A clustering algorithm for entropy-constrained vector quantizer design with applications in coding image pyramids

Abstract

{A clustering algorithm for the design of e cient vector quantizers to be followed by entropy coding is proposed. The algorithm, called entropy-constrained pairwise nearest neighbor (ECPNN), designs codebooks by merging the pair of Voronoi regions which gives the least increase in distortion for a given decrease in entropy. The algorithm is an entropy-constrained version of the pairwise nearest neighbor (PNN) clustering algorithm of Equitz and can be used as an alternative to the entropyconstrained vector quantizer design (ECVQ) proposed by Chou, Lookabaugh and Gray. By a natural extension of the ECPNN algorithm we develop another algorithm that designs alphabet-and entropy-constrained vector quantizers and call it alphabet-and entropy-constrained pairwise nearest neighbor (AECPNN) design. The AECPNN algorithm can be used as alternative to the alphabet-and entropy-constrained vector quantizer design (AECVQ) proposed by Rao and Pearlman, that is directly based on the ECVQ design algorithm. Through simulations on synthetic sources, we show that ECPNN and ECVQ have indistinguishable mean-square-error versus rate performance and that the ECPNN and AECPNN algorithms obtain as close performance by the same measure as the ECVQ and AECVQ algorithms. The advantages over

Conditional entropy-constrained vector quantization: high-rate theory and design algorithms

“…The use of this table is one of the keys to fast computation. This kind of operation is not possible for generalized Lloyd type algorithms, such as the CECVQ design algorithm [6].…”

“…The algorithm is suboptimal, because the procedure can not guarantee generation of the best quantizer in the distortion-rate sense. See [6] for a further discussion about this topic. Before describing the CECPNN algorithm, we introduce first some definitions and notation.…”

“…The equations (7) and (8) are the functionals that are respectively used in the minimization process of the design of memoryless VQ's carried out by the GLA and ECVQ design. Recently an entropy constrained version of the PNN design algorithm was proposed by Garrido, Pearlman and Finamore [6] and is called entropy-constrained pairwise nearest neighbor, or in short ECPNN.…”

“…Manipulating the equation (65), see [3] or [6], the increase of distortion takes the following form:…”

“…As a standard reference for this kind of algorithm, we cite Equitz [3]. The ECPNN developed in [6] is an algorithm that designs codebooks by merging the pair of Voronoi regions which gives the least increase of distortion for a given decrease in entropy. The algorithm is suboptimal, because the procedure can not guarantee generation of the best quantizer in the distortion-rate sense.…”