Optimizing Markov Models with Applications to Triangular Connectivity Coding

In this work Markov Models are constructed to describe the asymptotic stochastical behavior of regular languages, what allows for optimal arithmetic coding of words from the language. A new method is presented for the optimization of Markov Models such that also constraints are captured that cannot be described within a regular language. The new technique is applied to the encoding of the connectivity graph of triangle meshes of low genus and boundary fraction. The resulting compression rates are up to one percent optimal and the best known upper bound for this class of models