Some Extensions of the Spring Model for Image Processing

Abstract

A well known technique used in image reconstruction involves the use of Bayesian Estimation with prior Markov Random Field (MRF) Models. A particularly simple instance of these models is the “spring” (or membrane) model, in which the image is considered as a system of particles — one for each pixel — where each particle is connected to neighboring ones by ideal springs, which enforce a global smoothness constraint. In this paper we show that this model may be extended in several interesting ways: i) By allowing the state of the particles to take complex values and introducing a rotation of these local state spaces, one may use the spring model to construct adaptive pass-band (quadrature) filters wich are very effective —for example — for processing fringe pattern images. ii) We show that by allowing the state of the particles to take values on a space of discrete probability measures, one can use a generalized spring model for the empirical posterior marginal distributions of discrete MRF’s, such as the Ising model. This result allows one to find optimal estimators for discrete-valued fields more than 100 times faster than with conventional (stochastic) methods, which allows the efficient implementation of iterative procedures for fitting piecewise parametric models.