Mmp Presentation

8/3/2019 Mmp Presentation

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Signal Compression using MultiscaleRecurrent Patterns

Eduardo Ant onio Barros da Silva

[email protected]

Signal Processing Laboratory

Program of Electrical Engineering - COPPE

Federal University of Rio de Janeiro

Si nal Com ression usin Multiscale Recurrent Patterns . 1/96


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Summary

The LPS/UFRJ .

Data compression .Approximate multiscale pattern matching.

The MMP algorithm.

Multidimensional extension.

The three aspects of MMP

R-D optimization.

Source Coders using the MMP Paradigm

Conclusions .



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The LPS



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The LPS




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The LPS


Linked both to Graduate and UndergraduateDepartments at Universidade Federal do Rio deJaneiro (UFRJ):



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The LPS



Graduate: Program of ElectricalEngineering/COPPE



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The LPS




Undergraduate: Department of Electronics and

Computer Science



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The LPS





Computer Science

12 full-time professors;



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The LPS





Computer Science

12 full-time professors;

Around 40 Ph.D., 50 M.Sc. and 50 EngineeringStudents.



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Main Research Areas

Image Processing



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Main Research Areas

Image Processing

Data Compression



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Main Research Areas

Image Processing

Data CompressionAdaptive Systems



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Main Research Areas

Image Processing


Signal Processing for Communications



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Main Research Areas

Image Processing



Neural Networks



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Main Research Areas

Image Processing



Neural Networks

Voice and Audio Processing



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Main Research Areas

Image Processing



Neural Networks

Voice and Audio Processing

Analog Electronics



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Introduction: Data compression


d


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Data encoding

Let x be any data set. An encoder R maps each x to abinary string representation s .

xR

s = 00101110


D di


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Data encoding


xR

s = 00101110

Different data sets x can be mapped to different strings s :x

R s = 10011


D di


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Data encoding


xR

s = 00101110

Different data sets x can be mapped to different strings s :x

R s = 10011

Different encoders produce different representations

xR

s = 010110


D i


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Data compression

Lossless compression : Find an invertible encoder R thatminimizes the mean length of the representationss = R (x ), considering the set of all {x} of interest.


D t i


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Data compression

Lossless compression : Find an invertible encoder R thatminimizes the mean length of the representationss = R (x ), considering the set of all {x} of interest.

Lossy compression : Given a distortion metric D , nd a

family of encoders R d and a decoder R 1 such that, foreach d IR the mean length of the representationss = R d (x ) is minimum, subject to the constraint

D (x, x ) d, where x = R 1(s ).


Cl i l l i h d i bl


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Classical solutions to the data compression problem

Lossless compression : Optimal (at least in an assymptoticsense) solutions are known. Some examples are Huffman,arithmetic and Lempel-Ziv codes.


Cl i l l ti t th d t i bl


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Lossy compression : No optimal solutions are known (at

least implementable ones).


Cl ssic l sol tions to the d t compression problem


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least implementable ones).A popular approach is the three step method:




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Lossless compression : Optimal (at least in an assymptoticsense) solutions are known. Some examples are Huffman,

arithmetic and Lempel-Ziv codes.



a transformation step




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a quantization step




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a quantization step

a lossless compression (also called entropy coding)

step.



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In this work we propose to deviate from thethree-step encoding paradigm:



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In this work we propose to deviate from thethree-step encoding paradigm:

We use the concept of Multiscale Recurrent Pattern Matching



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Multiscale Pattern Matching


Ordinary pattern matching


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O d a y patte atc g

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Multiscale pattern matching


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Theoretical analysis


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It can be shown that the approximate multiscale patternmatching can outperform the ordinary approximate pattern

matching at low rates, in the Gaussian memoryless sourcecase.


Theoretical analysis


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It can be shown that the approximate multiscale patternmatching can outperform the ordinary approximate pattern

matching at low rates, in the Gaussian memoryless sourcecase.

The theoretical determination of the performance withother sources is an open problem.



