Robust Feature Detection and Local Classification for Surfaces Based on Moment Analysis

The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.

Axioms and Variational Problems in Surface Parameterization

For a surface patch on a smooth, two-dimensional surface in R³, low-distortion parameterizations are described in terms of minimizers of suitable energy functionals. Appropriate distortion measures are derived from principles of rational mechanics, closely related to the theory of non-linear elasticity. The parameterization can be optimized with respect to the varying importance of conformality, length preservation and area preservation. A finite element discretization is introduced and a constrained Newton method is used to minimize a corresponding discrete energy. Results of the new approach are compared with other recent parameterization methods