[1] U. Clarenz, M. Rumpf, and A. Telea. Robust feature detection and local classification for surfaces based on moment analysis. IEEE Transactions on Visualization and Computer Graphics, 10(5):516-524, 2004.
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The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions respectively is as well difficult 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 multi scale. 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 the scale parameter.

Perspective 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.