A Bayesian framework for 3D surface estimation

摘要

We develop an evidence-combining framework for extracting locally consistent differential 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 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 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 identification of non-linearities in the data from the fitting process itself. If outliers and discontinuities are accurately identified and excluded, then simple, linear processing techniques are effective for the fit, 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 refined differential structure come to bear simultaneously. This effectively abandons the multi-stage processing philosophy. Our investigation is firmly grounded as a global MAP estimate within a Bayesian framework. Our ideas are applicable to volumetric data. For simplicity, we choose to demonstrate their effectiveness on range data in this paper.