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1－Intoduction to Matlab & Curve Drawing

Examples:

1. Enter a 4 x 1 vector

>> x = [1; 2; 3; 4]

1. Enter a 4 x 1 vector

>> x= [1, 2, 3, 4]

1. Enter a 4 x 4 matrix

>> A = [1,2,3,4; 11,22,33,44; 111,222,333,444; 1111,2222,3333,4444]

Note that the rows of a matrix are separated by semicolons, while the entries on a row are separated by spaces (or commas).

4. Enter a vector:

>> V=[0 0.1 0.2 0.3]

Note that a semicolon after a written statement presents the echo on the screen; and it may be useful if long vectors are entered.

The vector V can be defined as follows:

>> V= 0 : 0.1 : 0.3

Creat a 4 x1 vector of ones

>> iota=ones(4,1)

Get the diagonal elements of a matrix

>> DA= diag(A)

Display the names of all defined variable and thier types

>> whos

Deleting Rows and Columns

You can delete rows and columns from a matrix using just a pair of square brackets.

>> X=A;

>> X(:, 2)=[] % to delete the second column of X

Arithmetic Operators

 + Addition * Multiplication - Subtraction / Division ^ Power >= Equal or greater than ./ Element-by-element division .* Element-by-element multiplication

Enter the following sequence of commands (press Enter after each command):

 1 5*5+2*2 2 9*(1/(12-3)-(1/3^2)) 3 s=2; h=3; g=s+h 4 pr=s*h 5 u=[1,2,3] 6 u=[1 2 3] 7 v=[-1, 0, -3] 8 w=u-2*v 9 range = 1:12 10 odd=1:2:12 11 down=20:-0.5:0 12 even=odd+1 13 u' 14 v' 15 w' 16 pi 17 xgrid=0:.05:1 18 x=xgrid*pi 19 y=sin(x) 20 a=2.; b=a^2 21 sqrt(9) 22 Z= zeros(2.5)

The Colon Operator

It occurs in different forms. Try the following exercises:

>> 1:10

(it is a row vector containing the integers from 1 to 10)

>> 100 : -7 : 50

>> 0 : pi/4 : pi

>>sum(A(1 : 4,4))

>>sum (A(:, end))

(it computes the sum of the elements in the last column of A)

>> sum( 1:16 )/4

II. Basic Plotting

Creating a Plot

The plot function has different forms and depends on the input arguments:

plot(y) , where y is a vector

plot (x,y) , where x and y are vectors.

Plotting in Polar Coordinates

polar is the function that is used for polar coordinate plot: e.g. polar ([0 2*pi], [0 1])

Controlling the Axis

* Matlab selects axis limits on the range of the plotted data. To specify the limits manually you need to use the axis command: axis ([xmin, xmax, ymin, ymax]) .

* The command axis('equal') makes the x- and y-axes equal in length. To make the x- and y-data units equal use the command: axis('square') .

* To add a title to the plot use: title ('Title of the Plot')

* To add x-, y- labels use: xlabel('x-Axis') and ylabel('y-Axis')

Grid Lines

The grid command sets grid lines.

III. Examples

Make m-files that plot the following functions:

III.1 Explain how the following function works. Find/define a problem.

 function drawline1 x = [1 2]; y = [1 4]; y= 2.*x+3.; plot(x,y); xlabel('x-Axis'); ylabel('y-Axis'); title('Plot of the Function','FontSize',12);

III.2

 function drawline2 x =[1,2]; y= 2.*x+3; plot(x,y, 'g'); xlabel('x-Axis'); ylabel('y-Axis'); title('Plot of the Function','FontSize', 12); axis([-10 5 -5 20]);

III.3

 function drawline3 x=[0 15]; y= x+1.; plot(y,'r'); xlabel('x-Axis'); ylabel('y-Axis'); title('Plot of the Function','FontSize', 12); axis([-10 5 -5 20]); grid

III.4

 function drawsin1 xlabel('x=0:2\pi') ylabel('Sine of x') title('Plot of the Sine Function','FontSize',12) x = 0:pi/100:2*pi; y=sin(x); plot(x,y)

III.5

 function drawsin2 plot(sin(0:.01:10));

III.6

 function drawsin3 x=0:.01:10; plot(sin(x));

III.7

 % generate a spiral in polar coordinates theta= 0:0.2:5*pi; rho=theta.^2; polar(theta, rho, 'go')

III.8

 function Drawsquare1; %To draw a square using nodes %First of all define the nodes Node = [-2 -2; -2 2; 2 2; 2 -2;-2 -2]; %Draw the square plot(Node(:,1),Node(:,2)) axis([-5,5,-5,5]); axis square;

III.9

 function Drawsquare2; %To draw a square using nodes %First of all define the nodes Node = [-2 -2; -2 2; 2 2; 2 -2;-2 -2]; %Draw the square fill(Node(:,1),Node(:,2),'red') axis([-5,5,-5,5]); axis square;

2－Intoduction to Matlab: Drawing the Curves and 2D Objects

I-1 Specifying Line Styles and Colours. Plotting Lines and Markers.

