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Digital Image Processing ECE.09.452/ECE.09.552 Fall 2009. Lecture 7 November 16, 2009. Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall09/dip/. Plan. Digital Image Compression Fundamental principles Image Compression Model

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Digital Image Processing ECE.09.452/ECE.09.552 Fall 2009


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digital image processing ece 09 452 ece 09 552 fall 2009

Digital Image ProcessingECE.09.452/ECE.09.552Fall 2009

Lecture 7November 16, 2009

Shreekanth Mandayam

ECE Department

Rowan University

http://engineering.rowan.edu/~shreek/fall09/dip/

slide3
Plan
  • Digital Image Compression
      • Fundamental principles
      • Image Compression Model
      • Recall: Information Theory
  • Image Compression Standards
    • DCT (JPEG): Lossy
    • LZW (GIF, TIFF, ZIP): Lossless
  • Lab 4: Digital Image Compression
  • Discussion: Final Project
fundamentals
Fundamentals
  • Justification
  • Applications
  • Principle
      • Redundancy
  • Types
      • Lossy
      • Lossless
  • demos/demo6dithering/
compression model

Transform

Quantize

  • Encode
  • Source
  • Channel

f(x,y)

Compression Model

>>dct2

/demo10dct/dctdemo

recall measures of information
Recall: Measures of Information
  • 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/spring09/ecomms/entropy.m

recall source encoding

Analog

Message

A/D

Converter

Source

Encoder

Digital

Source

Recall: Source Encoding
  • Why are we doing this?

Source

Symbols

(0/1)

Source Entropy

Encoded

Symbols

(0/1)

Source-Coded

Symbol Entropy

source encoding requirements
Source Encoding Requirements
  • Decrease Lav
  • Unique decoding
  • Instantaneous decoding
recall huffman coding
Recall: Huffman Coding

2-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
  • Example

m(j) A B C D E F G H

P(j) 0.1 0.18 0.4 0.05 0.06 0.1 0.07 0.04

discrete cosine transform
Information Concentration

Data Compaction

Feature Extraction

Discrete Cosine Transform

Discrete Cosine Transform

>>dct2

/demo10dct/dctdemo

laser based ultrasound
Laser Based Ultrasound*

*Karta Technologies Inc., San Antonio, TX

example photothermal shearography images
Example: Photothermal Shearography Images

Before Deformation - After Deformation = Fringe Pattern

Sample 10

0.254 mm depth

-605.36 MPa stress

preprocessing

1 2 3 4 5

1

2

3

4

5

Preprocessing

Fringe Pattern

DCT Coefficients

Zonal Mask

DCT

(1,1)

(1,2)

(2,1)

(2,2)

.

.

.

Artificial

Neural

Network

Feature

Vector

jpeg compression standard
JPEG Compression Standard

Compute

DCT

F(u,v)

Reorder to form

1-D Sequence

Level

Shift

f(x,y)

Normalize

Compute

DC Coefficient

Compute

AC Coefficients

http://www.jpeg.org/

lzw algorithm
LZW Algorithm

Initialize string table with single character strings

Read first input character = w

Read next input character = k

y

No more k’s?

Stop

Output = code(w)

n

y

wk in string table?

w = wk

n

Output = code(w)

Put wk in string table

w = k

United States Patent No. 4,558,302,

Patented by Unisys Corp.

karhunen loeve hotelling transform
Karhunen-Loeve (Hotelling) Transform

Hotelling transform of x

  • demos/demo7klt/
lab 3 digital image restoration
Lab 3: Digital Image Restoration

http://engineering.rowan.edu/~shreek/fall09/dip/lab3.html

lab 4 digital image compression
Lab 4: Digital Image Compression

http://engineering.rowan.edu/~shreek/fall09/dip/lab4.html