session 08 2

8/9/2019 Session 08 2

1/31

Special Module on Media Processingand Communication

Dayalbagh Educational Institute(DEI)

Dayalbagh Agra

Indian Institute of Technology Delhi(IITD)

New Delhi

8/9/2019 Session 08 2

2/31

SlideSlide 22Special Module on Media Processing and Communication http://www.it.iitd.ac.in/sil864.html

Recap

Lecture 1

Overview

Digital Representation

Audio

Image

Video

Geometry

Need of Compression

8/9/2019 Session 08 2

3/31


Image CompressionCompression Ratio

Cr = no/nc

no = Number of carrying units (bits) in the originaldata (image)

nr = Number of carrying units (bits) in the compresseddata (image)

Also,Rd = 1 1/ Cr

Rd = Relative data redundancy

8/9/2019 Session 08 2

4/31


Image CompressionFidelity Criteria

Measure of loss or degradation

Mean Square Error (MSE)

Signal to Noise Ratio (SNR) Subjective Voting

8/9/2019 Session 08 2

5/31


CompressionCompression Techniques

Loss-less CompressionInformation can be compressed andrestored without any loss of information

Lossy CompressionLarge compression, perfect recovery isnot possible

8/9/2019 Session 08 2

6/31


CompressionCompression Techniques

Symmetric Same time for compression (coding) and

decompression (decoding)

Used for dialog (interactive) mode applicationsAsymmetric

Compression is done once so can take longer Decompression is done frequently so should be fast Used for retrieval model applications

8/9/2019 Session 08 2

7/31


Image CompressionData Redundancy

CodingVariable length coding with shorter codesfor frequent symbols

InterpixelNeighboring pixels are similar

PsychovisualHuman visual perception - limited

8/9/2019 Session 08 2

8/31


Image CompressionCoding Redundancy

variable length codingAvg length=2.7 bits

fixed length codingAvg length=3 bits

Example: (from Digital Image Processing by Gonzalez and Woods)

8/9/2019 Session 08 2

9/31


Image CompressionInterpixel Redundancy

Image

Histogram


8/9/2019 Session 08 2

10/31


Image CompressionInterpixel Redundancy

Image

Histogram

High interpixel correlation


8/9/2019 Session 08 2

11/31


Image CompressionPsychovisual Redundancy

Original 256 levels 16 level quantization IGS quantization


8/9/2019 Session 08 2

12/31


Image CompressionLoss-less Techniques

Coding redundancyVariable length coding

Interpixel redundancyRun length codingPredictive coding

8/9/2019 Session 08 2

13/31


Image CompressionVariable Length Coding (Huffman Coding)

Sequence of symbols (a1, a2, a3, a4, a5) with associatedprobabilities (p1, p2, p3, p4, p5)

Start with two symbols of the least probabilitya1:p1a2:p2

Combine (a1 or a2) with probability (p1+p2)

Do it recursively (sort and combine) A binary tree construction

8/9/2019 Session 08 2

14/31


Image Compression

a2 (0.4)

a1(0.2)

a3(0.2)

a4(0.1)

a5(0.1)

Sort inprobability

Variable Length Coding (Huffman Coding)

Symbols and their probabilities of occurrencea1 (0.2), a2 (0.4), a3 (0.2), a4 (0.1), a5 (0.1)

Example:

8/9/2019 Session 08 2

15/31


Image Compression

a2 (0.4)

a1(0.2)

a3(0.2)

a4(0.1)

a5(0.1)

Sort


Example:

8/9/2019 Session 08 2

16/31


Image Compression

a2 (0.4)

a1(0.2)

a3(0.2)

a4(0.1)

a5(0.1)

Sort

0.2

combine


Example:

8/9/2019 Session 08 2

17/31


Image Compression

a2 (0.4)

a1(0.2)

a3(0.2)

a4(0.1)

a5(0.1)

Sort

0.2

combine


Example: Sort

0.4

0.2

0.2

0.2

8/9/2019 Session 08 2

18/31


Image Compression

a2 (0.4)

a1(0.2)

a3(0.2)

a4(0.1)

a5(0.1)

Sort

0.2

combine Sort

0.4

0.2

0.2

0.2

0.4

combine Sort

0.4

0.2

0.4

0.6

combine

0.6

0.4

Sort

1

combine


Example:

8/9/2019 Session 08 2

19/31


Image Compression

a2 (0.4)

a1(0.2)

a3(0.2)

a4(0.1)

a5(0.1)

Sort

0.2

combine Sort

0.4

0.2

0.2

0.2

0.4

combine Sort

0.4

0.2

0.4

0.6

combine

0.6

0.4

Sort

1

combine

Assign code

0

1

1

00

01

1

000

001

01

1

000

01

0010

0011

1

000

01

0010

0011


Example:

8/9/2019 Session 08 2

20/31


Image CompressionDecoding

Example:

00111010001

?

8/9/2019 Session 08 2

21/31


Image CompressionRun Length Coding

Run: a string of the same symbol

Example

input: AAABBCCCCCCCCCAAoutput: A3B2C9A2

compression ratio = 16/8 = 2

8/9/2019 Session 08 2

22/31

8/9/2019 Session 08 2

23/31


Image CompressionPredictive Coding

Compression

8/9/2019 Session 08 2

24/31


Image CompressionPredictive Coding

Decompression

8/9/2019 Session 08 2

25/31

8/9/2019 Session 08 2

26/31


Image CompressionLossy

Psychovisual redundancy Keep more important information Trade off between loss (degradation) and compression

Original Compression Ratio: 7.7 Compression Ratio: 12.3 Compression Ratio: 33.9

8/9/2019 Session 08 2

27/31


Image CompressionLossy

Recall QuantizationDiscrete value to represent range of valuesIrreversible operation

Information loss !

Predictive Coding Transform Coding

8/9/2019 Session 08 2

28/31


AudioDigital RepresentationAudio (Sound): continuous signal (wave form) in time

1D function f(x)

Continuous

Discrete

Slide 7 Lecture 1

8/9/2019 Session 08 2

29/31


Image

x

y

2D function f(x,y)

Sampling: Discretization in x and y QuantizationSlide 16 Lecture 1

8/9/2019 Session 08 2

30/31


VideoVideo is a sequence of images in time

Time

Image

(Frame)

Slide 23 Lecture 1

8/9/2019 Session 08 2

31/31


Graphics

Geometry Data: Meshes Points

Connectivity

Slide 26 Lecture 1

session 08 2

Documents