matlab中graph函數，begin entries matlab,Matlab-圖形算法和圖像處理指南

筆者前言

本指南一共9 章，由 Valentina Plekhanova 博士撰寫，鏈接地址http://osiris.sunderland.ac.uk/%7Ecs0vpl/GIP-VP%20Tutorials.htm。筆者花費了大量時間來找尋關于 Matlab 圖像處理方面的資料，很遺憾的是中文資料實在太少，可以說根本沒有！全國眾多高等院校、科研院所，竟然如此缺乏有奉獻精神的知識分子，筆者深感遺憾！

matlab中graph函數？本指南描述性的句子不多，文筆流暢，所以筆者放棄了翻譯的念頭。算是轉載一下吧，為國內關注圖像處理的研發人員盡綿薄之力。指南中用到的圖像可在

推薦比較好的論壇：仿真論壇 http://www.simwe.com/forum，如果你還在為 C++ 與 Matlab 混合編程以及調用發愁，請參考《深入淺出MATLAB 7.x混合編程》一書。

1－Intoduction to Matlab & Curve Drawing

figure matlab用法、I. Entering and Loading Data

Examples:

Enter a 4 x 1 vector

matlab趣味圖像處理？>> 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

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.

Themarker typesare

' + '

+

' 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';

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

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)));

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

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

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 0to 1as 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.

im2bwconverts image to binary image by thresholding.

I-2.

graythreshis used to determine a threshhold for converting the image to binary.

I-3.

bwlabelsearches for connected components and label them with unique numbers.bwlabeltakes 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.

STATSis a structure array of lengthmax(L(:)).

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

Use the Matlabhelpsystem to read more about this command.

I-5.

You can usefindfunction in conjunction withbwlabelto return vectors of indices for the pixels that make up a specific object.

I-6.

Use the Matlabhelpsystem to read about the following commands:max, min, find

II-1. Examples

Make m-files

II-1.functionHist1

% Basic Global Thresholding

% Select a Threshold Value from the Histogram

A=imread('Egik.jpg');

% imshow(A);

figure;

image(A);

A=rgb2gray(A);

imhist(A);

% figure;

% to define normalised gray level, seeimhiste.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.functionGlobalThresh

% Compute global image threshold usingOtsu'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.functionEdgeEgik

%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.functionConnectedObjects

A = imread('bean.jpg');

A=rgb2gray(A);

[BW,thresh] = edge(A,'sobel');

imshow(BW);

Title('BW Image');

thresh

% usebwlabelto return innumthe number of connected objects found inBW

[L,num] = bwlabel(BW,8);

% convert a label matrix into anRGBimage 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.functionSelectRegion

% savebean.jpg

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');

forj=1:num

ifSTATS(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 Matlabhelpsystem to read about the following commands:strel, imopen, imclose

I-2.

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

Use the Matlabhelpsystem to read more about this command.

II-1. Examples

Make m-files

II-1.functionMorDisk

% 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 of10, 25, 30, 40.

% The structuring element is created by thestrelfunction.

% The morphological opening has the effect of removing objects that cannot

% completely contain a disk of the given radious.

% tryRL=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.functionMorSquare

% 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 isWpixels.Wmust be a nonnegative integer scalar.

% tryRL = 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.functionTestMor

% 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 radius6to 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');

forj=1:num

ifSTATS(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.functionMorColor

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 theoutline 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.functionMorCO

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-6with the processes: Opening-Closing, i.e.functionMorOC

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.functionMorOCBean

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.functionCoordinateGenerator

% 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');

forj=1:num

ifSTATS(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. 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 useimpixel

% Note: a Vector Model of the bean profile is defined by a set of coordinates

forI=1:ystepsnum

ystep=1+(I-1)*step;

forK=1:boxsize(3)

Px=impixel(BWW,K,ystep);

ifPx>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 bean

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

axis equal

請注意！引用、轉貼本文應注明原收集者：Rosen Jiang 以及出處：http://www.blogjava.net/rosen