Paper Title : A Rate - Distortion Function for Vector Quantization witha Variable Block - Size Classi cation

In this paper, a rate-distortion function (RDF), R(D), is presented for a variable block-size classiication (VBSC) model. We obtain a theoretical R(D) bound on the performance of vector quantization (VQ) based on the VBSC model. It is theoretically proved that the R(D) bound of the VBSC model is lower than those of the Gaussian model and the xed block-size classiication (FBSC) model for the bitrates of interest. In the comparison tests of VBSC model-based VQ and FBSC model-based VQ, which were carried out by using a monochrome still image, it was seen that the former technique outperforms the latter technique, subjectively as well as objectively. We also experimentally evaluate a RDF for the VBSC model and compare with the theoretical RDF. There is a gap of 0:07 0:1 bpp between the theoretical RDF and the experimental RDF in VQ coding without entropy coding. We have reduced the gap to 0:02 0:03 bpp by subsequently employing a Huuman coder for entropy coding. It is expected that the theoretical bound can be approached more closely by the experimental RDF by using a modiied asymptotic RDF.