Computing variation modes for point set surfaces

Point sets have become a popular shape representation. In this paper, we present a novel approach to computing variation modes for point set surfaces, and represent the point set surface as a linear combination of the variation modes, called a generative representation for the point set surface. Given a point set, our approach consists of two steps: the first is to produce a set of new samples with increasing smoothness and less detailed features. We use a modified smoothing method based on moving least squares (MLS) surface to produce the samples. The second is to arrange the shape vectors of the new samples together with the original point set into a matrix, and then compute the singular value decomposition of the matrix, producing a set of variation modes (the eigen vectors). Using the variation modes and the generative representation, we can easily synthesize new shapes. Typical applications are low/high/band pass filtering as well as denoising and detail enhancement in multiple scales.