S. Mandayam/ DIP/ECE Dept./Rowan University

Digital Image ProcessingDigital Image Processing

0909.452.01/0909.552.010909.452.01/0909.552.01 Fall 2001Fall 2001

Shreekanth MandayamECE Department

Rowan University

http://engineering.rowan.edu/~shreek/fall01/dip/

Lecture 10Lecture 10November 19, 2001November 19, 2001

S. Mandayam/ DIP/ECE Dept./Rowan University

Grad Students:Grad Students:Final Project PresentationsFinal Project Presentations

Dec 10th

Dec 17th

S. Mandayam/ DIP/ECE Dept./Rowan University

PlanPlan

• Digital Image Compression• Fundamental principles• Image Compression Model• Recall: Information Theory

• Image Compression Standards• CCITT Group 3 (FAX): Lossless• LZW (GIF, TIFF, ZIP): Lossless• DCT (JPEG): Lossy

• Lab 4: Digital Image Compression

S. Mandayam/ DIP/ECE Dept./Rowan University

DIP: DetailsDIP: Details

G ray-level Histogram

Spatial

DF T DC T

Spectral

Digital Image Characteristics

Point Processing M asking Filtering

Enhancem ent

Degradation M odels Inverse Filtering W iener Filtering

Restoration

Pre-Processing

Inform ation Theory

LZW (gif)

Lossless

Transform -based (jpeg)

Lossy

Com pression

Edge Detection

Segm entation

Shape Descriptors Texture M orphology

Description

Digital Im age Processing

S. Mandayam/ DIP/ECE Dept./Rowan University

FundamentalsFundamentals

• Justification

• Applications

• Principle• Redundancy

• Types• Lossy• Lossless

demos/demo6dithering/

S. Mandayam/ DIP/ECE Dept./Rowan University

Compression ModelCompression Model

f(x,y) Transform QuantizeEncode• Source• Channel

S. Mandayam/ DIP/ECE Dept./Rowan University

Recall: Measures of Recall: Measures of InformationInformation

• Definitions• Probability• Information• Entropy• Source Rate

• Recall: Shannon’s Theorem• If R < C = B log2(1 + S/N), then we can have error-

free transmission in the presence of noise

MATLAB DEMO:http://engineering.rowan.edu/~shreek/spring01/ecomms/ entropy.m

S. Mandayam/ DIP/ECE Dept./Rowan University

Recall: Source EncodingRecall: Source Encoding

• Why are we doing this?

AnalogMessage

A/DConverter

DigitalSource

SourceEncoderSource

Symbols (0/1)

Source Entropy

EncodedSymbols

(0/1)

Source-CodedSymbol Entropy

S. Mandayam/ DIP/ECE Dept./Rowan University

Source Encoding Source Encoding RequirementsRequirements

• Decrease Lav

• Unique decoding

• Instantaneous decoding

S. Mandayam/ DIP/ECE Dept./Rowan University

Recall: Huffman CodingRecall: Huffman Coding2-Step Process• Reduction

• List symbols in descending order of probability• Reduce the two least probable symbols into one symbol equal to their

combined probability• Reorder in descending order of probability at each stage• Repeat until only two symbols remain

• Splitting• Assign 0 and 1 to the final two symbols remaining and work backwards• Expand code at each split by appending a 0 or 1 to each code word

• Examplem(j) A B C D E F G HP(j) 0.1 0.18 0.4 0.05 0.06 0.1 0.07 0.04

S. Mandayam/ DIP/ECE Dept./Rowan University

CCITT Group 3 1-D Standard CCITT Group 3 1-D Standard for Bilevel Image Compressionfor Bilevel Image Compression

• Determine “run lengths” of black and white pixels on each line

• Code these using a Huffman code• Conventions:

• Each line begins with a zero-run length white code word• Each line ends with a special EOL code

black run length white run length

http://www.itu.int/publibase/itu-t/

S. Mandayam/ DIP/ECE Dept./Rowan University

LZW AlgorithmLZW AlgorithmInitialize string table with single character strings

Read first input character = w

Read next input character = k

No more k’s? Output = code(w) Stop

wk in string table?

Output = code(w)

w = wk

w = k Put wk in string table

y

n

n

y

United States Patent No. 4,558,302, Patented by Unisys Corp.

S. Mandayam/ DIP/ECE Dept./Rowan University

Discrete Cosine TransformDiscrete Cosine Transform

• Information Concentration

• Data Compaction

• Feature Extraction

Discrete Cosine Transform

1-....N 1,2 u for

N2

0 u for N1

(u)

2N1)(2x

cos f(x) (u) C(u)1-N

0x

u

>>dctdemo

S. Mandayam/ DIP/ECE Dept./Rowan University

Laser Based Ultrasound*Laser Based Ultrasound*

*Karta Technologies Inc., San Antonio, TX

S. Mandayam/ DIP/ECE Dept./Rowan University

Example: Photothermal Example: Photothermal Shearography ImagesShearography Images

Before Deformation - After Deformation = Fringe Pattern

Sample 100.254 mm depth-605.36 MPa stress

S. Mandayam/ DIP/ECE Dept./Rowan University

PreprocessingPreprocessing

Fringe Pattern

DCT

DCT Coefficients

Zonal Mask

1 2

3

4

5

1 2 3 4 5

(1,1)(1,2)(2,1)(2,2)

.

.

.

FeatureVector

ArtificialNeuralNetwork

S. Mandayam/ DIP/ECE Dept./Rowan University

JPEG Compression JPEG Compression StandardStandard

f(x,y) LevelShift

ComputeDCTF(u,v)

Normalize Reorder to form 1-D Sequence

ComputeDC Coefficient

ComputeAC Coefficients

http://www.jpeg.org/

S. Mandayam/ DIP/ECE Dept./Rowan University

Karhunen-Loeve (Hotelling) Karhunen-Loeve (Hotelling) TransformTransform

i

ii

i

Txxx

x

eA

λe

Nixλ

mxmxEC

xEm

Nx

of rowsh Matrix wit :

toingcorrespond rsEigenvecto :

,...,2,1 ,of sEigenvalue :

matrix Covariance :))((

rmean vecto :

vector1:

)( xmxAy

Hotelling transform of x

demos/demo7klt/

S. Mandayam/ DIP/ECE Dept./Rowan University

Lab 4: Digital Image Lab 4: Digital Image CompressionCompression

http://engineering.rowan.edu/~shreek/fall01/dip/lab4.html

S. Mandayam/ DIP/ECE Dept./Rowan University

SummarySummary