Some extensions of the spring model for image processing (Q2724372)

The paper investigates several interesting extensions of the spring (membrane) model (SM), involved in the Bayesian estimation of the Markov Random Field (MRF) models for image reconstruction. In its classical form, the SM implements a prior global smoothness constraint and therefore behaves as an adaptive linear low-pass filter. A first extended approach to the SM is to allow the state of particles (e.g. one for each pixel) to take complex number values and to introduce a rotation of the local state spaces. The resulting SM is shown to be very effective in constructing adaptive pass-band (quadrature) filters for processing fringe pattern images. A second proposed extension of the SM allows the state of the particles to take values on a space of discrete probability measures. The generalized SM obtained is proved to be useful in the evaluation of the empirical posterior marginal distributions of discrete MRFs (Markov random fields). The author defines an ``MPM-MAP algorithm'' that permits a very fast computation of the optimal estimators (maximizing the posterior marginals) for discrete MRFs, obtaining effective iterative procedures for fitting mixtures of parametric models.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00036].