If we specify a marker style but not a line style, Matlab draws only the marker.

To specify colour use command plot (x,y, 'colour_style_marker') , where colour strings are

 'c' cyan 'r' red 'w' white 'g' green 'y' yellow 'b' blue 'k' black 'm' magenta

Line style strings are

 ' - ' solid ' - - ' dashed ' : ' dotted ' - . ' dash-dot

For example: plot (x, y, 'r : ') plots a red dotted line.

The marker types are

 ' + ' + ' s ' square ' x ' x ' p ' pentagram ' 0 ' 0 ' v ' down triangle ' * ' * ' d ' diamond

For example: plot (x, y, 'r :s ') plots a red dotted line and places square markers at each data point.

I-2 Knowing where you are:

Use the pwd command to know where you are

Use the dir command to list the files in your current directory

Use the cd command to change directory

I-3 Reminder: Read "Introduction to Matlab" and do Computer Graphics Exercises - pages 11-13.

II-1. Examples

Make m-files that plot the following graphs:

II.1

 function drawParabola; % To draw parabola y=(x+3)^2+25 in a figure window. % Define the start and end points on the x-axis x= - 18:15 ; y=(x+3).^2+25; plot(x,y, 'g');

Explain the program and results.

II.2

 function drawEllipse; % to draw the ellipse (x^2)/16 +(y^2)/4 = 1 %you need to get parametric representation of the ellipse, i.e. x=a cos(t); y=b sin(t) t=0:0.01:2*pi; a=16.; b=4.; x=a*cos(t); y=b*sin(t); plot(x,y, 'g'), grid

Explain the program and results. Is there any problem in the program?

II.3

 function drawHyperbola; % Draw hyperbola y=3/x in a figure window. x=0.01:0.01:1; y=3./x; plot(x,y,'r');

Explain the program and results.

II-2 Examples

II.4 Make NewObject.m file

 function NewObject; %To draw an object using fill %First of all define the nodes X1 = [-2 -2 0]; Y1 = [-1 1 0]; X2 = [-1 1 0]; Y2 = [2 2 0]; X3 = [2 2 0]; Y3 = [1 -1 0]; X4 = [1 -1 0]; Y4 = [-2 -2 0]; %Draw the object fill(X1,Y1,'green',X2,Y2,'green',X3,Y3,'green',X4,Y4,'green'); axis([-5,5,-5,5]); axis square;

Explain the program and results.

II.5

 function drawFig (N); % Hello I'm a function drawFig R = 10; t = 0:2*pi/N:2*pi; x = R*sin(t); y = R*cos(t); hold on plot(x,y,'linewidth',2) for J = 1:N for K = 1:J XP = [x(K) x(J)]; YP = [y(K) y(J)]; plot(XP,YP,'linewidth',2) end end ; axis square

1) Save this program with drawFig.m

2) In Matlab Command Window type help drawFig

3) Now type, e.g. drawFig(4)

Explain the program and results.

II.6

 function CircleSimple(R); %Draws a circle centred on the origin of radius R K = 0; for t = 0:pi/36:2*pi; K = K+1; X(K) = R*cos(t); Y(K) = R*sin(t); end fill(X,Y,'w'); axis square

Explain the program and results.

3－2D Transforms & Data Structures

I. Matlab Section

Use the Matlab help system to read about the following commands: tic, toc, drawnow , clock and etime.

II-1. Examples

II.1 Programming the rotation

First step : Make the following files (see programs below): testT1.m , Rotatesquare.m

Second step : Run testT1.m

Third step : Explain the program and results

Make testT1.m file

 function testT1 for theta = 0:360 Rotatesquare(theta); drawnow; t = clock; while etime(clock,t)<0.15 end end

Make Rotatesquare.m file

 function Rotatesquare(theta); %First of all define the nodes in the homogeneous format % see Topic 2 & "Mathematical Pages" Node = [-2 -2 2 2 -2; -2 2 2 -2 -2;1 1 1 1 1] %Now convert the rotation angle to radians %Remember 180 degs. = pi radians thetarad = pi*theta/180; %Now let us define the rotation matrix Ctheta = cos(thetarad); Stheta = sin(thetarad); Rot = [Ctheta -Stheta 0; Stheta Ctheta 0; 0 0 1] %Now rotate the square NewNode = Rot*Node; %Draw the square plot(NewNode(1,:),NewNode(2,:)); %Set the limits to the axes and ensure they are of equal dimension axis([-5,5,-5,5]); axis square;

Explain the program and results.

