comp slides4 b

8/8/2019 Comp Slides4 B

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GRAY CODE

( )1>>= BCBCGC

Logical operation XOR is Exclusive OR:

00=0 01=1

11=0 10=1

Examples

1) Value =127:Binary codeBC: 0111 1111

Gray code GC: 0111 1111

0011 1111

---------------

0100 0000

2) Value = 128Binary code BC: 1000 0000

Gray code GC: 1000 0000

0100 0000

---------------

1100 0000


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BINARY AND GRAY CODES (4 BITS):

0

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

1 5

0

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

1 5

B i n a r y c o d e G r a y c o d e


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Binary and Gray code bit planes:

q Encode each bit plane with JBIGq Typically, lossless JPEG is more efficient

than JBIG for images with more than 6 bits


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Binary code Gray code

7

6

5

4


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3

2

1

0


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JPEG: Joint Photographic Experts Group

JPEG Lossless mode


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Predictive coding in lossless JPEG

ALTERNATIVE PREDICTORS:

Mode: Predictor: Mode: Predictor:

0 Null 4 N+ W-NW

1 W 5 W+ (N-NW)/2

2 N 6 N+ (W-NW)/2

3 NW 7 (N+ W)/2

NW N

W x


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RESIDUAL CODING:

= x x

DECODER:

x x= +

ENTROPY CODING:

HUFFMAN CODING

ARITHMETIC CODING (QM-CODER)


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Huffman coding

Category Codeword Difference Codeword0 00 0 -

1 010 -1, 1 0, 1

2 011 -3, -2, 2, 3 00, 01, 10, 11

3 100 -7,..-4, 4..7 000,...011,

100...111

4 101 -15,..-8, 8..15 0000,...0111,

1000...11115 110 -31,..-16, 16..31 :

6 1110 -63,..-32, 32..63 :

7 11110 -127,..-64, 64..127 :

8 111110 -255,..-128,

128..255

:


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Binary arithmetic coding

0

1

2

3

7 8

::

{ 0 }

{ 1 }

{ 2 , 3 }

{ 4 , . . , 7 }

{ 6 3 , . . , 1 2 7 } { 1 2 8 , . . , 2 5 5 }


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Lossless JPEG: example

Pixel sequence: 10, 12, 10, 7, 8, 8, 12.Prediction mode: 1 (previous pixel value)

Static Huffman codingPixel: 10 12 10 7 8 8 12

+10 +2 -2 -3 +1 0 +4Category: 4 2 2 2 1 0 3

Bits: 101 1010 011 10 011 01 011 00 010 1 00 100 100


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FELICS

Fast and Efficient Lossless

Image Compression SystemP.Howard and J.Vitter

PREDICTION MODEL:

L=min{a,b}, H=max{a,b}.

L = The smaller of the two neighbor pixel value

H= The larger of the two neighbor pixel value

b

a x


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ASSUMPTION OF DISTRIBUTION:

L H

b e lo w

r a n g e

a b o v e

r a n g e

i n

r a n g e

p r o b a b i l i t y

i n t e n s i t y

CODING THE PIXEL VALUE:

IF P [L,H] THEN

Output(0);

Encode =P-L by adjusted binary code;

ELSE IF P


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ADJUSTED BINARY CODING:

Let =H-L. There are +1 possible values in the

range.

If +1 is a power of two, a binary code with

log2(+1) bits is used.

Otherwise ( ) 1log 2 + are used for middle values and( ) 1log 2 + bits for the outer values.

For example, if=4 there are five values (0, 1, 2, 3,

4) and their corresponding adjusted binary

codewords are (111, 10, 00, 01, 110).

RICE CODING:

For determining the Rice coding parameter k, the is used as a context.

For each context , a cumulative total bit rate is

maintained for each reasonable Rice parameter

value k, of the code length that would have

resulted if the parameter kwere used to encode all

values encountered so far in the context.

The parameter with the smallest cumulative code

length is used to encode the next value

encountered in the context.

The allowed parameter values are k=0, 1, 2, and

3.


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CALIC:

Context-based Adaptive LosslessImage Codec

CALIC [X.Wu,1995] is ranked top among

the schemes that were evaluated by the JPEG

committee prior to the development JPEG-Lossless standard.

but rather elaborate scheme.


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LOCO-I:

LOw-COmplexity

LOssless COmpression for Images

Features Context modeling (365 contexts)

Run-length coder: Run-lengths are coded withGolomb-Rice method.

Nonlinear predictor

Golomb-Rice entropy coder: the parameterkdepends on the context, and is adapted to theaverage absolute value of residuals.


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Model structure of JPEG-LS

G r a d i e n t s

F l a tr e g i o n ?

F i x e d

p r e d i c t o r

A d a p t i v ec o r r e c t i o n

C o n t e x t

m o d e l e r

R u n c o u n t e r

i m a g es a m p l e s

p r e d i c t i o n

e r r o r s


p r e d i c t e d v a l u e s


r u n l e n g s t a t i s t i c s

p r e d . e r r s t a t i s t i c s

+

-

c o n t e x t M o d e l e r

m o d er e g u l a r

r u n


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COMPONENTS OF THE MODEL:

1. Prediction

2. Determination of context.

3. Probability model for the prediction errors.


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PREDICTOR:

( )

( )

otherwise

),min(if

),max(if

,max

,min

bac

bac

cba

ba

ba

x

+

=

Examples:

20 12

10 10

1) c=20 > max(10,12) predictor =

min(10,12)=10

10 20

18 20

2) c=10 < max(18,20) predictor =

max(18,20)=20

12 20

10 18

2) 10


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RESIDUAL CODING:

= x x

DECODER:

x x= +


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JPEG-LS context model

The distributoin of prediction residuals in

continuous tone images can be approximatedby a Laplacian distribution, i.e. a two-sided

exponential decay centered at zero.

In a one-pass scheme, the encoder cannot

tune an optimal Huffman table to each

possible distribution of prediction residuals.

Adaptive construction of optimal tables is

ruled out by the complexity contsraints.

Solution: For each context the encoder

adaotively chooses the best among a limitedset of Huffman codes, matched to

exponentially decaying distributions, based

on the past performance.


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GRADIENT DETERMINATION:

g1 = d- b

g2 = b - c

g1 = c - a

CONTEXT QUANTIZATION:

gi qi

{0}

{1,2}

{3,4,5,6}

{7,8,...,20}

{e 20}

NUMBER OF DIFFERENT CONTEXTS: 365

( )( )C

T=

+ +2 1 1

2

3

T=4, |C|=365: balance storage requirements with

high-order conditioning


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JPEG-LS coding

VALUE MAPPING FROM [-127,127] TO [0, 255]:( )

( ) 0if,12

0if,2


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JPEG-LS: Part 2

Difference from Part-1

1. No run mode2. 4 5 reference points

3. Modified prediction for images with

sparse histograms

4. Binarization and its arithmetic coding

Part-1:

Context modeling Prediction or Run mode

Golomb Coding

Part-2:

Context modeling Prediction Binarization

Arithemtic Coding


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Comparison of lossless methods

Source: http://www.hpl.hp.com/research/itc/csl/vcd/infotheory/loco.html

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