optimized entropy-constrained vector quantization of lossy vector map compression
DESCRIPTION
Optimized entropy-constrained vector quantization of lossy vector map compression Minjie Chen 1 , Mantao Xu 2 , Pasi Fränti 1 1 Speech and Image Processing Unit, School of Computing, Univ. of Eastern Finland, Finland 2 School of Electronics & Information, Shanghai DianJi University, China. - PowerPoint PPT PresentationTRANSCRIPT
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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e of
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ECPNNProposed
2 4 6 8 1010
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ECPNNUniformProposed
2 4 6 8 1010
-7
10-6
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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