Markov Random Field Restoration of Point Correspondences for Active Shape Modelling  Klaus Baggesen Hilger, Rasmus Reinhold Paulsen, Rasmus Larsen
 Abstract  In this paper it is described how to build a statistical shape model using a training set with a sparse of landmarks. A well defined model mesh is selected and fitted to all shapes in the training set using thin plate spline warping. This is followed by a projection of the points of the warped model mesh to the target shapes. When this is done by a nearest neighbour projection it can result in folds and inhomogeneities in the correspondence vector field. The novelty in this paper is the use and extension of a Markov random field regularisation of the correspondence field. The correspondence field is regarded as a collection of random variables, and using the HammersleyClifford theorem it is proved that it can be treated as a Markov Random Field. The problem of finding the optimal correspondence field is cast into a Bayesian framework for Markov Random Field restoration, where the prior distribution is a smoothness term and the observation model is the curvature of the shapes. The Markov Random Field is optimised using a combination of Gibbs sampling and the MetropolisHasting algorithm. The parameters of the model is found using a leaveoneout approach. The method leads to a generative model that produces highly homogeneous polygonised shapes with improved reconstruction capabilities of the training data. Furthermore, the method leads to an overall reduction in the total variance of the resulting point distribution model. The method is demonstrated on a set of human ear canals extracted from 3Dlaser scans.  Keywords  Bayesian statistics, Markov Random Field restoration, 3D statistical shape model, Point Correspondence, Thin Plate Spline Warping, Leaveoneout parameter estimation, Surface Curvature  Type  Conference paper [With referee]  Conference  SPIE  Medical Imaging  Year  2004  BibTeX data  [bibtex]  IMM Group(s)  Image Analysis & Computer Graphics 
Back :: IMM Publications