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The MMP Algorithm


Multidimensional Multiscale Parser - MMP


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The MMP ( Multi-dimensional Multiscale Parser ) algorithmis a universal data compression algorithm based on

multiscale pattern matching




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multiscale pattern matchingIt uses a dictionary of patterns that is adaptively built whilethe input data is encoded.




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multiscale pattern matchingIt uses a dictionary of patterns that is adaptively built whilethe input data is encoded.

The dictionary is updated by the inclusion ofconcatenations (in a Lempel-Ziv fashion) of

dilated/contracted versions of input blocks previouslyencoded.



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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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MMP


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Segmentation Tree


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X 0


Segmentation Tree


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node 0

X 0


Segmentation Tree


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X 1 X 2

node 1 node 2

node 0

X 0


Segmentation Tree


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node 6node 5

X 1 X6

X 5

X 1 X 2

node 1 node 2

node 0

X 0


Output sequence


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node 6node 5

node 1 node 2

node 0

X 0


Output sequence


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node 6node 5

node 1 node 2

node 0

X 0

Output: 0


Output sequence


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node 6node 5

node 1 node 2

node 0

X 1

Output: 0


Output sequence


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node 6node 5

node 1 node 2

node 0

X 1

Output: 0, 1


Output sequence


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node 6node 5

node 1 node 2

node 0

X 1

X 1

Output: 0, 1, i1


Output sequence


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node 6node 5

node 1 node 2

node 0

X 2

Output: 0, 1, i1


Output sequence


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node 6node 5

node 1 node 2

node 0

X 2

Output: 0, 1, i1, 0


Output sequence


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node 6node 5

node 1 node 2

node 0

X 5

Output: 0, 1, i1, 0


Output sequence


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node 6node 5

node 1 node 2

node 0

X 5

Output: 0, 1, i1, 0, 1


Output sequence


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node 6node 5

node 1 node 2

node 0

X 5

X 5

Output: 0, 1, i1, 0, 1, i5


Output sequence


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node 6node 5

node 1 node 2

node 0

X 6

Output: 0, 1, i1, 0, 1, i5


Output sequence


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node 6node 5

node 1 node 2

node 0

X 6

Output: 0, 1, i1, 0, 1, i5, 1


Output sequence


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node 6node 5

node 1 node 2

node 0

X 6

X 6

Output: 0, 1, i1, 0, 1, i5, 1, i6


Output sequence


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node 6node 5

node 1 node 2

node 0

X 0

X 0

Output: 0, 1, i1, 0, 1, i5, 1, i6


Decoding


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node 0


Decoding


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node 1 node 2

node 0

Output: 0


Decoding


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node 1 node 2

node 0

Output: 0, 1


Decoding

X 1


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node 1 node 2

node 0

X 1

Output: 0, 1, i1


Decoding


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node 6node 5

node 1 node 2

node 0

Output: 0, 1, i1, 0


Decoding


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node 6node 5

node 1 node 2

node 0

Output: 0, 1, i1, 0, 1


Decoding


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node 6node 5

node 1 node 2

node 0

X 5

Output: 0, 1, i1, 0, 1, i5


Decoding


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node 6node 5

node 1 node 2

node 0

Output: 0, 1, i1, 0, 1, i5, 1


Decoding


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node 6node 5

node 1 node 2

node 0

X 6

Output: 0, 1, i1, 0, 1, i5, 1, i6


Decoding

X 0


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=+

=+node 6node 5

node 1 node 2

node 0

X 0

X 2X 6X 5

X 1 X 2 X 0

Output: 0, 1, i1, 0, 1, i5, 1, i6


Block coding


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Block coding


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Block coding


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Block coding


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Block coding


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Block coding


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Block coding


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Implementation issues

The block size M = 2 K is a power of 2.


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There are only K + 1 different scales.

To avoid the computation of scaletransformations at each mach attempt, wecan use several copies of the dictionary, oneat each possible scale.





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There are only K + 1 different scales.

To avoid the computation of scaletransformations at each mach attempt, wecan use several copies of the dictionary, oneat each possible scale.

