The object of this dissertation is to investigate rate-distortion optimization and to evaluate the prospects of adaptive vector quantization for digital video compression. Rate-distortion optimization aims to improve compression performance using discrete optimization algorithms. We first describe and classify algorithms that have been developed in the literature to date. One algorithms is exte...

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry group.) In preparation for the main result, the quantization of coadjoint orbits is discussed in detail. This subject should not be confused with the quanti...

The kernel trick is a well known approach allowing to implicitly cast a linear method into a nonlinear one by replacing any dot product by a kernel function. However few vector quantization algorithms have been kernelized. Indeed, they usually imply to compute linear transformations (e.g., moving prototypes), what is not easily kernelizable. This paper introduces the Kernel-based Vector Quantiz...

This paper presents a vector quantization system that limits the maximum distortion introduced to a pre-selected threshold value. This system uses a recently introduced variation of the L 1 distortion measure that attempts to minimize the occurrences of quantization errors above a preselected threshold. The vectors are rst coded using the new distortion measure. The quantization error vectors i...

Quantization is the process of mapping a continuous or discrete scalar or vector, produced by a source, into a set of digital symbols that can be transmitted or stored using a finite number of bits. In the case of continuous sources (with values in R or Rn) quantization must necessarily be used if the output of the source is to be communicated over a digital channel. In this case, it is, in gen...

-We propose a memory-based parallel processor for vector quantization called a functional memory type parallel processor for vector quantization (FMPP-VQ). It accelerates nearest neighbor search of vector quantization. All distances between an input vector and reference vectors in a codebook are computed simultaneously in all PEs. The minimum value of all distances is searched in parallel. The ...

The kernel trick is a well known approach allowing to implicitly cast a linear method into a nonlinear one by replacing any dot product by a kernel function. However few vector quantization algorithms have been kernelized. Indeed, they usually imply to compute linear transformations (e.g. moving prototypes), what is not easily kernelizable. This paper introduces the Kernel-based Vector Quantiza...

The paper deals with the concept of relevance learning in learning vector quantization. Recent approaches are considered: the generalized learning vector quantization as well as the soft learning vector quantization. It is shown that relevance learning can be included in both methods obtaining similar structured learning rules for prototype learning as well as relevance factor adaptation. We sh...

Vector quantization and clustering are two different problems for which similar techniques are used. We analyze some approaches to the synthesis of a vector quantization codebook, and their similarities with corresponding clustering algorithms. We outline the role of fuzzy concepts in the performance of these algorithms, and propose an alternative way to use fuzzy concepts as a modeling tool fo...

We investigate the greedy version of the L-optimal vector quantization problem for an Rvalued random vector X ∈ L. We show the existence of a sequence (aN )N≥1 such that aN minimizes a 7→ ∥min1≤i≤N−1 |X−ai| ∧ |X−a| ∥∥ Lp (L-mean quantization error at level N induced by (a1, . . . , aN−1, a)). We show that this sequence produces L -rate optimal N -tuples a = (a1, . . . , aN ) (i.e. the L -mean q...