lec1_matlab.ppt basic all operations matlab operations

Tools and Prerequisites for
Image Processing
Lecture 1, Jan 28th, 2008
Part 2 by Lexing Xie
EE4830 Digital Image Processing
http://www.ee.columbia.edu/~xlx/ee4830/

-2-
Outline
 Review and intro in MATLAB
 A light-weight review of linear algebra and
probability
 An introduction to image processing
toolbox
 A few demo applications
 Image formats in a nutshell
 Pointers to image processing software
and programming packages

-3-
Matlab is …
 : a numerical computing environment and programming
language. Created by The MathWorks, MATLAB allows easy matrix
manipulation, plotting of functions and data, implementation of
algorithms, creation of user interfaces, and interfacing with programs
in other languages.
 Main Features:
 basic data structure is matrix
 optimized in speed and syntax for matrix computation
 Accessing Matlab on campus
 Student Version
 Matlab + Simulink $99
 Image Processing Toolbox $59
 Other relevant toolboxes $29~59 (signal processing, statistics,
optimization, …)
 CUNIX and EE lab (12th floor) has Matlab installed with CU site-
license

-4-
Why MATLAB?
 Shorter code, faster computation
 Focus on ideas, not implementation
 C:
#include <math.h>
double x, f[500];
for( x=1.; x < 1000; x=x+2)
f[(x-1)/2]=2*sin(pow(x,3.))/3+4.56;
 MATLAB:
f=2*sin((1:2:1000).^3)/3+4.56;
But: scripting language, interpreted, … …

-5-
matrices
 … are rectangular “tables” of entries where the
entries are numbers or abstract quantities …
 Some build-in matrix constructors
 a = rand(2), b = ones(2), c=eye(2),
 Addition and scalar product
 d = c*2;
 Dot product, dot-multiply and matrix
multiplication
 c(:)’*a(:), d.*a, d*a
 Matrix inverse, dot divide, etc.
 inv(a), a./d

-6-
matrixes as images, and vice versa
 x = 1 : 256;
 y = ones(256,1);
 a = x*y;
b = y*x;
size(a) = ? size(b) = ?
?
imagesc(b); colormap(gray(256))
256x256 chess board
b = ones(1,8); b(2:2:end)=0
b = [b; b(end:-1:1)]
b = repmat(b, [4 1])
chessb = kron(b,ones(32));
imagesc(checkerboard(32)>.5);
or, from scratch:

-7-
eigen vectors and eigen values
 “eigenvectors” are exceptional vectors in the same
direction as Ax
Ax =  x
  are called eigenvalues
 Examples:
 A = [.8 .3; .2 .7]
 [v, d] = eig(A);
 A*v(:, 1)
 A*v(:, 2)
 properties of :
 i=1
n aii= i=1
n i
= trace(A)
 1
¢ 2
¢ … n
= det(A)
 eigshow
 eigen-vectors and values are
useful for:
 Getting exponents of a matrix A100000
 Image compression
 Object recognition
 The search algorithm behind Google
 …

-8-
matlab quiz
 Chessboard + noise
 x = chessb + randn(256);
 How to get the minimum and maximum value of x
(in one line, with one function call) ?
[min(x(:)) max(x(:))] prctile(x(:), [0 100])
the handy, esp. if x is more
than three dimensions
the obscure, but exactly one
function call.

-9-
probability
 probability refers to the chance that a particular event (or
set of events) will occur.
-50 0 50 100 150 200 250 300
0
1
2
3
4
x 10
-3
-4 -3 -2 -1 0 1 2 3 4
0
0.1
0.2
0.3
0.4
Pr(head)=1/2,
Pr(tail)=1/2
p = pdf('normal', -4:.1:4, 0, 1);
plot(-4:.1:4, p)
p = pdf('uniform', -1:256, 0, 255);
plot(-1:256, p)
 probability density function p(x) is a non-negative
intergrable function RR such that for any interval [a, b]:
Pr(x 2 [a,b]) = sa
b p(x)dx

-10-
probability
 Suppose you’re blind-folded and points to a point in a
cardboard with the following prints, after a friend rotates
and shifts it randomly (i.e. randomly draw a pixel from
the following images)
-50 0 50 100 150 200 250 300
0
1
2
3
4
x 10
-3
-4 -3 -2 -1 0 1 2 3 4
0
0.1
0.2
0.3
0.4
p( )=1/2 p( )=1/2
p( )=p( )=… = p( ) = 1/256

-11-
mean and std
 Mean
 mx = E[x]= s x p(x) dx
 Standard-deviation
 x
2 = E[(x-mx)2] = s (x-mx)2 p(x) dx
(a)
(b)
(a) and (b) are afore-
mentioned gray-scale
images with values
between [0,1]. Which
one of the following
holds, if any?
ma < mb
a < b
ma = mb
a > b
X
X

-12-
MATLAB (contd.)
 M-files:
 functions
 scripts
 Language constructs
 Comment: %
 if .. else… for… while… end
 Help:
 help function_name, helpwin, helpdesk
 lookfor, demo

-13-
Image Processing Toolbox
 File I/O and display
 imread(), imwrite()
 imshow(), image(), imagesc(), movie()
? how different are these two images?
cu_home_low.bmp (382 KB) cu_home_low_j40.jpg (29KB)
im1 = imread('cu_home_low_treebranch.bmp');
im2 = imread('cu_home_low_treebranch_j40.jpg');
sqrt( sum( (im1(:)-im2(:)).^2 ) / prod(size(im1)) )
imshow(im1- im2)

