Efficient product code vector quantisation using the switched split vector quantiser
Digital Signal Processing
Sample-size adaptive self-organization map for color images quantization
Pattern Recognition Letters
Content-based image retrieval with the normalized information distance
Computer Vision and Image Understanding
Optimal companding vector quantization for circularly symmetric sources
Information Sciences: an International Journal
Direct sampling on surfaces for high quality remeshing
Computer Aided Geometric Design
An efficient bit allocation for compressing normal meshes with an error-driven quantization
Computer Aided Geometric Design - Special issue: Geometry processing
Using self-organizing maps to visualize high-dimensional data
Computers & Geosciences
Image categorization via robust pLSA
Pattern Recognition Letters
Clustering: A neural network approach
Neural Networks
Computers & Mathematics with Applications
Wireless link state-aware H.264 MGS coding-based mobile IPTV system over WiMAX network
Journal of Visual Communication and Image Representation
Computation of the complexity of vector quantizers by affine modeling
Signal Processing
Geometric piecewise uniform lattice vector quantization of the memoryless Gaussian source
Information Sciences: an International Journal
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
Computer Aided Geometric Design
Obtuse triangle suppression in anisotropic meshes
Computer Aided Geometric Design
Robust modeling of constant mean curvature surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Multi-dimensional mechanism design with limited information
Proceedings of the 13th ACM Conference on Electronic Commerce
Exponential stabilisability of finite-dimensional linear systems with limited data rates
Automatica (Journal of IFAC)
Aesthetic placement of points using generalized Lloyd relaxation
Computational Aesthetics'09 Proceedings of the Fifth Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging
| Hi-index | 754.84 |
In 1948 W. R. Bennett used a companding model for nonuniform quantization and proposed the formulaD : = : frac{1}{12N^{2}} : int : p(x) [ É(x) ]^{-2} dxfor the mean-square quantizing error whereNis the number of levels,p(x) is the probability density of the input, andE prime(x) is the slope of the compressor curve. The formula, an approximation based on the assumption that the number of levels is large and overload distortion is negligible, is a useful tool for analytical studies of quantization. This paper gives a heuristic argument generalizing Bennett's formula to block quantization where a vector of random variables is quantized. The approach is again based on the asymptotic situation whereN, the number of quantized output vectors, is very large. Using the resulting heuristic formula, an optimization is performed leading to an expression for the minimum quantizing noise attainable for any block quantizer of a given block sizek. The results are consistent with Zador's results and specialize to known results for the one- and two-dimensional cases and for the case of infinite block length(k rightarrow infty). The same heuristic approach also gives an alternate derivation of a bound of Elias for multidimensional quantization. Our approach leads to a rigorous method for obtaining upper bounds on the minimum distortion for block quantizers. In particular, fork = 3we give a tight upper bound that may in fact be exact. The idea of representing a block quantizer by a block "compressor" mapping followed with an optimal quantizer for uniformly distributed random vectors is also explored. It is not always possible to represent an optimal quantizer with this block companding model.