Editing PlotsProperty Editor
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2-D PlottingSyntax:
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 PlotTitle
Ylabel
Xlabel
Grid
Legend
26
Subplot
subplot(m,n,p)
income = [3.2 4.1 5.0 5.6];outgo = [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];outgo = [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];outgo = [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];outgo = [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
SubplotsSyntax:
»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)
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Programming andApplication 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;endy = sum(x)/m;
Output Arguments Input ArgumentsFunction 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')
otherwise
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')
otherwise
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 matrixs = svd(X);if (nargin == 1)
tol = max(size(X)) * s(1)* eps;endr = sum(s > tol);
function r = ourrank(X,tol)% rank of a matrixs = svd(X);if (nargin == 1)
tol = max(size(X)) * s(1)* eps;endr = sum(s > tol);
function [mean,stdev] = ourstat(x)[m,n] = size(x);if m == 1
m = n;endmean = 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;endmean = sum(x)/m;stdev = sqrt(sum(x.^2)/m – mean.^2);
Multiple Input Argumentsuse ( )
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 ImageRead in an imageValidates the graphic format
(bmp, hdf, jpeg, pcx, png, tiff, xwd)
Store it in an arrayclear, close all;I = imread(‘pout.tif`);[X, map] = imread(‘pout.tif’);
Display an Imageimshow(I)
Check the Image in Memory< Name, Size, Bytes, Class >
whosName Size Bytes Classans 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 EqualizationHistogram: 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 extensionWrites the image to disk
imwrite(I2, ’pout2.png’);imwrite(I2, ‘pout2.png’, ‘BitDepth’, 4);
Filtering Using imfilter
Filtering of images, either by correlation or 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 filterfilter..
Filtering Using imfilterI = 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.
Syntaxh = 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
imabsdiffimaddimcomplementimdivide
imlincombimmultiplyimsubtract
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 scenerice = imread(‘rice.tif’);background = imopen(rice, strel(‘disk’, 15));rice2 = imsubtract(rice, background);imshow(rice), figure, imshow(rice2);
Negative valuesimabsdiff
Subtracting Images (cont.)
Multiplying Images
Scaling: multiply by a constant(brightens >1, darkens <1)
Preserves relative contrastI = 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
ResizingRotationCropping
Resizing Images
Change the size of an imageI = 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 degreesI = 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.tifI = imcrop;
GUIDE
GUIDE:Graphical User Interface Design Environment
GUIDE
Morphological Opening
Remove objects that cannot completely contain a structuring element
Estimate background illuminationclear, close allI = imread(‘rice.png’);imshow(I)background = imopen(I, strel(‘disk’, 15));imshow(background)
Morphological Opening (cont.)
Subtract Images
Create a more uniform backgroundI2 = 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 image1. Compute a threshold to convert the intensity
image to binary2. 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 imageAccuracy
(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 selectiongrain = imcrop(labeled)
Colormap creation functionRGB_label = label2rgb(labeled,
@spring, ‘c’, ‘shuffle’);imshow(RGB_label);rect = [15 25 10 10];roi = imcrop(labeled, rect)
Object Properties
Measure object or region propertiesgraindata = 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 sizemean(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)doubleim2double (automatic rescale and offsetting)RGB2 = im2uint8(RGB1);im2uint16imapprox (reduce number of colors: indexed images)
Image Types
IndexData 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
dithergray2indgraysliceim2bwind2gray
ind2rgbmat2grayrgb2grayrgb2ind
Multiframe Image Arrays
Same size, #planes, colormapStore separate images into one multiframe array
A = cat(4, A1, A2, A3, A4, A5)
Extract frames from a multiframe arrayFRM3 = MULTI(:, :, :, 3)
Display a frameimshow(MULTI(:, :, :, 7))
Coordinate Systems
Pixel CoordinatesDiscrete unit (integer)(r, c)⎡ = (1, 1)
Spatial CoordinatesContinuous 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))
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