A Bayesian framework for 3D surface estimation

We develop an evidence-combining framework for extracting locally consisten t differential structure from curved surfaces. Existing approaches are rest ricted by their sequential multi-stage philosophy, since important informat ion concerning the salient features of surfaces may be discarded as necessa rily condensed information is passed from stage to stage. Furthermore, sinc e data representations are invariably unaccompanied by any index of evident ial significance, the scope for subsequently refining 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 n on-linearities, such as outliers or discontinuities. If linear processing t echniques are employed covariances may be readily computed: but will be unr eliable. On the other hand, if more powerful non-linear processing techniqu es are applied, there are severe technical problems in computing the covari ances themselves. We sidestep this dilemma by decoupling the identification of non-linearities in the data from the fitting process itself. If outlier s and discontinuities are accurately identified and excluded, then simple, linear processing techniques are effective for the fit, and reliable covari ance estimates can be readily obtained. Furthermore, decoupling permits non -linearity estimation to be cast within a powerful evidence combining frame work in which both surface parameters and refined differential structure co me to bear simultaneously. This effectively abandons the multi-stage proces sing philosophy. Our investigation is firmly grounded as a global MAP estim ate within a Bayesian framework. Our ideas are applicable to volumetric dat a. For simplicity, we choose to demonstrate their effectiveness on range da ta in this paper. (C) 2001 Pattern Recognition Society. Published by Elsevi er Science Ltd. All rights reserved.