1. Introduction to Image Processing with MATLAB
EE4212 GA: Cui Zhaopeng
January, 2014

2. Outline Basics about images in MATLAB Some useful commands
(Some slides are adopted from Amin Allalou)
Some useful commands
Performance issues
Simple examples

3. MATLAB and Images An image in MATLAB is treated as a matrix
Every pixel is a matrix element
All the operators in MATLAB defined on matrices can be used on images: +, -, *, /, ^, sqrt, sin, cos etc.

4. Images in MATLAB MATLAB can import/export several image formats
BMP (Microsoft Windows Bitmap)
GIF (Graphics Interchange Files)
HDF (Hierarchical Data Format)
JPEG (Joint Photographic Experts Group)
PCX (Paintbrush)
PNG (Portable Network Graphics)
TIFF (Tagged Image File Format)
XWD (X Window Dump)
MATLAB can also load raw-data or other types of image data
Data types in MATLAB
Double (64-bit double-precision floating point)
Single (32-bit single-precision floating point)
Int32 (32-bit signed integer)
Int16 (16-bit signed integer)
Int8 (8-bit signed integer)
Uint32 (32-bit unsigned integer)
Uint16 (16-bit unsigned integer)
Uint8 (8-bit unsigned integer)

5. Images in MATLAB
• Binary images : {0,1} • Intensity images : [0,1] or uint8, double etc. • RGB images : m-by-n-by-3 • Indexed images : m-by-3 color map • Multidimensional images m-by-n-by-p (p is the number of layers)

6. Image Import and Export
Read and write images in Matlab
I=imread(LED_RGB.jpg');
figure,imshow(I)
Igrey=rgb2gray(I);
figure(2); imshow(Igrey)
imwrite(lgrey, 'LED_GRAY.jpg', 'jpg')
Alternatives to imshow
image -- create and display image object
imagesc -- scale and display as image
imtool -- opens a new Image Tool

7. Image Sizes and RGB Planes
Sizes of images:
Show red plane
>> size(I)
ans =
266
R G B
The RGB image is a 3D matrix of RGB planes
257
Note: the size of an image matrix in MATLAB is different from that shown in other softwares.
>> I_R = I;
>> I_R(:,:,2:3) = 0;
>> figure(3),imshow(I_R)

8. Images and Matrices How to build a matrix (or image)?
>> B = zeros(3,3)
B =
>> C = ones(3,3)
C =
>>imshow(A,[],'InitialMagnification','fit')

9. Images and Matrices Accesing image elements (row, column)X Y
Accesing image elements (row, column)
: can be used to extract a whole column or row
or a part of a column or row
>> A(2,1)
ans = 4
>> A(:,2)
ans = 2 5 8
A =
>> A(1:2,2)
ans = 2 5

10. Image Arithmetic
Arithmetic operations such as addition, subtraction, multiplication and division can be applied to images in MATLAB
+, -, *, / performs matrix operations
To perform an elementwise operation use . (.*, ./, .*, .^ etc)
>> A+A
ans =
A =
>> A*A
ans =
>> A.*A
ans =

11. Some Useful Commands Image Display
imagesc(I) - scale and display as image
imshow(I) - display image
getimage - get image data from axes
truesize - adjust display size of image
plot(x,y,’b*’) - plot points given by the coordinates (x,y); The point plotted is a blue asterisk’*’. See the help page for more information about colors and markers.
“hold on” causes subsequent image operations to display results on top of image, instead of replacing image.

12. Some Useful Commands Image Conversion im2bw(I) - image to binary
im2double(I) - image to double precision
im2uint8(I) - image to 8-bit unsigned integers
im2uint16(I) - image to 16-bit unsigned integers
mat2gray(A) - matrix to intensity image
rgb2gray(I) - RGB image to grayscale

13. Some Useful Commands Matrix Transformation
B = reshape(A,m,n) returns the mn matrix B whose elements are taken columnwise from matrix A . The product of the specified dimensions, m*n, must be the same as prod(size(A)).
B = repmat(A,m,n) creates a large matrix consisting of an m-by-n tiling of copies of A. The size of B is [size(A,1)*m, (size(A,2)*n].
>> A = [1 2 3; 4 5 6]
A =
>> B =reshape(A,3,2)
B =
>> C = reshape(A,1,[])
C =
‘[]’ here means that the length of the dimension will be calculated
such that the product of the dimensions equals prod(size(A)).

