Optimized entropy-constrained vector quantization of lossy vector map compression

1. Optimized entropy-constrained vector quantization of lossy vector map compression Minjie Chen1, Mantao Xu2, Pasi Fränti1 1Speech and Image Processing Unit, School of Computing, Univ. of Eastern Finland, Finland 2 School of Electronics & Information, Shanghai DianJi University, China Methodology Introduction 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. • Size of codebook: 78 • bit-rate: 5 bit/point • Minimize: J = ∑D(Distortion) +λR(Rate) • Initialized by entropy-constrained pair-wise nearest neighbour (ECPNN) • MSE = 8.7∙10-6 Britain Map with 10910 points and its differential coordinates 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 Experiments • 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) When λ is known, optimal l is determined! This is derived by setting ∂∑Joi/∂l=0 Workflow λ is updated by binary search to find the best solution under given bit constraint • Size of codebook: 30 • bit-rate: 5 bit/point • MSE = 6.3∙10-6 • Better performance than both method Conclusions Two-level strategy is employed to optimize the codebook design. 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 For further information: http://cs.joensuu.fi/sipu