Image Processing with MATLAB Lab of COMP 319 Image Processing with MATLAB Lab tutor : Shenghua ZHONG Email: zsh696@gmail.com csshzhong@comp.polyu.edu.hk Lab 2: Nov 9, 2011

Outline of Lab 3 Review of Lab 2 User defined function Execution control Plots and graphs using Matlab Basic manipulation in image processing Color image compression

Outline of Lab 3 Review of Lab 2 User defined function Execution control Plots and graphs using Matlab Basic manipulation in image processing Color image compression

Review of Lab 2 about Data Structure Introduction the basic data structure in Matlab Vector and Array The distinct attributes of these data structures Numerical Value Index

Review of Lab 2 about Data Structure 3. What we have learnt How to create them For example: A = [3, 4, 5; 6, 5.5, 0] How to manipulate them For example: A(1,1:2) = A(1,1:2) + 2 How to access their elements For example: B = A(1,1:2) How to perform mathematical and logical operations on them For example: C = A./2.5; D = sum(sum(A)) For example: E = A > 0.5

Review of Lab 2 about M file “File” - “New” - “Script”/“Function”

Review of Lab 2 about M file Open the M-file’s and run it.

Outline of Lab 3 Review of Lab 2 User defined function Execution control Plots and graphs using Matlab Basic manipulation in image processing Color image compression

User-Defined Function A function is a piece of computer code that accepts an input argument from the user and provides output to the program. You may wish to define your own functions-those which are used commonly in your programming. User-defined functions are stored as M-files and can be accessed by Matlab if they are in the current directory.

User-Defined Function Each function consists of a name, user-provided input, and calculated output. For example, the function: my_function(x) is named my_function, takes user input inside the parentheses (in this case, x), and calculate a result. The user does not see the calculations performed, but just accepts the answer. The function could be regarded as a black box. input output function

User-Defined Function User-defined functions are stored as M-files. Each must start with a function definition line that contains the word “function”, one or several variables that defines the function output, a function name, and one or several variables used for the input argument. Save the function as M-file using the same name in your function Some examples: function output = my_function(x) function [output1, output2] = my_function(x1,x2,x3) Hints: The function name and the names of the input and output variables are arbitrary and selected by the programmer, but the word “function” can not be changed.

User-Defined Function function output = my_poly(x) % This function calculates the value of a third-order % polynomial output = 3*x.^3+5*x.^2-2*x+1 comments Save above commands into an M-file and then type the below commands in command window to observe the results: >> a=4; >> my_poly(a) >> b=1:5; >> my_poly(b)

Outline of Lab 3 Review of Lab 2 User defined function Execution control Plots and graphs using Matlab Basic manipulation in image processing Color image compression

Objectives of Execution Control Why need execution control You may want to execute some parts of the code under certain circumstances only; You may want to repeat a section of code a certain number of times. 14

Conditional Execution General concepts if statements 15

General Concepts Generally speaking, the statements written in our scripts have been executed in sequence from the top (the first line) to the bottom (the last line). However, it is frequently necessary to make choices about how to process a set of data based on some characteristic of that data. 16

if Statements A set of statements (the code block to be executed) is shown as a rectangle, a decision point is shown as a diamond, and the flow of program control is indicated by arrows. The execution of a code block is based on some conditional test. If the result of the test is true, the code block is executed. Otherwise, the code block is omitted and the instructions after the end of that code block are executed. if condition false true statements A simple if statement 17

if Statements Examples: Suppose Test =[2 0 0 0 ; 3 0 0 0; 4 0 0 0; 0 0 0 1] Type if Test(1,1)>0 | Test(2,4)==0 display(‘TRUE’) else display(‘FALSE’) end Matlab displays ans = TRUE Type if Test(4,4)>0 display(‘Condition is true’) end Matlab displays ans = Condition is true

A compound if statement (more than one conditional test) if Statements if condition false elseif condition false … elseif condition false else true true true statements(1) statements(2) statements(n) statements(n+1) A compound if statement (more than one conditional test) In the compound if statement, if the first logical test returns false, a second test is performed to determine whether the second code block should be executed. If that test returns false, as many further tests as necessary may be performed, each with the appropriate code block to be implemented when the result is true. Finally, if none of these tests returns true, the last code block (with the keyword else) is executed. 19

A compound if statement (more than one conditional test) if Statements if condition false elseif condition false … elseif condition false else true true true statements(1) statements(2) statements(n) statements(n+1) A compound if statement (more than one conditional test) If one of the code blocks is executed, the next instruction to execute is the one that follows the conditional code after the end statement. In particular, if there is no else clause, it is possible that no code at all is executed in this conditional statement. 20

