A Baum-Welch Algorithm for Noisy Vector Fields for Classification and Synthesis of Textures Using Non-Symmetric Half-Plane

: In this paper we present a statistical model with a non-symmetric half-plane (NSHP) region of support for two-dimensional continuous-valued vector fields. It has the simplicity, efficiency, and ease of use of the well-known hidden Markov model (HMM) and associated Baum-Welch algorithms for time-series and other one-dimensional problems. At the same time, it is able to learn textures on a two-dimensional field. We describe a fast approximate forward procedure for computation of the joint probability density function (PDF) of the vector field as well as an approximate Baum-Welch algorithm for parameter re-estimation. We test the method using synthetic textures.