age is segmented into blocks of various size, and each In this paper, a rate-distortion function (RDF), R(D), is pre-segmented region is encoded at a different rate according sented for a variable block-size classification (VBSC) model. to its level of detail. We obtain a theoretical R(D) bound on the performance of VBSC model-based VQ has been successfully applied vector quantization (VQ) based on the VBSC model. It is theofor both still-image coding [4] and low-bit-rate video coding retically proved that the R(D) bound of the VBSC model is [5]. In this technique, a quadtree is used to efficiently lower lower than those of the Gaussian model and the fixed blockthe encoding bitrate by segmenting an image into variable size classification (FBSC) model for the bit rates of interest. In size blocks, in which larger blocks are classified into the the comparison tests of VBSC model-based VQ and FBSC low-detail class and are encoded at very low bit rates with model-based VQ, which were carried out by using a monolittle perceptual degradation. High-detail regions, which chrome still image, it was seen that the former technique outperforms the latter technique, subjectively as well as objectively. are isolated into the smallest blocks during the growth of We also experimentally evaluate a RDF for the VBSC model the quadtree, are classified into various edges which are and compare this with the theoretical RDF. There is a gap of separately encoded by VQ. 0.07-0.1 bpp between the theoretical RDF and the experimental The rate-distortion function (RDF), R(D), of a source RDF in VQ coding without entropy coding. We have reduced determines the minimum rate required to code the source the gap to 0.02-0.03 bpp by subsequently employing a Huffman output as a function of the desired minimum average discoder for entropy coding. It is expected that the theoretical tortion. This concept originated with Shannon [10], who bound can be approached more closely by the experimental computed the RDF for certain sources including a RDF by using a modified asymptotic RDF.