General Template of if Statements if <logical expression 1> <code block 1> elseif <logical expression 2> <code block 2> elseif <logical expression n> <code block n> else <default code block> end … 21

Important Notes of if Statements The only essential ingredients are the first if statement, one code block, and the end statement. All other features may be added as the logical requires. The code blocks may contain any sequence of legal Matlab statements, including other if statements (nested ifs). Nested if statements with a code block are an alternative implementation of a logical and statement. clear all; a = 5; if a>3 if a-4 == 1 b=6 end % if a>3 & a-4==1 clear all; a = 5; if a>3 if a-4 == 1 b=6 end clear all; a = 5; if a>3 & a-4==1 b=6 end 22

Iteration General concepts for loops 23

General Concepts Iteration allow controlled repetition of a code block. Control statements at the beginning of the code block specify the manner and extent of the repetition. The for loop is designed to repeat its code block a fixed number of times and largely automates the process of managing the iteration. 24

for Loops The repeated execution of the code block is performed under the control of a loop-control variable. It is first set to an initial value that is tested against a terminating condition. If the terminating test succeeds, the program leaves the for loop. Otherwise, the computations in the code block are performed using the current value of that variable. When one pass through the code block is finished, the variable is updated to its next value, and control returns to the termination test. for <loop> Done computations Structure of a for loop 25

General Template of for Loops for <variable specification> <code block> end All of the mechanics of iteration control are handled automatically in the variable specification section. 26

Important Notes of for Loops The core concept in the Matlab for loop implementation is in the style of the variable specification, which is accomplished as follows: <variable specification>: <variable> = <vector> where <variable> is the name of the loop control variable and <vector> is any vector that can be created by the techniques discussed in this lab. 27

for Statements Example: Type for k = 1:10 Remember - the colon operator k indicates every integer between end the start and end OR Matlab displays start : increment : end k = 1 2 and so on, through k = 10. Type for counter = 2:2:10 counter notice that counter increments end by 2 with each time thru the loop

Exercise 1 (Control Structure) Create a M-file and write these codes down. % use the percent sign to Mymatrix = [1:5; 14:2:22; 50:-7:22]; % indicate comments for i = 1:3 for j = 1:5 if Mymatrix(i,j)< 5 | Mymatrix(i,j) > 20 newmatrix(i,j) = Mymatrix(i,j); elseif Mymatrix(i,j) == 20 newmatrix(i,j) = 100; else newmatrix(i,j) = 0; %semicolon means end %Matlab won’t display end

Outline of Lab 3 Review of Lab 2 User defined function Execution control Plots and graphs using Matlab Basic manipulation in image processing Color image compression

Basic Plotting Simple x-y plots: >> x=[0:2:18]; >> plot(x,y) Hint: The number of elements in vector x must be equal to the number of elements in vector y, otherwise it will make an error.

Basic Plotting Titles, Labels, and Grids: >> x=[0:2:18]; >> y=[0,0.33,4.13,6.29,6.85,11.19,13.19,13.96,16.33,18.17]; >> plot(x,y), title('Lab Experiment 1'), xlabel('Time'), ylabel('Distance'), grid on Hint: You must create a graph before you add the title and labels. If you specify the title and labels first, they are erased when the plot command executes.

Basic Plotting Line, Color, and Mark style: >> x=[0:2:18]; >> plot(x,y,':ok',x,y*2,'--xr',x,y/2,'-b') Hint: You plot three different x-y plots in one image, using different line type, point type and color.

Basic Plotting Line, Color, and Mark style: Line Type Indicator Point Type Color solid - point . blue b dotted : circle o green g dash-dot -. x-mark x red r dashed -- plus + cyan c star * magenta m square s yellow y diamond d black k

Exercise 2 (Basic Plotting) Plot x versus y for y=sin(x). Let x vary from 0 to 2pi in increments of 0.1pi. Add a title and labels to your plot. Plot x versus y1 and y2 for y1=sin(x) and y2=cos(x). Let x vary from 0 to 2*pi in increments of 0.1*pi. Add a title and labels to your plot. Re-create the plot from step 3, but make the sin(x) line dashed and red. Make the cos(x) line green and dotted. Use the M file to write and run it.

Subplots The subplot command allows you to subdivide the graphing window into a grid of m rows and n columns. The function: subplot(m,n,p) split the figure into m*n matrix. The variable p identifies the portion of the window where the current plot will be drawn.

Subplots For example, if the command subplot(2,2,1) is used, the window is divided into two rows and two columns, and the plot is drawn in the upper left-hand window. The windows are numbered from left to right, top to bottom. p=1 p=2 p=3 p=4

Subplots >> x=0:pi/20:2*pi; >> subplot(2,1,1) >> plot(x,sin(x)) >> subplot(2,1,2) >> plot(x,sin(2*x)) Simple x-y plots, in the first part of figure, y = sin(x). And in the second part of figure, y= sin(2*x).

