Joint Content and Shape Adaptive Transforms Based on a GMRF Model for Coding Arbitrarily Shaped Image Segments

It is known that shape-adaptive (SA) transform coding can outperform block-based transform coding for images. However, there is no simple way to construct optimal transforms for arbitrarily shaped image segments. We present a novel method for constructing SA transforms using a non-causal finite lattice homogeneous Gauss-Markov random field (GMRF) model. Karhunen-Loéve transform (KLT) of the GMRF model serves as a compact parameterized model for the KLT of an arbitrarily shaped segment, where the model parameters represent the image texture. In contrast to other SA transforms considered in the literature, our approach makes it possible to optimize the transform to an image segment in the sense that if the GMRF model is exact for the texture, the resulting KLT is the optimal transform for the image segment. An important part of the proposed GMRF model is a modified version of asymmetric Neumann boundary conditions designed to ensure a high transform coding gain for arbitrarily shaped image segments. By using a candidate set of GMRF parameters estimated from a training set of images, our KLT model can be used for joint content and shape adaptive transform (JCSAT) coding. Experimental results show that JCSAT coding outperforms other known SA transforms, as well as the standard 2D-DCT.