Computing principal direction fields as frame bundle cross sections

Essential information about the differential structure of smooth surfaces is embodied in their principal curvature and principal direction fields. A particular type of fibre bundle, a frame bundle, is defined over estimated surface trace points and the computation of these fields is presented as the determination of the appropriate cross section through the frame bundle. Any approach to the recovery of surface structure must deal with the inherent limitations of local computations-an iterative constraint-satisfaction process is developed for the reliable extraction of the principal-direction cross section. Present methods are applied to the synthetic images corrupted by noise and to magnetic resonance imagery.<>