14. Some Useful Commands Others Use the help page to find more functions.
diag(A), where A is a vector with n components, returns an n-by-n diagonal matrix having A as its main diagonal. If A is a square symbolic matrix, diag(A) returns the main diagonal of A.
M = dlmread(filename) reads from the ASCII-delimited numeric data file filename to output matrix M. The filename input is a string enclosed in single quotes, e.g. ‘myfile.txt’.
dlmwrite(filename, M) writes matrix M into an ASCII format file using the default delimiter (,) to separate matrix elements.
[U, S, V] = svd(A) return numeric unitary matrices U and V with the columns containing the singular vectors and a diagonal matrix S containing the singular values.
listing = dir('name') returns attributes about name to an m-by-1 structure, where m is the number of files and folders in name.
cpselect(‘name1’, ‘name2’) displays 2 images side by side, allowing you to click on corresponding points.
Use the help page to find more functions.

15. Performance Issues Characters of MATLAB Improve the performance
very fast on vector and matrix operations;
Correspondingly slow with loops;
Improve the performance
Try to preallocate arrays;
Try to avoid loops;
Try to vectorize code.
Use stopwatch or profile to identify where you need to work on speed improvements.

16. Example (1)
Generate a sequence with 𝑥 𝑘 = 𝑥 𝑘−1 +5, 𝑘=2~ 𝑥 1 =0
% Poor style
tic
x = 0;
for k = 2:
x(k) = x(k-1) + 5;
end
toc
Elapsed time is seconds.
% Better style
tic
x = zeros(1, );
for k = 2:
x(k) = x(k-1) + 5;
end
toc
Elapsed time is seconds.
Preallocating the vector makes it faster.
Results are from

17. Example (2)
Given two image matrices FImg and Bimg with the same size (400*600*3), blend these two images using a matrix Alpha (400*600).
clear;clc;
FImg = im2double(imread('Foreground.jpg'));
figure;imshow(FImg);
BImg = im2double(imread('Background.jpg'));
figure;imshow(BImg);
Alpha = dlmread('Alpha.txt');

18. Example (2) We can vectorize this part to avoid loops. % Poor style
tic % measure performance using stopwatch timer
BlendingImg = zeros(size(FImg));
for i = 1 : size(FImg, 1)
for j = 1 : size(FImg, 2)
for k = 1 : size(FImg, 3)
BlendingImg(i, j, k) = (FImg(i, j, k)*Alpha(i,j) + (1-Alpha(i,j))*BImg(i, j, k));
end
toc
Elapsed time is seconds.
We can vectorize this part to avoid loops.
% Better style
tic % measure performance using stopwatch timer
BlendingImg = FImg.*repmat(Alpha,[1,1,3]) + BImg.*repmat(1-Alpha,[1,1,3]);
toc
Elapsed time is seconds.

19. Example (3)
Compute Eigenfaces. (You are not expected to know the detail.)
% Compute Eigenfaces
clear;
clc;
%Some parameters
ImgSize = [64 64];
VectorDim = prod(ImgSize);
%Read images from files
FileName = './Faces/';
FaceImgs = dir([FileName '*.png']);
FaceNum = length(FaceImgs);
InputFaces = zeros(VectorDim,FaceNum);
for i=1:FaceNum
InputFaces(:,i) = reshape(imread([FileName FaceImgs(i).name]),[],1);
end
% Preallocating the matrix

20. Example (3) %Calculate the mean face and shifted faces
MeanFace = mean(InputFaces, 2);
ShiftedFaces = InputFaces - repmat(MeanFace, 1, FaceNum);
%Calculate the eigenvectors and eigenvalues using SVD
[U S V] = svd(ShiftedFaces);
%Display the top 10 EigenFaces
figure;
title('The first 10 Eigenfaces.');
for n = 1:10
subplot(2, 5, n);
Temp = (255/(max(U(:,n))-min(U(:,n)))).* (U(:,n)-min(U(:,n))); %scale the vector to [0 255]
imshow(uint8(reshape(Temp, ImgSize)));
end
% Vectorizing code to avoid loops