Therefore we have K + 1 dictionaries, D (0) , D (1) ,. . . , D (K )


Output entropy coding

The output is encoded by an adaptive arithmeticcoder


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coder.





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coder.

There are K + 1 independent models to encondethe ags dening the segmentation tree, eachone corresponding to a different scale.





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coder.

There are K + 1 independent models to encondethe ags dening the segmentation tree, eachone corresponding to a different scale.

There are k + 1 independent models used toencode the indices in D .



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Multidimensional extensions


MMP segmentation

When the imput signal is one-dimensional, MMPcan split an input block of lenght N in two


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can split an input block of lenght N in twosub-blocks of length N/ 2. This is equivalent tochoose a segmentation point p in a onedimensional-space as p = N/ 2.


MMP segmentation

When the imput signal is one-dimensional, MMPcan split an input block of lenght N in two


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can split an input block of lenght N in twosub-blocks of length N/ 2. This is equivalent tochoose a segmentation point p in a onedimensional-space as p = N/ 2.

When the input signal is multi-dimensional, we just have to choose a segmentation point p in amulti-dimensional space.



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2D segmentation: quad-tree

P


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P


2D segmentation: quad-tree


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MMP segmentation variations

There are many different ways to choose thesegmentation point in the multi-dimensional


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segmentation point in the multi dimensionalspace.


MMP segmentation variations

There are many different ways to choose thesegmentation point in the multi-dimensional


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g pspace.

The two-dimensional segmentation presentedpreviously does not preserve the binary treesegmentation structure.


2D segmentation: binary tree


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Scale Transformations



The scale transformations are simple samplingrate change operations.


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Good results are usually obtained with linearinterpolation and decimation.





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Good results are usually obtained with linearinterpolation and decimation.

Zero order interpolation also works. Moresophisticated interpolation schemes, like splines,make little difference in the performance.



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Initial Dictionary


Initial Dictionary

MMP builds the dictionary as it encodes the data.


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Initial Dictionary


Therefore, the initial dictionary can be very


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simple, with no need for any kind of training.


Initial Dictionary




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, y y

simple, with no need for any kind of training.For images, it is common to initialize the

dictionary at scale 1

1 (D

0) with the impulseshaving all integer amplitudes from 0 to 255.


Initial Dictionary




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, y y

simple, with no need for any kind of training.For images, it is common to initialize the

dictionary at scale 1

1 (D

0) with the impulseshaving all integer amplitudes from 0 to 255.

The initial dictionaries at other scales can bederived from the one at scale D 0 by the scaletransformations. Thus, they will be composed oftwo-dimensional rectangular pulses.



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Initial Dictionary

Using this initial dictionary, MMP can have good results fora large class of image data, ranging from smooth imagesto document and graphics images It even works for white


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to document and graphics images. It even works for whitegaussian noise.

One can thus say that MMP has a universal character.


Initial Dictionary

Using this initial dictionary, MMP can have good results fora large class of image data, ranging from smooth imagesto document and graphics images. It even works for white


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Also using this initial dictionary, one can achieve losslesscompression.


Initial Dictionary

Using this initial dictionary, MMP can have good results fora large class of image data, ranging from smooth imagesto document and graphics images. It even works for white


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Also using this initial dictionary, one can achieve losslesscompression.

For lossy image compression, it sufces to quantize theamplitudes of the initial dictionaries with step size 4.



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Dictionary Updating


Dictionary Updating

In MMP, the dictionary is updated byconcatenations of previously encoded segments.


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Dictionary Updating

In MMP, the dictionary is updated byconcatenations of previously encoded segments.


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Dictionary Updating

However, the dictionary can be updated usingother criteria, depending of the source to beencoded.


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Dictionary Updating

However, the dictionary can be updated usingother criteria, depending of the source to beencoded.


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For example, for smooth images, a deblockinglter could be applied to a block before it is

included in the dictionary, or a block could beincluded or not according to perceptual criteria.


