13 Image Compression

7/31/2019 13 Image Compression

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7/14/2012 Image Compression 1

Image Compression


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Reference

[1] Gonzalez and Woods, Digital Image

Processing.


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Objective

Reduce the number of bytes required to

represent a digital image

Redundant data reduction

Remove patterns

Uncorrelated data confirms redundant data

elimination Auto correlation?


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Enabling Technology

Compressions is used in

FAX

RPV

Teleconference

REMOTE DEMO

etc


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Review

What and how to exploit data redundancy

Model based approach to compression

Information theory principles

Types of compression

Lossless, lossy


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Information recovery

We want to recover the information, with reduceddata volumes.

Reduce data redundancy.

How to measure the data redundancy.

ProcessingData Information


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Relative Data Redundancy

Assume that we have two data sets D1 and D2.

Both on processing yield the same information.

Let n1 and n2 be the infocarrying units of therespective data sets.

Relative data redundancy is defined on comparing the

relative dataset sizes

RD = 11/CR

where CR is the compression ratio

CR = n1/ n2


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Examples

RD = 11/CR

CR = n1/ n2

D1 is the original and D2 is compressed.

When CR = 1, i.e. n1 = n2 then RD=0; no data

redundancy relative to D1 .

When CR = 10, i.e. n1 = 10 n2 then RD=0.9; impliesthat 90% of the data in D1 is redundant.

What does it mean if n1


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Coding Redundancy

How to assign codes to alphabet

In digital image processing

Code = gray level value or color value Alphabet is used conceptually

General approach

Find the more frequently used alphabet

Use fewer bits to represent the more frequently used

alphabet, and use more bits for the less frequently used

alphabet


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Coding Redundancy 2

Focus on gray value images

Histogram shows the frequency of occurrence of aparticular gray level

Normalize the histogram and convert to a pdfrepresentationlet rkbe the random variable

pr(rk) = nk/n ; k = 0, 1,2 ., L-1, where L is the number of gray levelvalues

l(rk) = number of bits to represent rk

Lavg = k=0 to L-1 l(rk) pr(rk) = average number of bits to encode onepixel. For M x N image, bits required is MN Lavg

For an image using an 8 bit code, l(rk) = 8, Lavg = 8.

Fixed length codes.


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Fixed vs Variable Length Codes

From [1]

Lavg = 2.7

CR= 3/2.7 = 1.11

RD = 11/1.11 = 0.099


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Code assignment view

From [1]


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Interpixel Redundancy

From [1]


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Run Length Coding

From [1]

CR=1024*343/12166*11

= 2.63

RD = 1-1/2.63 = 0.62


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Psychovisual Redundancy

Some visual characteristics are less

important than others.

In general observers seeks out certain

characteristicsedges, textures, etcand

the mentally combine them to recognize the

scene.


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From [1]


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From [1]


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Fidelity Criteria

Subjective

Objective

Sum of the absolute error

RMS value of the error

Signal to Noise Ratio


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Subjective scale

From [1]


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Image Compression Model

Run length JPEG Huffman

From [1]

Documents

13 Image Compression