Analytical Rate-Distortion-Complexity Modeling of Wavelet-Based Video Coders

Analytical modeling of the performance of video coders is essential in a variety of applications, such as power-constrained processing, complexity-driven video streaming, etc., where information concerning rate, distortion, or complexity (and their interrelation) is required. In this paper, we present a novel rate-distortion-complexity (R-D-C) analysis for state-of-the-art wavelet video coding methods by explicitly modeling several aspects found in operational coders, i.e., embedded quantization, quadtree decompositions of block significance maps and context-adaptive entropy coding of subband blocks. This paper achieves two main goals. First, unlike existing R-D models for wavelet video coders, the proposed derivations reveal for the first time the expected coding behavior of specific coding algorithms (e.g., quadtree decompositions, coefficient significance, and refinement coding) and, therefore, can be used for a variety of coding mechanisms incorporating some or all the coding algorithms discussed. Second, the proposed modeling derives for the first time analytical estimates of the expected number of operations (complexity) of a broad class of wavelet video coding algorithms based on stochastic source models, the coding algorithm characteristics and the system parameters. This enables the formulation of an analytical model characterizing the complexity of various video decoding operations. As a result, this paper complements prior complexity-prediction research that is based on operational measurements. The accuracy of the proposed analytical R-D-C expressions is justified against experimental data obtained with a state-of-the-art motion-compensated temporal filtering based wavelet video coder, and several new insights are revealed on the different tradeoffs between rate-distortion performance and the required decoding complexity.