Dictionary Updating

The dictionary could also be updated usingdisplaced blocks belonging to the blockscausal neighborhood


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Dictionary Updating



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Dictionary Updating



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Dictionary Updating



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Dictionary Updating

Rotated blocks could also be used.


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Dictionary Updating

Rotated blocks could also be used.

Other option is to only insert words that are


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sufciently distant from the others.

d

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Source of blockiness in MMP

MMP parses the input signal in variable sizedblocks. As a lossy compressor, MMP replaceseach input block by a distorted version of it.


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Each block is independently processed. Thismeans that even if the dictionary is composedof smooth functions, MMP makes no attemptto control the smoothness of theconcatenation of blocks.

In image compression applications atmoderate compression ratios, the resultingblockiness tends to become highly visible.



X 0


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X 1 X 2

X 5 X 6

(a)

(a) Before coding;



X 0 ^X 0


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X 1 X 2

X 5 X 6

^ ^

^ ^

(b)

X 1 X 2

X 5 X 6

(a)

(a) Before coding; (b) After Coding.



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The three aspects of MMP



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Quantization Method

Since MMP encodes segments of a signal withvectors from a dictionary, it can be regarded as avector quantizer.


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It is an adaptive, multiscale vector quantizer.


Encoding Method

Since MMP encodes segments of an imageusing concatenations of previously occurredpatterns, it can be regarded as a method based

hi L l Zi


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on recurrent pattern matching, as Lempel-Zivencoders.


Encoding Method

Since MMP encodes segments of an imageusing concatenations of previously occurredpatterns, it can be regarded as a method based

hi L l Zi


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on recurrent pattern matching, as Lempel-Zivencoders.

It is a multiscale, lossy recurrent patternmatching method.


Transform-based Method

The dictionary in MMP grows withconcatenations of words previously present inthe dictionary.


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The dictionary in MMP grows withconcatenations of words previously present inthe dictionary.


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If the initial dictionary has only pulse functionswith several amplitudes and scales, then the

dictionary is built by functions that areconcatenations of pulses with several scales.

Then the signal is eventually approximated withconcatenations of expansions and contractionsof pulses




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X (t) =k

k t

k k



X (t) =k

k t

k k


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X (t) =k

k t

k k


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(t), its expansions, contractions and translations

form an orthogonal basis. (t)



Using this knowledge, one can devise apost-processing method that can greatly reducethe blockiness inherent in MMP-based methods.


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Using this knowledge, one can devise apost-processing method that can greatly reducethe blockiness inherent in MMP-based methods.


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One lters the decoded signal with a smoothinglter whose kernel depends on the support of thebasis function it is ltering.


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One lters the decoded signal with a smoothinglter whose kernel depends on the support of thebasis function it is ltering.


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The best results are usually obtained with agaussian kernel


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Without post-lter - PSNR = [email protected];




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Without post-lter: PSNR = [email protected] post-lter: PSNR = [email protected]


R-D optimization


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R-D optimization


Segmentation tree

The segmentation tree described so far was builtconsidering local decisions based on distortioncalculations.


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Segmentation tree

The segmentation tree described so far was builtconsidering local decisions based on distortioncalculations.

We can expect an improved compression


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We can expect an improved compressionperformance if we build the segmentation tree

using a global criterium based on distortion andrate evaluations.


Notation

node 6node 5

node 1 node 2

node 0


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Segmentation tree: S = {0, 1, 2, 5, 6}



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Notation

node 6node 5

node 1 node 2

node 0


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Distortion of node l: D (l) = X l S i l

Rate of index i l : R (l) = log2(Pr( i l |k l ))


Notation

node 6node 5

node 1 node 2

node 0


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Distortion of the Segmentation tree: D (S ) =lS F

D (l)


Notation

node 6node 5

node 1 node 2

node 0

{ }


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Distortion of the Segmentation tree: D (S ) =lS F

D (l)

Rate of the segmentation tree: R A (S ) +lS F

R (l)


The optimization problem

Given a target rate R

, nd S such that

minimize D (S )

constrained to R (S ) = R


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, nd S such that

minimize D (S )



