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Optimized entropy-constrained vector quantization of lossy vector map compression
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Optimized entropy-constrained Optimized entropy-constrained vector quantization of lossy vector vector quantization of lossy vector map compression 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 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 comparison All 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 codebook When 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 v i represent by j th element in codebook: SET Estimate cost when value [v i /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 /ln2 l 2 || || , 1,2..., ij j J r j k i j v c () , argmin ( ), 0,1.., j ij Q j J j k i j v c 2 * 0 0 0 ( ) 6 i i l J r r When λ is known, optimal l is determined! This is derived by setting ∂ J ∑ oi /∂l=0 λ is updated by binary search to find the best solution under given bit constraint 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 Rate P ercentage ofoutliers -6 -4 -2 0 2 50 52 54 56 58 Longitude Latitude -0.05 0 0.05 -0.05 0 0.05 dx dy -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 dx dy -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 dx dy Workflow 2 4 6 8 10 0 100 200 300 400 Rate S ize ofC odebook ECPNN P roposed 2 4 6 8 10 10 -7 10 -6 10 -5 10 -4 Rate MSE ECPNN U niform P roposed 2 4 6 8 10 10 -7 10 -6 10 -5 10 -4 Rate MSE CBC RL OCVQ DQ O C V Q +D Q Get Residual Vectors Initial Codebook by ECPNN Create outlier cluster with step length l Re-partition and update codebook Get λ under given bit-rate constraint Residual Quantization Entropy Encoding Reconstruct curve using closed- loop form with dynamic programming Update Residual Vectors Update λ Coding Scheme End
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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 Presentation
Transcript of Optimized entropy-constrained vector quantization of lossy vector map compression
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
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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
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Reconstruct curve usi ng cl osed-l oop form wi th dynami c programmi ng
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