An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
Multidimensional binary search trees used for associative searching
Communications of the ACM
Combining Image Compression and Classification Using Vector Quantization
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
Optimal variable-rate mean-gain-shape vector quantization for image coding
IEEE Transactions on Circuits and Systems for Video Technology
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Many approaches have been designed over the years that aim at providing good rate-distortion (RD) performance with limited complexity. One such approach is product vector quantization (VQ) where sub-vectors within a vector are encoded separately. Optimal product VQ (PVQ) aims at maximizing the RD performance, ideally approaching that of the higher dimensional unstructured VQ. In this paper we consider scenarios where PVQ is used to approximate the labeling obtained from an existing higher dimension quantizer or classifier. This problem differs in that the metric of interest is no longer (or not only) RD but the degree to which the PVQ approximates the labeling. In this paper we will present an efficient design technique under the labeling constraints and we show that performance is significantly improved if these are taken into account, as compared to using a standard PVQ design. We will present two examples where this technique can be used. First we consider a PVQ designed to approximate a higher dimension classifier. In this case we show that with a small penalty in distortion (e.g., 0.04 dB loss) we can reduce significantly the misclassification (e.g., 48% relative reduction, 4.6% absolute reduction) with respect to a standard PVQ design. In our second example we show how hierarchical VQ (HVQ) can be used as a preprocessing stage for a standard unstructured VQ, such that the HVQ stage enables a significant reduction of the codeword candidates to be searched in the VQ stage. Here again we show how HVQ designed to optimize the labeling enables a further reduction in complexity as the HVQ partition is designed to approximate the standard VQ partition. As an example, with this approach, the overall complexity is reduced by 98.7% with respect to a full search VQ, with only a 0.13 dB loss in performance. The performance is better than when using HVQ alone, and the complexity is reduced with respect to a preprocessing where the HVQ used was not designed under the labeling constraint.