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Introducing the Lagrange multiplier 0 we have theequivalent unconstrained problem:

minimize J (S ) = D (S ) + R (S )




, nd S such that

minimize D (S )



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Introducing the Lagrange multiplier 0 we have theequivalent unconstrained problem:

minimize J (S ) = D (S ) + R (S )

Dening J (l) = D (l) + R (l), we have

J (S ) = R A (S ) +lS F

J (l)


Sub-Trees

node 0Tree S


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node 6node 5

node 1 node 2


Sub-Trees

node 0Tree S


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node 6node 5

node 1 node 2

The sub-tree S (2)


Sub-Trees

node 0Tree S


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node 6node 5

node 1 node 2

The sub-tree S (2)

J (S (l)) = R A (S (l)) +lS F S ( l )

J (l)


Lagrangian costs

If l is a leaf node ,

J (S (l)) = D (l) + (R 1l + R (l))


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Lagrangian costs


J (S (l)) = D (l) + (R 1l + R (l))

If l is not a leaf node,


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J (S (l)) = R 0l + J (S (2l + 1)) + J (S (2l + 2))


Lagrangian costs


J (S (l)) = D (l) + (R 1l + R (l))

If l is not a leaf node,


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J (S (l)) = R 0l + J (S (2l + 1)) + J (S (2l + 2))

Then we must prune S (2l + 1) and S (2l + 2) whenever

D (l) + (R 1l + R (l)) < R 0l + J (S (2l + 1)) + J (S (2l + 2))


Coupling throughD

The previous strategy is sub-optimal in the sense that itassumes that the costs of the nodes are not coupled. Thisis not true because of the dictionary updating procedure.

node 0


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node 1 node 2

node 3 node 4



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Optimization procedure

We initialize S as a full tree.


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We initialize S as a full tree.The tree is traversed from the leaf nodestowards the root node.


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We initialize S as a full tree.The tree is traversed from the leaf nodestowards the root node.

We must prune the descendants of the node lif


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if

J (l)+ R 1l + J l < J (S (2l+1))+ J (S (2l+2))+ R 0l

where J l = r S l J (r ) r S l J (r ).

The procedure is repeated until convergence


Source Coders using the MMPParadigm


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g


Side-Match MMP

Uses a subset of the dictionary D , the statedictionary D s , to encode a given input block.


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Side-Match MMP

Uses a subset of the dictionary D , the statedictionary D s , to encode a given input block.D s is composed of vectors that comply to asmoothness criterion, considering a causalneighborhood.


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Side-Match MMP

U

L

j

j j X


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Side-Match MMP

U

L

j

j j X


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D s is evaluated prior to the processing of

each block.


Experimental results

Simulation Parameters:


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Simulation Parameters:Two-dimensional MMP was applied tocompress gray scale images.


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Maximum input block size 16 16.


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Maximum input block size 16 16.Maximum dictionary size 32768


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Maximum dictionary size 32768

Initial dictionary at scale 0:Range from 0 to 255; step size 4.


Images used


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PSNR x rate for image Cameraman

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R (

d B )

SMMMPRDJPEG2000


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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

P S N

R (bpp)



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PSNR x rate for image pp1205

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( d B )

SM-MMP-RDMMP-RD

MMPSPIHTJPEG


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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

P S N R

R (bits/pixel



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R (

d B )


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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

P S N R

R (bits/pixel

SM-MMP-RDMMP-RD

MMPSPIHTJPEG


MMP x SM-MMP - Lena


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Left: MMP; Right - SM-MMP


MMP x SPIHT - Lena


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MMP x SPIHT - pp1205


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MMP x SPIHT - pp1209


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MMP-Intra

It encodes with MMP the residual of the an Intraprediction similar to the one used in H.264.


