Iterative spline relaxation with the EM algorithm

José A. F. Leite, Edwin R. Hancock

Abstract: This paper describes how the early visual process of contour organisation can be realised using the expectation and maximization (EM) algorithm of Dempster, Laird and Rubin (1977). The underlying computational representation is based on Zucker's (1988) idea of fine spline coverings. According to our EM approach the adjustment of spline parameters draws on an iterative weighted least-squares fitting process. The expectation step of our EM procedure computes the likelihood of the data using a mixture model defined over the set of spline coverings. These splines are limited in their spatial extent using Gaussian windowing functions. The maximisation of the likelihood leads to a set of linear equations in the spline parameters which solve the weighted least squares problem. We evaluate the technique on the localisation of road structures in aerial infrared images.