II.2

First step: Make the following files (see programs below): fig1. txt , Tut3.m , rotate.m, scale.m, Readobject.m

Second step : Run Tut3.m

Third step : Explain the program and results

Make fig1.txt file

 0,6 6,0 0,-6 -6,0

Make Tut3.m file

 function Tut3 N = readobject(' fig1.txt '); NP = N; hold off patch(NP(:,1),NP(:,2),'green','edgecolor','green'); hold on axis([-10,10,-10,10]); axis square tic timeinterval = 0; while timeinterval<1 timeinterval = toc end NR = rotate(N,45); NR = scale(NR',0.8,0.8); NP = NR'; patch(NP(:,1),NP(:,2),'blue','edgecolor','blue'); % NR = rotate(N,150); NR = scale(NR',0.5,0.5); NP = NR'; patch(NP(:,1),NP(:,2),'red','edgecolor','red'); % hold off

Make rotate.m file

 function NR = rotate(N,theta) %To rotate the node array N by the angle theta thetarad = pi*theta/180; Ctheta = cos(thetarad); Stheta = sin(thetarad); R = zeros(3,3); R(1,1) = Ctheta; R(2,2) = Ctheta; R(1,2) = -Stheta; R(2,1) = Stheta; R(3,3) = 1; NR = R*N';

Make scale.m file

 function NS = scale(N,SX,SY) %To scale the node array N by SX and SY S = zeros(3,3); S(1,1) = SX; S(2,2) = SY; S(3,3) = 1; NS = S*N';

 function N = Readobject(FN) %To load data from a text file 'FN' into a node array N temp = dlmread(FN); [a,b] = size(temp); N = ones(a,3); N(:,1)=temp(:,1); N(:,2)=temp(:,2);

Explain the program and results.

II-3

 function Spiral %To draw a 3D spiral %For efficiency we calculate X,Y and Z for a single turn R = 5; C = 2; thetastep = 10*pi/180; theta = [0:thetastep:2*pi]; X = R*cos(theta); Y = R*sin(theta); Z = C*theta; %Now extend to the second term of the spiral [dummy numpoints] = size(X); X(numpoints+1:2*numpoints)= X; Y(numpoints+1:2*numpoints)= Y; Z(numpoints+1:2*numpoints)= Z + C*2*pi; plot3(X,Y,Z,'linewidth',5);

Explain the program and results.

4－3D Transforms & Data Structures

I. Matlab Section

Use the Matlab help system to read about the following commands: dlmread, rotate3d on, patch, Nan , set

II-1. Examples

II.1

First step : Make the following file (see program below): CubeProject.m

Second step : Run CubeProject.m

Third step : Explain the program and results

Make CubeProject.m file

 function CubeProject %To illustrate normal perspective projection %Currently this progam only rotates and displays the cube %First define the basic cube V = [2 -2 -2 1; 2 -2 2 1; 2 2 2 1; 2 2 -2 1; -2 -2 -2 1; -2 -2 2 1; -2 2 2 1; -2 2 -2 1]; F = [1 2 3 4; 3 7 8 4; 7 6 5 8; 6 2 1 5; 2 6 7 3; 4 8 5 1]; VT = V'; %Define sutable rotation angles to orientate the cube theta thetaY = 60*pi/180; thetaX = 30*pi/180; %Set up a rotation matrix for the Y axis YROT = [cos(thetaY) 0 -sin(thetaY) 0 ; 0 1 0 0; sin(thetaY) 0 cos(thetaY) 0; 0 0 0 1]; XROT = [1 0 0 0 ; 0 cos(thetaX) -sin(thetaX) 0; 0 sin(thetaX) cos(thetaX) 0; 0 0 0 1]; %Now do the rotations VT = XROT*YROT*VT; %Strip off the homogeneous co_ordinate to use the patch command VP = zeros(3,8); VP=VT(1:3,:); colourset = [0 1 0;1 0 0;0 0 1;1 1 0;0 1 1;1 1 1]; patch('Vertices',VP','Faces',F,'FaceVertexCData',colourset,'facecolor','flat') axisarray = [-5 5 -5 5 -5 5 0 1]; axis(axisarray)

II.2

Step 1: Make the following files (see programs below): DisplayBuilding.m; Nhouse. txt ; Phouse. txt

Step 2 : Run DisplayBuilding.m

Step 3 : Explain the program and results

Make Nhouse.txt file

 -10,-20,0 -10,-20,20 0,-20,30 10,-20,20 10,-20,0 -10,20,0 -10,20,20 0,20,30 10,20,20 10,20,0

Make Phouse.txt file

 1,2,3,4,5 5,4,9,10, NaN 6,7,2,1, NaN 4,3,8,9, NaN 7,8,3,2, NaN 10,9,8,7,6 1,5,10,6, NaN

Make DisplayBuilding.m file

 function DisplayBuilding %To display a basic Building Node = dlmread('Nhouse.txt'); Face = dlmread('Phouse.txt'); patch('vertices',Node,'faces',Face,'facecolor','b'); %Depending on the size of the building you may need to change the axes range axis([-100 100 -100 100 -100 100 0 1]); grid; axis square set(gcf,'renderer','zbuffer')

II-3

Step 1: Make the following file: HouseDraw1.m; and check that you already have files: NHouse.txt & PHouse.txt

Step 2 : Run HouseDraw1.m

Step 3 : Explain the program and results

 function HouseDraw1 %Draws a simple house %Data on nodes is read from a text file NHouse.txt %Data on patches is read from a text file PHouse.txt Node = dlmread('NHouse.txt'); Face = dlmread('PHouse.txt'); %Draw the house colourset = [0.2 0.8 0.2]; patch('vertices',Node,'faces',Face,'FaceVertexCData',colourset,'FaceColor','flat'); axis_data = [-40 40 -40 40 -40 40 0 1]; grid; axis(axis_data); axis square; rotate3d on

II-4.