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MMP-Intra

M i : partition for prediction;i i : partition for MMP encoding

i0

i1

M2 M1


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i0

i3i2


MMP-Intra

M i : partition for prediction;i i : partition for MMP encoding

i0

i1

M2 M1


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i0

i3i2

They are optimized according to RD criteria


PSNR x rate for image Lena

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P S N R

( d B )


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0 0.2 0.4 0.6 0.8 1 1.2 1.4

P

bpp

MMPIntra w/ new Dic designH.264/AVC High

JPEG2000


PSNR x rate for image Gold

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P S N R

( d B )


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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

P

bpp


JPEG2000


PSNR x rate for image Cameraman

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P S N R

( d B )


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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

P

bpp


JPEG2000



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P S N R

( d B )


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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

P

bpp


JPEG2000



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P S N R

( d B )


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0 0.2 0.4 0.6 0.8 1 1.2

P

bpp


JPEG2000


MMP-Video

The universal character of MMP makes it a goodcandidate for encoding displaced framedifferences.


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MMP-Video


The initial dictionary at frame n + 1 is the sameas the one at the end of encoding frame n .


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MMP-Video


The initial dictionary at frame n + 1 is the sameas the one at the end of encoding frame n .


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Different probability models are used for vectorsentering the dictionary during the encoding of P,B, luminance and chrominance frames.


MMP-Video

This proposal has been tested by replacing theINTER encoding of displaced frame differencesin an H.264 encoder by the MMP.


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MMP-Video

This proposal has been tested by replacing theINTER encoding of displaced frame differencesin an H.264 encoder by the MMP.

We have used as a starting point the JM9.6H.264 software.


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Results for Foreman - P Slices

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e r a g e

P S N R

Foreman.cif P slices


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0 10000 20000 30000 40000 50000 60000 70000 80000 90000100000

A v e

Average bits/frame

MMPVideo YH.264 high Y

MMPVideo UH.264 high U

MMPVideo VH.264 high V


Results for Foreman - B Slices

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P S N R

Foreman.cif B slices


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28

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0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

A v e

Average bits/frame

MMPVideo YH.264 high Y

MMPVideo UH.264 high U

MMPVideo VH.264 high V


Other Developments


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MMP for Stereo Pairs


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The dictionary learnt while encoding the left viewis used to encode the right view.




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The dictionary learnt while encoding the left viewis used to encode the right view.

Good results have been reported.



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MMP for ECG

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0 0.5 1 1.5 2 2.5 3


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t (seconds)

The quasi-periodic nature of the ECG makes it a

good candidate for encoding with MMP.

Si nal Com ression usin Multiscale Recurrent Patterns 89/96

MMP for ECG

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0 0.5 1 1.5 2 2.5 3

( d )


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t (seconds)

The quasi-periodic nature of the ECG makes it a

good candidate for encoding with MMP.Good results have been reported.


Conclusions


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Conclusions

We developed the MMP, an universallossy/lossless compressor based onmultiscale pattern matching.


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Conclusions


Differently from many other coders, MMPdoes not rely on thetransformation-quantization-entropy coding

di


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paradigm.


Conclusions


Differently from many other coders, MMPdoes not rely on thetransformation-quantization-entropy coding

di


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paradigm.It was succesfully applied to lossy compressdifferent sets of data, such as still images,mixed compounds (graphics+text+stillimages), video, stereo pairs and ECG data.


Conclusions

Its complexity is equivalent to the one ofvector quantization.


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Conclusions

Its complexity is equivalent to the one ofvector quantization.

Therefore, its computational complexity is an

important issue.


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Future work

Development of fast versions of MMP.


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Future work


Development of speech and audio codecsusing the MMP paradigm.


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Future work



Further improvement in its coding efciencyin image and video coding.


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Future work



Further improvement in its coding efciencyin image and video coding.

Theoretical analysis of MMP performancewith sources other than the memoryless


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with sources other than the memorylessGaussian source.

Si l C i i M lti l R t P tt 93/96

References


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References

Can be found inhttp://www.lps.ufrj.br/profs/eduardo/

Alternatively, email [email protected]


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Thank you!


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Si l C i i M l i l R P 95/96

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Mmp Presentation

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