  Forward adaptive transform coding of images requires a codebook of transform
matrices from which the best transform can be chosen for each macroblock.
Codebook construction is a problem of designing a quantizer for
Karhunen-L\'{o}eve transform (KLT) matrices estimated from sample image blocks.
We present a novel method for KLT matrix quantization based on a finite-lattice
non-causal homogeneous Gauss-Markov random field (GMRF) model with asymmetric
Neumann boundary conditions for blocks in natural images. The matrix
quantization problem is solved in the GMRF parameter space, simplifying the
harder problem of quantizing a large matrix subject to an orthonormality
constraint to a low-dimensional vector quantization problem. Typically used
GMRF parameter estimation methods such as maximum-likelihood (ML) do not
necessarily maximize the coding performance of the resulting transform
matrices. To this end we propose a method for GMRF parameter estimation from
sample image data, which maximizes the high-rate transform coding gain. We also
investigate the application of GMRF-based transforms to variable block-size
adaptive transform coding.
