Optimized entropy-constrained vector Optimized entropy-constrained vector quantization of lossy vector map quantization of lossy vector map

compressioncompressionMinjie Chen1, Mantao Xu2, Pasi Fränti1

1Speech and Image Processing Unit, School of Computing, Univ. of Eastern Finland, Finland2 School of Electronics & Information, Shanghai DianJi University, China

For further information: http://cs.joensuu.fi/sipu

Methodology

Conclusions

Introduction

Experiments

• Size of codebook: 78• bit-rate: 5 bit/point• Minimize: J = ∑D(Distortion) + λ R(Rate)• Initialized by entropy-constrained pair-wise nearest neighbour (ECPNN)• MSE = 8.7∙10-6

Vector map, which consists of geographic information such as waypoints, routes and areas, is represented as a sequence of points in a given coordinate system.

Differential coordinates of subsequent sampling points are considered as the prediction error and vector quantization are designed on these residual vectors.

Vector quantization (with codebook) is designed for most common vectors, and the remaining vectors (outliers) are coded by additional bits using uniform quantization (without codebook).

Dynamic programming method is then utilized to improve the quantized vector selection in closed-loop framework.

Britain Map with 10910 points and its differential coordinates

• Size of codebook: 30• bit-rate: 5 bit/point• MSE = 6.3∙10-6

• Better performance than both method

Two-level strategy is employed to optimize the codebook design.

Performance comparisonAll points are encoded:•Clustering-based method (CBC)•Reference Line (RL)•Optimal entropy-constrained vector quantization (OCVQ)

An approximated curve is encoded:•Dynamic Quantization (DQ)•OCVQ integrated into DQ (OCVQ +DQ)

Proposed method has an optimal size of codebookWhen high bit-rate is required, most vectors are coded as “outlier”

When high compression-rate is required, most vectors are coded by codebook vectors

Cost of Residual vector vi represent by jth element in codebook:

SET

Estimate cost when value [vi/l] is coded (any distribution fit the data e.g. geometric, uniform, Poisson, negative binomial…)

Iterated process like k-means, but with one additional “outlier” cluster

6 / ln 2l

2|| || , 1,2...,ij jJ r j k i jv c

( ) , arg min ( ), 0,1..,j ijQ j J j k i jv c

2*

0 0 0( )6i i

lJ r r

When λ is known, optimal l is determined!

This is derived by setting ∂∑Joi/∂l=0

λ is updated by binary search to find the best solution under

given bit constraint

2 4 6 8 100

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Workflow

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ECPNNProposed

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ECPNNUniformProposed

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CBCRLOCVQDQOCVQ+DQ

Get Resi dual Vectors

I ni t i al Codebook by ECPNN

Create outl i er cl uster wi th step l ength l

Re-parti t i on and update codebook

Get λ under gi ven bi t- rate

constrai nt

Resi dual Quanti zati on

Entropy Encodi ng

Reconstruct curve usi ng cl osed-l oop form wi th dynami c programmi ng

Update Resi dual Vectors

Update λ

Codi ng SchemeEnd