Abstract
This paper further develops the recently proposed two-dimensional quarter-plane autoregressive (AR) lattice parameter modelling of two-dimensional (2-D) fields to three-dimensional (3-D) case with cubic-space support. Starting from the original 3-D random field, eight prediction error fields are generated at each lattice stage. The relationships between the prediction errors of successive lattice stage is defined by seven reflection coefficients. Besides the basic theory, an algorithm for determining the 3-D cubic-space recursive transfer function from the reflection coefficients is presented. A synthesis model for regenerating the original random field from a white noise field and the sufficient lattice parameter stability conditions are also included. In order to verify the theory, two numerical examples on modelling of random fields are given. Finally, an interframe predictive coding system based on the 3-D lattice model is presented to demonstrate the usefulness of the formulation. Results indicate that its performance is almost the same as that of the conventional DPCM system.
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