Kernel Methods for Implicit Surface Modeling

We describe methods for computing an implicit model of a hypersurface that is given only by a finite sampling. The methods work by mapping the sample points into a reproducing kernel Hilbert space and then deter- mining regions in terms of hyperplanes. Suppose we are given a finite sampling (in machine learning terms, training data) x1, . . . The case d 3 is especially interesting since these days there are many devices, e.g., laser range scanners, that allow the acquisition of point data from the boundary surfaces of solids. For further processing it is often necessary to transform this data into a continu- ous model. Today the most popular approach is to add connectivity information to the data by transforming them into a triangle mesh (see [4] for an example of such a transformation algorithm).