Step 1: Make the following file: HouseDraw2.m; and check that you already have files: NHouse.txt & PHouse.txt

Step 2 : Run HouseDraw2.m

Step 3 : Explain the program and results

Step 4 : Compare results with Example II-3

Step 5: Delete NaN s from PHouse.txt file

Step 6 : Explain and Compare results with Example II-3

Make HouseDraw2.m file:

 function HouseDraw2 %Draws a simple house %Data on nodes is read from a text file NHouse.txt %Data on patches is read from a text file PHouse.txt Node = dlmread('NHouse.txt'); %Now read in the uncorrected patch data UPatch = dlmread('PHouse.txt'); %First find how many patches we need %We don't care about the other dimension X [numpatches,X]=size(UPatch); %Now lets sort into 4 node & 5 node faces num4 = 0; for k = 1:numpatches if UPatch(k,5)==0 num4 = num4 + 1; end end Face4 = zeros(num4,4); Face5 = zeros(numpatches-num4,5); j = 1; i=1; for k = 1:numpatches if UPatch(k,5)==0 Face4(j,:)=UPatch(k,1:4); j=j+1; else Face5(i,:)=UPatch(k,:); i = i+1; end end colourset = [0]; % patch('Vertices',Node,'Faces',Face4,'FaceVertexCData',colourset,'FaceColor','r') patch('Vertices',Node,'Faces',Face5,'FaceVertexCData',colourset,'FaceColor','flat') axis_data = [-40 40 -40 40 -40 40 0 1]; grid; axis(axis_data); axis square; rotate3d on

II-5.

First step: Make the following files: testCone.m & Cone.m

Second step : Run testCone.m

Third step : Explain the program and results

Make testCone.m file:

 function testCone; % How to colour a face R = 4; h = 2; L = 10; [X,Y,Z] = Cone; surf(X,Y,Z,'facecolor',[0.2 0.8 0.2]) axis equal axis square rotate3D on

Make Cone.m file:

 function [X,Y,Z] = Cone(R,h,L) % To create X,Y,Z data to draw a truncated cone. % R = base radius of the cone. % h = height to which the cone is drawn % L = apex of the cone % Note setting h = L will draw the full cone if nargin < 3, L = 1; end if nargin < 2, h = L; end if nargin == 0, R = 1; end stepsize = h/10; t = 0:stepsize:h; [X,Y,Z] = cylinder((R*(1-t/L)));

I. Matlab Section

Use the Matlab help system to read about the following commands: light, lighting gouraud, cylinder, sphere

II-1. Examples

II.1

First step : Make the following file (see program below): LightDemo.m

Second step : Run LightDemo.m

Third step : Explain the program and results

Make LightDemo.m file

 function LightDemo %To demonstrate some of the properties of lighting %Create a sphere with a red colour and draw it with the surf command [X,Y,Z] = sphere(30); surf(X,Y,Z,'FaceColor','red','EdgeColor','none'); %Try changing the material to dull, shiny, metal and see the effect material shiny; %material metal; %material dull; %Light is incident along the X axis and is located an infinite distance away %Try changing the colour of the light (e.g. 'white', 'green', 'blue' etc.) light('Position',[1 0 0],'Style','infinite','color','white'); %Try the effects of flat, gouraud or phong shading lighting gouraud axis square rotate3D on

II.2

Step 1: Make the following files: goblet. txt & gobletprofile.m & RevObject.m

Step 2: Run gobletprofile.m

Step 3: Run RevObject(6)

Step 4 : Explain the program and results

Make gobletprofile.m file:

 function gobletprofile %To display the outline profile of a the goblet U = dlmread('goblet.txt'); [a,b] = size(U); plot(U(:,1),U(:,2),'-o','linewidth',2) axis([0 12 0 12]) axis square

Make goblet. txt file (i.e. the digitised profile of the object is presented as follows):

