Delaunay space division for RBF image reconstruction

Abstract

The Radial Basis Function method (RBF) provides a generic mathematical tool for various interpolation and smoothing problems in computer graphics and vision, such as surface reconstruction from scattered data, smoothing of noisy data, filling gaps and restoring missing data. As the radial function uses distances in the data set, it does not depend on the dimension of the problem. Thus, RBF can be used for 2D data processing (images, height fields), 3D data processing (surfaces, volumes), 4D data processing (time-varying data) or even higher. In this paper, we present a novel RBF based approach for reconstruction of images and height fields from highly corrupted data, which can handle large images in feasible time, while being very simple to program. Our approach uses an image partitioning via Delaunay triangulation of the dataset. The advantage of our approach is that it can be combined with fast evaluation of RBF using R-expansion [Zandifar et al. 2004] of the basis function.