Mesh Representation Driven by Variance Normalized Neighborhood in Scale Space

In this paper, we extend our previous work on regular mesh simplification using scale-space filtering (SSF), to arbitrary meshes. Additional challenges in using arbitrary meshes involve accurately defining a geodesic distance and a structure attribute. Since our SSF method is based on Laplacian smoothing, which filters finer local details before larger global structures, it preserves perceptual quality that is consistent with how the human visual system looks at 3D objects moving from close to farther away. By keeping the simplified mesh vertices as a subset of the denser meshes, versus using the vertex split operation, bandwidth is utilized more efficiently during refinement. Our contribution lies in applying the shortest path normalized by variance, instead of using an un-normalized geodesic distance to weight the influence of a neighborhood. Variance normalization ensures that the global smoothing property is preserved. We build a priority list to facilitate vertex removal and insertion. Experimental results are presented to support our approach.