 5,10 5,6 2,4 2,2 5,0

Make RevObject.m file:

 function RevObject(n) %To generate a 3D object from the digitised profile in 'goblet.txt' %NOTE this version only works with 5 nodes in the profile %First read in the data, set the number of nodes and faces U = dlmread('goblet.txt'); [a,b] = size(U); numnodes = a*n; numpatch = (a-1)*n; Node = zeros(numnodes,3); PSet = zeros(numpatch,4); %Now calculate all the node values for k = 0:n-1 for L = 1:a theta = 2*k*pi/n; Node(L+a*k,1) = U(L,1)*cos(theta); Node(L+a*k,2) = U(L,1)*sin(theta); Node(L+a*k,3) = U(L,2); end ; end ; %Uncomment the following line if you want to see the node list %Node %Now assign nodes to faces (or patches) for k = 1:n term = 5*(k-1); for L = 1:4 Pset(4*(k-1)+L,:) = [(term+L) (term+L+1) (term+L+a+1) (term+L+a)]; end ; end ; %Finally ensure that the last but one profile connects to the first %Pset for k = numpatch-3:numpatch Pset(k,3)=Pset(k,3)-numnodes; Pset(k,4) = Pset(k,4) - numnodes; end %Uncomment the following line if you want to see the patch array %Pset patch('Vertices',Node,'Faces',Pset,'facecolor',[0.2 0.8 0.2],'edgecolor',[0 0 0]) %alpha(0.3) %light('Position',[1 0 0],'Style','infinite'); axis square rotate3d on

6－Image Analysis - Basics

I. Matlab Section

We can load an image with the ‘ imread ’ function and display an image with the ‘ imshow ’ function.

In the first form the image is read into the array A and the format of the image ‘ fmt ’ is optional.

In the second form the image is read into the array X and the associated indexed map into ‘ map ’ scaled 0 to 1 as double.

imshow(A)

imshow(X,map)

imshow has many other formats

I-2. Image Type Conversions

MatLab allows easy conversion between image types using :

rgb2hsv to convert to a HSV image

rgb2gray to convert to a grey scale image (note American spelling).

rgb2ind to convert to an indexed image

You should check the details in the MatLab help files.

With the addition of the following line (and a variable name change) the previous example can be used to display the HSV components.

B = rgb2hsv(A);

I-3. Inspecting and Recording Image Colours

improfile : which will reveal the colour intensity profile along a line defined on the image.

Simply placing improfile on a line will allow you to interactively explore the colour profile alternatively using :

c = improfile(image,xi,yi,n);

will record in the array ‘ c ’ the RGB values from image image with line segment end points defined by xi & yi using ‘ n ’ equally spaced points

pixval : which will interactively record the location and colour components of each pixel as you move a cursor across the image.

impixel : returns the RGB values for a specified pixel.

I-4. Histogram Manipulation

The histogram of an image is a simple way to see how the gray level (i.e. the information) is spread over the available range of grey levels. This in turn can be used to highlight problems during the acquisition. The histogram can also be modified to make better use of the available range for further processing and display.

Matlab has several functions available to calculate and process histograms:

imhist : Display the histogram of an image. Synthax:

hist = imhist(image,nb_boxes)

imhist works with uint8 types images.

histeq : histogram equalisation and specification. Synthax:

ima1 = histeq(image,hgram)

where hgram is a specified histogram. If hgram is not present, histogram equalisation is performed.

II-1. Examples

Make m-files

II.1

 function colourdisplay %Displaying the individual colours %To demonstrate the splitting of an image into its primary colours % Save an image, for example Egik.jpg A = imread('Egik.jpg'); subplot(2,2,1); imshow(A); title('RGB image'); Redimage = A(:,:,1); subplot(2,2,2); imshow(Redimage); title('Red image'); Greenimage = A(:,:,2); subplot(2,2,3); imshow(Greenimage); title('Green image'); Blueimage = A(:,:,3); subplot(2,2,4); imshow(Blueimage); title('Blue image');

Explain the program and results.

Select color which gives the best contrast.

II-2.

 function ImageTest A = imread('Egik.jpg'); %Check that it was indeed loaded whos % Display the image imshow(A) % Convert the variable into double A=im2double(A); % Check that the variable indeed was converted into double whos % The next procedure cuts out the upper left corner % (i.e. the leaf) of the image % and stores the reduced image as Ared for i=1:145 for j=1:180 Ared(i,j)=A(i,j); end end %Check what variables you now have stored whos % Display the reduced image imshow (Ared)

Explain the program and results.

II.3

 function AnalyseImage %To demonstrate using arithmetic on image data % Save an image Egik.jpg myfilename = 'Egik.jpg'; A = imread(myfilename); R = A(:,:,1); G = A(:,:,2); B = A(:,:,3); subplot(2,2,1);imshow(A); title('Original'); subplot(2,2,2);imshow(R); title('Red'); subplot(2,2,3);imshow(G); Title('Green'); Rconverted = double(R) + 1; Gconverted = double(G) + 1; Dconverted = Rconverted - Gconverted; D = uint8(Dconverted - 1); subplot(2,2,4);imshow(D); title('Difference red - green');

Explain the program and results.

