Generic curvature features from 3-D images

The author presents a method for the computation of certain singularities-parabolic and umbilic points-of the principal curvature and direction fields of surfaces in three-dimensional images. He shows that the fields themselves must be estimated with sufficient accuracy to support the singularity computation, and he develops a refinement algorithm to that end on the basis of an iterative minimization over the estimated local structure at surface trace points. At each iteration, the information at each point is updated to best fit, in the least-squared-error sense, the information at its neighboring points. Most important to the minimization process is the development of a method permitting the comparison of information at spatially separate trace points, which makes explicit the assumption that the points are actually on an underlying smooth two-dimensional surface. The effectiveness of this approach on synthetic images to which controlled amounts of noise has been added, as well as on clinical magnetic resonance imagery, is shown