Enhanced vector quantization for data reduction and filtering

Modern automatic digitizers can sample huge amounts of 3D data points on the object surface in a short time. Point based graphics is becoming a popular framework to reduce the cardinality of these data sets and to filter measurement noise, without having to store in memory and process mesh connectivity. Main contribution of this paper is the introduction of soft clustering techniques in the field of point clouds processing. In this approach data points are not assigned to a single cluster, but they contribute in the determination of the position of several cluster centres. As a result a better representation of the data is achieved. In soft clustering techniques, a data set is represented with a reduced number of points called reference vectors (RV), which minimize an adequate error measure. As the position of the RVs is determined by "learning", which can be viewed as an iterative optimization procedure, they are inherently slow. We show here how partitioning the data domain into disjointed regions called hyperboxes (HB), the computation can be localized and the computational time reduced to linear in the number of data points (O(N)), saving more than 75% on real applications with respect to classical soft-VQ solutions, making therefore VQ suitable to the task. The procedure is suitable for a parallel HW implementation, which would lead to a complexity sublinear in N. An automatic procedure for setting the voxel side and the other parameters can be derived from the data-set analysis. Results obtained in the reconstruction of faces of both humans and puppets as well as on models from clouds of points made available on the Web are reported and discussed in comparison with other available methods.