II.4

 function TestTry %First load an image and display filename = ['Egik.jpg']; J = imread(filename); figure; subplot(2,2,1),imshow(J); Title('Original'); % In order to convert the indexed image into an intensity % (gray scale) image use the ind2gray command J=rgb2gray(J); whos % now the size indicates that our image is a regular matrix. subplot(2,2,2),imhist(J); Title('imhist'); %Use only one of the following 3 lines at a time %I = (J>35) & (J<60); %I = (J>70) & (J<110); %I = (J>110); %figure, imshow(I); lowin = 35/255; highin = 60/255; K = imadjust(J,[lowin highin],[ ]); subplot(2,2,3),imshow(K); Title('imadjust');

Explain the program and results.

II-5.

 function ThreshHold %To demonstrate thresholding an image J = imread('Egik.jpg'); subplot(2,1,1);imshow(J); BW = im2bw(J,0.6); subplot(2,1,2);imshow(BW);

II-6.

 function Equalise %To show the effects of histogram equalisation J = imread('Egik.jpg'); J=rgb2gray(J); subplot(2,1,1);imshow(J); K = histeq(J); subplot(2,1,2);imshow(K);
Explain the program and results.

7－Image Segmentation

I. Matlab Section

I-1.

im2bw converts image to binary image by thresholding.

I-2.

graythresh is used to determine a threshhold for converting the image to binary.

I-3.

bwlabelsearches for connected components and label them with unique numbers. bwlabel takes a binary input image and a value specifying the connectivity of objects.

I-4.

STATS = regionprops (L,PROPERTIES) measures a set of properties for each labeled region in the label matrix L.

Positive integer elements of L correspond to different regions. For example, the set of elements of L equal to 1 corresponds to region 1; the set of elements of L equal to 2 corresponds to region 2; and so on.

STATS is a structure array of length max(L(:)).

The fields of the structure array denote different properties for each region, as specified by PROPERTIES.

I-5.

You can use find function in conjunction with bwlabel to return vectors of indices for the pixels that make up a specific object.

I-6.

Use the Matlab help system to read about the following commands: max, min, find

II-1. Examples

Make m-files

II-1.

 function Hist1 % Basic Global Thresholding % Select a Threshold Value from the Histogram% note that Egik.jpg is from Collection of ImagesA=imread('Egik.jpg'); % imshow(A); figure; image(A); A=rgb2gray(A); imhist(A); % figure; % to define normalised gray level, see imhist e.g. k1=200/255k1=200/255;BW1=im2bw(A,k1); % imshow(BW1); % figure; k2=20/255;BW2=im2bw(A,k2); % imshow(BW2); % figure; k3=150/255;BW3=im2bw(A,k3); % imshow(BW3); figure; subplot(2,2,1), imhist(A); Title('imhist of Image'); subplot(2,2,2), imshow(BW1); Title(['BW1 Image with k1=', num2str(k1)]); subplot(2,2,3), imshow(BW2); Title(['BW2 Image with k2=', num2str(k2)]); subplot(2,2,4), imshow(BW3); Title(['BW3 Image with k3=', num2str(k3)]);

Explain the program and results.

II-2.

 function GlobalThresh% Compute global image threshold using Otsu's methodA = imread('Egik.jpg'); A=rgb2gray(A); level=graythresh(A); level BW6 = im2bw(A,level); figure, imshow(BW6);Title(['BW6 Image with global threshold level = ', num2str(level)]);

Explain the program and results.

II-3.

 function EdgeEgik%To edge detect an EgikA = imread('Egik.jpg'); A=rgb2gray(A); [BW,thresh] = edge(A,'sobel'); imshow(BW); thresh

Explain the program and results.

II-4.

 function ConnectedObjects % % savebean.jpgimage from Collection of ImagesA = imread('bean.jpg'); A=rgb2gray(A); [BW,thresh] = edge(A,'sobel'); imshow(BW); Title('BW Image'); thresh % use bwlabel to return in num the number of connected objects found in BW[L,num] = bwlabel(BW,8); % convert a label matrix into an RGB image for the purpose of visualising % the labeled regions % use the following two lines to view the regions found and % to decide on the selection criteria RGB=label2rgb(L); figure, imshow(RGB); Title('RGB Image'); num

Explain the program and results.

II-5.

 function SelectRegion % savebean.jpgimage from Collection of ImagesA = imread('bean.jpg'); A=rgb2gray(A); BW = edge(A,'sobel',0.04); imshow(BW); Title('BW Image'); [L,num] = bwlabel(BW,8);RGB=label2rgb(L); figure, imshow(RGB); Title('RGB Image'); num % Measure properties of image regions. % Consider the following approach to selecting the image profile STATS = regionprops(L,'BoundingBox','MajorAxisLength'); for j=1:num if STATS(j).MajorAxisLength>100 maxobject=j; end end maxobject boxsize=STATS(maxobject).BoundingBox; % The bounding box represents the smallest rectangle that can contain a region. %The four element vector returned by the BoundingBox field. % Two first elements show the upper left corner of the bounding box % and two last ones represent a width and a hight of the box. boxsize xb1 = round(boxsize(1)); xb2= round(boxsize(1)+boxsize(3)); yb1=round(boxsize(2)); yb2= round(boxsize(2)+boxsize(4)); BWW=BW(yb1:yb2, xb1:xb2); figure, imshow(BWW)
Explain the program and results.