21. Example (4) Compute the homography matrix between two sets of points.
There are two sets of 2d points 𝑋 1 , 𝑋 2 , 𝑋 3 …, 𝑋 𝑚 and 𝑋 1 ′ , 𝑋 2 ′ , 𝑋 3 ′ …, 𝑋 𝑚 ′ . 𝑋 𝑛 =[ 𝑥 𝑛 , 𝑦 𝑛 , 𝑧 𝑛 ]′ and 𝑋 𝑛 ′ =[ 𝑥 𝑛 ′ , 𝑦 𝑛 ′ , 𝑧 𝑛 ′ ]′ (𝑛=1,…,𝑚)are homogenous vectors. We want to compute the homography matrix 𝐻 which satisfies
𝑥 𝑛 ′ 𝑦 𝑛 ′ 𝑧 𝑛 ′ =𝜆 ℎ 11 ℎ 12 ℎ 13 ℎ 21 ℎ 22 ℎ 23 ℎ 31 ℎ 32 ℎ 𝑥 𝑛 𝑦 𝑛 𝑧 𝑛 , 𝑤ℎ𝑒𝑟𝑒 𝐻= ℎ 11 ℎ 12 ℎ 13 ℎ 21 ℎ 22 ℎ 23 ℎ 31 ℎ 32 ℎ
After simple derivation, we can get 𝐻 by solving the following linear system,
𝑥 1 𝑧 1 ′ 𝑦 1 𝑧 1 ′ 𝑧 1 𝑧 1 ′ −𝑥 1 𝑥 1 ′ −𝑦 1 𝑥 1 ′ −𝑧 1 𝑥 1 ′ 𝑥 1 𝑧 1 ′ 𝑦 1 𝑧 1 ′ 𝑧 1 𝑧 1 ′ −𝑥 1 𝑦 1 ′ −𝑦 1 𝑦 1 ′ −𝑧 1 𝑦 1 ′ 𝑥 2 𝑧 2 ′ 𝑦 2 𝑧 2 ′ 𝑧 2 𝑧 2 ′ −𝑥 2 𝑥 2 ′ −𝑦 2 𝑥 2 ′ −𝑧 2 𝑥 2 ′ 𝑥 2 𝑧 2 ′ 𝑦 2 𝑧 2 ′ 𝑧 2 𝑧 2 ′ −𝑥 2 𝑦 2 ′ −𝑦 2 𝑦 2 ′ −𝑧 2 𝑦 2 ′ … … 𝑥 𝑚 𝑧 𝑚 ′ 𝑦 𝑚 𝑧 𝑚 ′ 𝑧 𝑚 𝑧 𝑚 ′ −𝑥 𝑚 𝑥 𝑚 ′ −𝑦 𝑚 𝑥 𝑚 ′ −𝑧 𝑚 𝑥 𝑚 ′ 𝑥 𝑚 𝑧 𝑚 ′ 𝑦 𝑚 𝑧 𝑚 ′ 𝑧 𝑚 𝑧 𝑚 ′ −𝑥 𝑚 𝑦 𝑚 ′ −𝑦 𝑚 𝑦 𝑚 ′ −𝑧 𝑚 𝑦 𝑚 ′ ℎ 11 ℎ 12 ℎ 13 ℎ 21 ℎ 22 ℎ 23 ℎ 31 ℎ 32 ℎ 33 =0

22. Example (4) Compute the homography matrix between two sets of points.
%Poor style
clear; clc;
load points1.txt; %suppose the points have been normalized
load points2.txt;
for i=1:size(points1,1)
A(2*i-1,1:3) = points1(i,:)*points2(i,3);
A(2*i-1,4:6) = 0;
A(2*i-1,7:9) = -points1(i,:)*points2(i,1);
A(2*i,1:3) = 0;
A(2*i,4:6) = points1(i,:)*points2(i,3);
A(2*i,7:9) = -points1(i,:)*points2(i,2);
End
% Extract nullspace
[U S V] = svd(A);
s = diag(S);
nullspace_dimension = sum(s < eps * s(1) * 1e3);
if nullspace_dimension > 1
fprintf('Nullspace is a bit roomy...');
end
h = V(:,9);
H = reshape(h,3,3)'
% It does not preallocate A here,
%e.g. A = zeros(size(points1,1)*2,9).
%Actually we do not need loops here.

23. Example (4) Compute Homography between two sets of points
%Better style
clear; clc;
load points1.txt; %suppose the points have been normalized
load points2.txt;
Num = size(points1,1);
A=[points1.*repmat(points2(:,3), 1,3), zeros(Num,3), -points1.*repmat(points2(:,1), 1,3);
zeros(Num,3), points1.*repmat(points2(:,3), 1,3), -points1.*repmat(points2(:,2), 1,3)];
% Extract nullspace
[U S V] = svd(A);
s = diag(S);
nullspace_dimension = sum(s < eps * s(1) * 1e3);
if nullspace_dimension > 1
fprintf('Nullspace is a bit roomy...');
end
h = V(:,9);
H = reshape(h,3,3)'
% Vectorizing code to avoid loops

24. Useful Links Online tutorial or codes:
Writing Fast MATLAB Code: Profiling, vectorization, and more.
VGG MultiView Compute Library:
Codes for some basic algorithms in Computer Vision
A basic tutorial for MATLAB Image Processing Toolbox:
MATLAB documentation:

25. GA Hours
My contact:
Laboratory: E
(Note: As E4 may be renovated this semester, I will inform you if there is a change.)
Friday 4:00-5:30pm (Week 2, 3, 5, 7, 8, 9, 10, 11, 12, 13)