Exercise 3 (Subplots) Subdivided a figure window into one row and two columns. In the left window, plot y=tan(x) Let x vary from -1.5 to 1.5 in increment of 0.1. Add a title and axis labels to your graph. In the right window, plot y=sinh(x) for the same x range. (Hyperbolic sine function) Add a title and axis labels to this graph. Use the M file to write and run it.

Histograms A histogram is a special type of graph that is particularly useful for the statistical analysis of data. A histogram is a plot showing the distribution of a set of values. In Matlab, the histogram compute the number of values falling into 10 bins (categories) that are equally spaced between the minimum and maximum values. >> x=[100,96,74,87,75,22,56,78,34,35,93,88,86,42,55,48,9,6]; >> hist(x)

Histograms The default number of bins is 10, but if we have a large data set, we may want to divide the data up into more bins. For example, to create a histogram with 25 bins, the command would be hist(x, 25) .

Exercise 4 (Histogram) Suppose that x = [1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 14, 17, 19, 23, 29, 30, 31, 32, 35, 40, 57,66,67,68,80,90,91,100] Subdivided a figure window into two rows and one column. In the top window, plot the histogram of x with the default number of bins. Add a title to your graph. In the bottom window, plot the histogram of x with 20 bins. Add a title to this graph. Use the M file to write and run it.

Outline of Lab 3 Review of Lab 2 User defined function Execution control Plots and graphs using Matlab Basic manipulation in image processing Color image compression

The MATLAB Image Processing Toolbox The Image Processing Toolbox is a collection of MATLAB functions (called M-functions or M-files) that extend the capability of the MATLAB environment for the solution of digital image processing problems.

The MATLAB Image Processing Toolbox Including: Spatial transformations and image registration Linear filtering and transforms Image enhancement and restoration Image analysis and statistics

How to Find Suitable M-function? Find it in Matlab Help. -by category -by alphabetical list Find it on the textbook. Find in the sub-folder in Matlab

Where is Image Processing Toolbox

Matlab Built-in Images Path: \Matlab\R2011a\toolbox\images\imdemos Y:\Win32\Matlab\R2011a\toolbox\images\imdemos They are built-in images in Matlab which can be used directly. It is very convenient to use these images to observe some image processing results. coins onion

Reading Image Function: Goal: Method: Examples: imread() Load the image and save it as the array format. Method: I = imread(filename); [I,map] = imread(filename); Examples: I = imread('pout.tif'); I = imread('rice.png'); pout rice

Displaying Image Function: Goal: Method: imshow() Open a window to show the image Method: imshow(I) Open a new window to show the image figure,imshow(I)

Displaying Image(cont.) Function: colorbar Goal: To display an image with a colorbar that indicates the range of intensity values. Method: imshow(I), colorbar Example: I = imread('pout.tif'); imshow(I) , colorbar

Writing Image Function: Goal: Method: Example: imwrite() Function: write the image out as a file Method: imwrite(I,filename,format) Example: imwrite(I, ‘pout.jpg’, ‘JPEG’);

Image Information Function: Goal: Method: Example: size() Returns the number of rows and columns of an matrix/image Method: [M,N] = size(I) for matrix/image I, returns the number of rows and columns in X as separate output variables. Example: I= imread('saturn.png'); % I is a gray image [I_x,I_y] = size(I) % I_x= height of the image, I_y= width of the image M = SIZE(X,DIM) returns the length of the dimension specified

Image Information Function: Goal: Example: whos Display information about a variable . Example: whos I imfinfo() display information about image file . info = imfinfo('saturn.png')

Digital Image Processing Function: im2bw() Goal: Convert intensity image I to binary image g using threshold T, where T must be in range [0, 1]. Method: g = im2bw(I, T); Example: I= imread('pout.tif'); g = im2bw(I, 0.4); imshow(g) ,colorbar

Digital Image Processing (cont.) Function: rgb2gray() Goal: Transform RGB color model image into gray-level image. Example: I= imread ('saturn.png'); imshow(I); g = rgb2gray(I); figure, imshow(g), colorbar

Digital Image Processing (cont.) Function: imresize() Goal: Change the size of an image. Method: imresize(A, SCALE, METHOD) Example: I = imread('circuit.tif'); J = imresize(I,1.25); imshow(I) figure, imshow(J) Method: imresize(A, [NUMROWS NUMCOLS], METHOD) Example: I = imread('circuit.tif'); J = imresize(I,[100 150], 'bilinear'); imshow(I) figure, imshow(J) Interpolation method