8、9－Morphological Image Processing

I. Matlab Section

I-1.

Use the Matlab help system to read about the following commands: strel, imopen, imclose

I-2.

Reminder: impixel can return values and/or coordinates (in ROW/COL)

II-1. Examples

Make m-files

II-1.

 function MorDisk% Create morphological structuring element with a disk of the given radiousclear, close all, A = imread('bean.jpg'); A=rgb2gray(A); BW = edge(A,'sobel',0.04); imshow(BW); Title('BW Image'); [L,num] = bwlabel(BW,8); % Label components RGB=label2rgb(L); figure, imshow(RGB); Title('RGB Image'); num figure, subplot(2,2,1), imshow(A); Title('Original'); % Perform a morphological opening operation by calling imopen with a disk-shaped % structuring element with radiouses of 10, 25, 30, 40. % The structuring element is created by the strel function. % The morphological opening has the effect of removing objects that cannot % completely contain a disk of the given radious. % try RL=imopen(A,strel('disk', 40)); % RL=imopen(A,strel('disk', 25)); RL=imopen(A,strel('disk', 3)); subplot(2,2,2), imshow(RL) Title('RL Image');

Explain the program and results.

II-2.

 function MorSquare% Create morphological structuring element with a sguare clear, close all, A = imread('bean.jpg'); A=rgb2gray(A); BW = edge(A,'sobel',0.04); imshow(BW); Title('BW Image'); [L,num] = bwlabel(BW,8); % Label components RGB=label2rgb(L); figure, imshow(RGB); Title('RGB Image'); num figure, subplot(2,2,1), imshow(A); Title('Original'); % Perform a morphological opening operation by calling imopen with a sguare structuring element % SE = strel('square',W) creates a square structuring element whose width is W pixels. W must be a nonnegative integer scalar. % try RL = imopen(A,strel('square',100));% RL = imopen(A,strel('square',10));RL = imopen(A,strel('square',40));subplot(2,2,2), imshow(RL) Title('RL Image');

Explain the program and results.

II-3.

 function TestMor % Step 1: Threshold the image A = imread('bean.jpg'); BW = ~im2bw(A,graythresh(A)); % tryBW = im2bw(A,graythresh(A)); imshow(A), title('Original') figure, imshow(BW); Title('Step 1: Thresholded Image') %Step 2: Create morphological structuring element with a disk-shaped % structuring element with a given radius MR = strel('disk',6); % Step 3: Close with a disk of radius 6 to merge % together small features that are close together. BW2 = imclose(BW,MR); figure, imshow(BW2); Title('Step 3: Closing') % Step 4: Follow with an opening to remove the isolated white pixels. BW3 = imopen(BW2,MR); figure, imshow(BW3); Title('Step 4: Opening')

Explain the program and results.

II-4.

 function MorNum % Step 1: Threshold the image A = imread('bean.jpg'); BW = ~im2bw(A,graythresh(A)); imshow(A), title('Original') figure, imshow(BW); Title('Step 1: Thresholded Image') %Step 2: Create morphological structuring element with a disk-shaped % structuring element with a given radius MR = strel('disk',6); % Step 3: Close with a disk of radius 6 to merge % together small features that are close together. BW2 = imclose(BW,MR); figure, imshow(BW2); Title('Step 3: Closing') % Step 4: Follow with an opening to remove the isolated white pixels. BW3 = imopen(BW2,MR); figure, imshow(BW3); Title('Step 4: Opening')% Determine the Number of Objects in the Image[L,num] = bwlabel(BW2,8); % compare the number of beans on the image with num that you have received % after opening process num STATS = regionprops(L,'BoundingBox','MajorAxisLength'); for j=1:num if STATS(j).MajorAxisLength>100 maxobject=j; end end maxobject boxsize=STATS(maxobject).BoundingBox; boxsize xb1 = round(boxsize(1)); xb2= round(boxsize(1)+boxsize(3)); yb1=round(boxsize(2)); yb2= round(boxsize(2)+boxsize(4)); BWW=BW(yb1:yb2, xb1:xb2); figure, imshow(BWW)

Explain the program and results.

II-5.

 function MorColor A = imread('bean.jpg'); BW = ~im2bw(A,graythresh(A)); imshow(A), title('Original') figure, imshow(BW); Title('Step 1: Thresholded Image') % Step 2: Create morphological structuring element MR = strel('disk',6); BW2 = imclose(BW,MR); figure, imshow(BW2); Title('Step 3: Closing') BW3 = imopen(BW2,MR); figure, imshow(BW3); Title('Step 4: Opening') [L,num] = bwlabel(BW2,8); num % Now draw the outline profile (note that an outline profile is a graphic summary of the object presented by the line by which the object is defined or bounded; contour)imwrite(BW2,'BW.jpg'); % saves the imageD = imread('BW.jpg');ED = edge(D,'sobel'); % creates a binary image using the Sobel approximationimshow(ED); % displays imageTitle('Outline profiles - Image'); %RGB=label2rgb(L); figure, imshow(RGB); Title('RGB Image');

Explain the program and results.

