A Bayesian Approach to 3D Surface Fitting and Refinement

This paper presents a novel methodology for extracting differential structure from noisy and discontinuous surfaces. We formulate the problem as a global MAP estimate which we develop under Bayesian principles. Development leads to two distinct MAP estimates for initial surface patch fitting and for subsequent surface refinement. Each estimate is realised through an iterative scheme which gauges the effects on consistency of updating single local surfaces. In turn, each update is itself realised by iterating between two modes, for surface smoothing and outlier identification, respectively. Smoothing reduces to a simple weighted least-squares technique which delivers robust surface estimates and covariances. Outlier estimation is achieved by a powerful non-linear method which incorporates feedback. As a consequence, the two processing levels become strongly coupled since curvature information from the refinement level can influence patch estimation. The net effect is a robust, evidence-combining scheme in which early fit and segmentation errors can be rectified. We demonstrate the utility of the scheme on range data.