Digital Image Processing (cont.) Function: imrotate(); Goal: Rotate image A by ANGLE degrees in a counterclockwise direction around its center point. Method: imrotate(I, angle); Example: I = imread('pout.tif'); J = imrotate(I,35); imshow(J)

More Example (cont.) How to use this function ? imfilter() Find instructions about it by help Help imfilter Write this code and see what will happen? I = imread('coins.png'); h = ones(5,5) / 25; I2 = imfilter(I,h); imshow(I), title('Original Image'); figure, imshow(I2), title('Filtered Image')

More Example (cont.) Write this code and see what will happen? I = imread('cameraman.tif'); h = fspecial('unsharp'); I2 = imfilter(I,h); imshow(I), title('Original Image') figure, imshow(I2), title('Filtered Image')

Outline of Lab 3 Review of Lab 2 User defined function Execution control Plots and graphs using Matlab Basic manipulation in image processing Color image compression

Color Image Compression Color image in Matlab General processing of color image Color image compression

Color Image in Matlab Since a color image requires three separate items of information for each pixel, a (true) color image of size m*n is represented in Matlab by an array of size m*n*3: a three dimensional array. >> x=imread('onion.png'); >> size(x) ans = 135 198 3

Color Image in Matlab We can isolate each color component by the colon operator: x(:,:,1) is the first, red component. x(:,:,2) is the second, green component. x(:,:,3) is the third, blue component. The color components can all be viewed with ‘imshow’ function >> figure, imshow(x(:,:,1)) >> figure, imshow(x(:,:,2)) >> figure, imshow(x(:,:,3)) Red component Green component Blue component The RGB components

Processing of Color Images B Processing Processing Processing R’ G’ B’ Output RGB processing: process each RGB matrix separately

Framework of Image Compression Original image DCT Quantization Compressed image Inverse quantization Recovered image IDCT Reminder: Do not forget reprocessing of color images

An example >> a = imread('onion.png'); >> a1=a(1:8,1:8,1) 63 67 65 68 66 64 63 66 61 61 64 66 67 67 66 66 61 61 64 65 66 65 65 67 65 63 64 65 65 63 66 64 62 60 60 65 66 64 64 64 66 64 63 64 67 67 68 65 62 64 64 67 66 63 64 65 65 60 61 66 66 61 63 66 Red component

DCT in Matlab >> da1=dct2(a1) da1 = 515.1250 -6.9009 -4.4097 -0.1354 5.6250 0.7751 -1.8265 0.4425 2.2310 -0.9758 -1.7370 -1.8775 -2.6824 -1.3261 1.0516 -1.0729 1.2950 1.6965 -0.8687 -3.0164 1.8362 -1.5076 -0.1527 -1.4253 2.7060 1.6665 -0.1457 1.5836 -2.0586 -1.2816 -1.3506 -1.4155 -2.6250 3.0794 1.0312 -0.4235 2.8750 0.4794 -1.1036 -0.5436 1.9798 3.9761 0.6547 -2.9155 -1.5988 -0.7426 -1.2419 -0.3764 1.4931 0.1617 2.0973 0.9814 0.1865 -0.4356 0.3687 0.4056 -3.0155 -1.2068 -1.9821 -2.1311 1.4400 -1.4382 0.0831 -1.3652

Quantization in Matlab Two different forms of quantization: Uniform scalar quantization: All elements in a matrix are divided by the same number. Non-uniform scalar quantization: All elements in a matrix are divided by different numbers. There is usually a quantization table for the compression task.

Uniform Scalar Quantization >> qa1=round(da1/q) qa1 = 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Non-uniform Scalar Quantization 12 12 14 19 26 58 60 55;... 14 13 16 24 40 57 69 56;... 14 17 22 29 51 87 80 62;... 18 22 37 56 68 109 103 77;... 24 35 55 64 81 104 113 92;... 49 64 78 87 103 121 120 101;... 72 92 95 98 112 100 103 99]; >> qa1=round(da1./q) qa1 = 32 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Inverse Quantization in Matlab >> qa2=qa1.*q qa2 = 512 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Inverse DCT in Matlab >> da2=idct2(qa2) da2 = 62.0928 62.3832 62.9197 63.6206 64.3794 65.0803 65.6168 65.9072

Difference between Two Matrices Below is the difference between the original matrix and recovered matrix: >> diff=double(round(da2))-double(a1) diff = -1 -5 -2 -4 -2 1 3 0 1 1 -1 -2 -3 -2 0 0 1 1 -1 -1 -2 0 1 -1 -3 -1 -1 -1 -1 2 0 2 0 2 3 -1 -2 1 2 2 -4 -2 0 0 -3 -2 -2 1 0 -2 -1 -3 -2 2 2 1 -3 2 2 -2 -2 4 3 0

Next Lab Course Introduction of the final project Do final project by yourself