II-6. Run the following program with the processes: Closing-Opening, i.e.

 function MorCO A = imread('Egik.jpg'); BW = ~im2bw(A,graythresh(A)); MR = strel('disk',6); BW2 = imclose(BW,MR); BW3 = imopen(BW2,MR); figure, subplot (2,2,1), imshow(A); Title('Original') subplot(2,2,2), imshow(BW); Title('Step 1: Thresholded Image') % Note that Step 2: Create morphological structuring element subplot(2,2,3), imshow(BW2); Title('Step 3: Closing') subplot(2,2,4), imshow(BW3); Title('Step 4: Opening') [L,num] = bwlabel(BW2,4); num

Explain the program and results.

II-7. Now we modify and run the program II-6 with the processes: Opening-Closing, i.e.

 function MorOCA = imread('Egik.jpg'); BW = ~im2bw(A,graythresh(A)); MR = strel('disk',6); BW2 = imopen(BW,MR); BW3 = imclose(BW2,MR); figure, subplot (2,2,1), imshow(A); Title('Original') subplot(2,2,2),imshow(BW); Title('Step 1: Thresholded Image') % Note that Step 2: Create morphological structuring element subplot(2,2,3),imshow(BW2); Title('Step 3: Opening') subplot(2,2,4), imshow(BW3); Title('Step 4: Closing') [L,num] = bwlabel(BW2,4); num

Explain the program and results.

II-8. Run the following program with the processes: Closing-Opening, i.e.

 function MorCOBeanA = imread('bean.jpg'); BW = ~im2bw(A,graythresh(A)); MR = strel('disk',6); BW2 = imclose(BW,MR); BW3 = imopen(BW2,MR); [L,num] = bwlabel(BW2,4); num % find All Beans beandata=regionprops(L,'basic'); allbeans=[beandata.Area]; % find max & min Beansmaxbean=max(allbeans); maxbean minbean=min(allbeans); minbean % find Big Bean bigbean=find(allbeans==maxbean); bigbean % find Small Bean smallbean=find(allbeans==minbean); smallbean

Explain the program and results (find in Matlab Command Window).

II-9. Now we modify and run the program II-8 with the processes: Opening-Closing, i.e.

 function MorOCBeanA = imread('bean.jpg'); BW = ~im2bw(A,graythresh(A)); MR = strel('disk',6); BW2 = imopen(BW,MR); BW3 = imclose(BW2,MR); [L,num] = bwlabel(BW2,4); num % find All Beans beandata=regionprops(L,'basic'); allbeans=[beandata.Area]; % find max & min Beansmaxbean=max(allbeans); maxbean minbean=min(allbeans); minbean % find Big Bean bigbean=find(allbeans==maxbean); bigbean % find Small Bean smallbean=find(allbeans==minbean); smallbean

Explain the program and results (find in Matlab Command Window).

II-10.

 function CoordinateGenerator % generate a Vector Model of the object profile clear, close all, A = imread('bean.jpg'); BW = ~im2bw(A,graythresh(A)); MR = strel('disk',6); BW2 = imclose(BW,MR); [L,num] = bwlabel(BW2,8); num STATS = regionprops(L,'BoundingBox','MajorAxisLength'); for j=1:num if STATS(j).MajorAxisLength>100 maxobject=j; end end maxobject boxsize=STATS(maxobject).BoundingBox; boxsize xb1 = round(boxsize(1)); xb2 = round(boxsize(1)+boxsize(3)); yb1 = round(boxsize(2)); yb2= round(boxsize(2)+boxsize(4)); BWW=BW2(yb1:yb2, xb1:xb2); figure, subplot(2,2,1), imshow(BWW) % to digitise an object (e.g. image, profile) means to convert this object into numbers % to digitise the outline profile generate Coordinates for a Vector Model as follows:% define/set a number of steps, e.g. 100ystepsnum= 100; % to define the step size use a hight of the box, % i.e. boxsize(4)-see Tutorial 7, Example II-5. step=round((boxsize(4))/ystepsnum); % to generate coordinates of the bean use impixel% Note: a Vector Model of the bean profile is defined by a set of coordinatesfor I=1:ystepsnum ystep=1+(I-1)*step; for K=1:boxsize(3) Px=impixel(BWW,K,ystep); if Px>0 X(I)= K- boxsize(3)/2; Y(I)= boxsize(4)- ystep; break end end end %use theVector Model to plot the profile of the beansubplot (2,2,2), plot(X,Y) axis equal

posted on 2006-10-11 21:02 Rosen 阅读(8494) 评论(4)  编辑  收藏 所属分类: MatLab

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# re: Matlab-图形算法和图像处理指南 2006-10-12 17:19 水滴

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# re: Matlab-图形算法和图像处理指南 2009-01-10 20:14 vvvvvvvv

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