-14-
Image Processing Toolbox (contd)
 Linear operations
 fft2(), dct2(), conv2(), filter2()
 Non-linear operations
 median(), dilate(), erode(), histeq()
 Statistics and analysis
 imhist(), ,mean2(), corr2(), std2()
 Colormap and type conversions
 colormap(), brighten(), rgbplot()
 rgb2ycbcr(), hsv2rgb(), im2uint8()…

-15-
Outline
 Review and intro in MATLAB
 A light-weight review of linear algebra and
probability
 An introduction to image processing
toolbox
 introduction and pointers to other image
processing software and programming
packages

-16-
Demo of image processing software
 Enhancement
“equalize” (lecture 4)
 Compression (lecture 12)
 Color manipulation (lecture 3)
with GIMP www.gimp.org
 “unshake” http://www.hamangia.freeserve.co.uk/ (lecture 7)
before after
before after

-17-
Image Processing Software
 Bitmap editing: Adobe Photoshop,
Macromedia Fireworks
 Vector graphics editing: Adobe Illustrator,
Corel Draw
 Consumer photo tools: Picassa, ACDSee,
Windows Paint, XV, Photoshop Elements …
 GIMP
Send me <xlx@ee.columbia.edu> your suggestions
of image editing/processing tools!

-18-
Video processing software
 Player
 Windows media player, Real, Quicktime,
iTunes, intervideo WinDVD, …
 Format conversion
 ffmpeg
 Editing
 Adobe premier, muvee,
Resource sites .. http://doom9.net/

-19-
Image Processing Toolboxes
 In C/C++
 IPL … http://www.cs.nott.ac.uk/~jzg/nottsvision/old/index.html
 OpenCV http://sourceforge.net/projects/opencvlibrary
http://tech.groups.yahoo.com/group/OpenCV/
 ImageMagick http://www.imagemagick.org/
 Insight Toolkit ITK (medical image) http://www.itk.org/
 List of tools at mathtools.net
http://www.mathtools.net/C_C__/Image_Processing/
 In Java
 Java Media APIs: JAI, JMF, Java image I/O …
http://java.sun.com/javase/technologies/desktop/media/
 http://www.mathtools.net/Java/Image_Processing/index.html
 Other
 Python Imaging Library (PIL) http://www.pythonware.com/products/pil/
numpy, scipy

-20-
Image Data Types
 Basic unit in disk: byte (8 bits)
 Images are stored as unsigned integers (0-
255)
 Depends on the color space and the
precision / bit depth
 1bit, 4bit, 8bit, 24bit, 32bit (+alpha channel),
indexed colors (gif, 2-8 bits)
 In MATLAB:
 uint8doubleuint8

-21-
File Formats
 Why different file formats?
 Convenient to use
 Compact representation
 How many formats do we have?
 e.g. 30+ in a consumer image software
(ACDSee)
 There are much more out there:
raster, vector, metafile, … and growing
 Basic structure: Header + Data

-22-
Format Comparison
Format RAW BMP GIF PNG JPG
Lossy? N N N N Y
Compressed? N N Y Y Y
192K 193K 52.2K 106K 16K
192K 193K 5K
(4bit)
23K 20K
Fine prints Raw
data
Header
~1K
Look-up
table +
data
Quality
factor 80
Two 256x256 color images
Why do the two images have different sizes as GIF/PNG/JPG files ?

-23-
Image Format Classification
 Types that MATLAB supports:
 BMP, JPEG, PNG, GIF, TIFF, XWD, HDF, PCX, …
 Other open-source libraries from “google”
Image
(bitmap)
lossless
compression
no compression
no loss
raw, bmp,
pgm, ppm,
gif, tiff …
png, jpeg,
gif, tiff,
jpeg2000…
lossy
compression
jpeg, tiff,
jpeg2000
…

-24-
Resources and pointers
 Google, Wikipedia, Mathworld …
 Getting Help in Matlab
 Matlab help, Image Processing Demos
 DIP matlab tutorial online
 Usenet groups

-25-
Summary
 Review of matrixes and probability
 MATLAB for image processing
 Data type and file formats
 Resources and pointers

-28-
Working With Matrices in MATLAB
 Everything is treated as a matrix
 Elementary matrix manipulation
 zeros(), ones(), size(), eig(), inv()
 Operators and special characters
 a(: ,1:2:256)=b’.*c
 String
 imstr=[‘this is lena’];
imglena=imread([imstr(9:end),’.png’]);
 ischar(), num2str(), …

-29-
 Review of linear algebra
 Point operation and matrix
operations
 Eigen vectors, .. eigen values
 Images as matrices, and
matrices as images …
 Question: max/min,
subsampling,
 Review of probability
 Coin-tossing, pdf, cdf,
gaussian pdf
 Expectations, std, variance
 Question: pdf shape,
expectation/expected value,
 Matlab
 Getting started
 Image I/O and display
 Matrix manipulation
 Image processing demos
 The daily practice of image
manipulation
 Image processing tools in
C, Java, … and everything
else
 Data types and file
formats
 Resources, pointers and
getting help

lec1_matlab.ppt basic all operations matlab operations

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