We discuss space-efficient encoding schemes for planar graphs and maps. Our results improve on the constants of previous schemes and can be achieved with simple encoding algorithms. They are near-optimal in number of bits per edge.

The Bayesian segmentation model developed is motivated by consideration of the information needed for higher-level visual processing. A segmentation is regarded as a collection of parameters defining an image-valued stochastic process by separating topological (adjacency) and metric (shape) properties of the subdivision and intensity properties of each region. The prior selection is structured accordingly. The novel part of the representation, the subdivision topology, is assigned a prior by universal coding arguments, using the minimum description-length philosophy that the best segmentation allows the most efficient representation of visual data.>