Matlab-图形算法和图像处理指南

笔者前言

本指南一共 9 章，由 Valentina Plekhanova 博士撰写，链接地址http://osiris.sunderland.ac.uk/%7Ecs0vpl/GIP-VP%20Tutorials.htm。笔者花费了大量时间来找寻关于 Matlab 图像处理方面的资料，很遗憾的是中文资料实在太少，可以说根本没有！全国众多高等院校、科研院所，竟然如此缺乏有奉献精神的知识分子，笔者深感遗憾！

本指南描述性的句子不多，文笔流畅，所以笔者放弃了翻译的念头。算是转载一下吧，为国内关注图像处理的研发人员尽绵薄之力。指南中用到的图像可在 http://osiris.sunderland.ac.uk/%7Ecs0vpl/Com366-Images.htm 找到，所采用的 Matlab 版本是 7.1.0.246 (R14)。

推荐比较好的论坛：仿真论坛 http://www.simwe.com/forum，如果你还在为 C++ 与 Matlab 混合编程以及调用发愁，请参考《深入浅出MATLAB 7.x混合编程》一书。

1－Intoduction to Matlab & Curve Drawing

I. Entering and Loading Data

Examples:

Enter a 4 x 1 vector

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

Enter a 4 x 1 vector

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

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	55+22
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

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';

Make Readobject.m file

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

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

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)));

5－3D Transforms; Shading,Light & Colour

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

Read Sweep Generation Help

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 ;

%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 ;

%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

I-1. Loading & Displaying an Images

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

A = imread(filename,fmt)

[X,map] = imread(filename,fmt)

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 from Collection of Images

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

%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 from Collection of Images

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.

Use the Matlab help system to read more about this command.

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 Images

A=imread('Egik.jpg');

% imshow(A);

figure;

image(A);

A=rgb2gray(A);

imhist(A);

% figure;

% to define normalised gray level, see imhist e.g. k1=200/255

k1=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 method

A = 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 Egik

A = 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 Images

A = 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 Images

A = 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

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)

Use the Matlab help system to read more about this command.

II-1. Examples

Make m-files

II-1.

function MorDisk

% Create morphological structuring element with a disk of the given radious

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 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

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 image

D = imread('BW.jpg');

ED = edge(D,'sobel'); % creates a binary image using the Sobel approximation

imshow(ED); % displays image

Title('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 MorOC

A = 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 MorCOBean

A = 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 Beans

maxbean=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 MorOCBean

A = 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 Beans

maxbean=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

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. 100

ystepsnum= 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 coordinates

for 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

%use theVector Model to plot the profile of the bean

subplot (2,2,2), plot(X,Y)

axis equal

请注意！引用、转贴本文应注明原收集者：Rosen Jiang 以及出处：http://www.blogjava.net/rosen

Matlab-图形算法和图像处理指南

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