A Bayesian framework for 3D surface estimation

We develop an evidence-combining framework for extracting locally consistent di!erential structure from curved surfaces. Existing approaches are restricted by their sequential multi-stage philosophy, since important information concerning the salient features of surfaces may be discarded as necessarily condensed information is passed from stage to stage. Furthermore, since data representations are invariably unaccompanied by any index of evidential signi"cance, the scope for subsequently re"ning them is limited. One way of attaching evidential support is to propagate covariances through the processing chain. However, severe problems arise in the presence of data non-linearities, such as outliers or discontinuities. If linear processing techniques are employed covariances may be readily computed, but will be unreliable. On the other hand, if more powerful non-linear processing techniques are applied, there are severe technical problems in computing the covariances themselves. We sidestep this dilemma by decoupling the identi"cation of non-linearities in the data from the "tting process itself. If outliers and discontinuities are accurately identi"ed and excluded, then simple, linear processing techniques are e!ective for the "t, and reliable covariance estimates can be readily obtained. Furthermore, decoupling permits non-linearity estimation to be cast within a powerful evidence combining framework in which both surface parameters and re"ned di!erential structure come to bear simultaneously. This e!ectively abandons the multi-stage processing philosophy. Our investigation is "rmly grounded as a global MAP estimate within a Bayesian framework. Our ideas are applicable to volumetric data. For simplicity, we choose to demonstrate their e!ectiveness on range data in this paper. ( 2001 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.