I will define a new distance function on an unoriented 3D point set and describe how it may be used to reconstruct a surface approximating these points. This distance function is shown to be a Mahalanobis distance in a higher-dimensional embedding space of the points, and the resulting reconstruction algorithm is a natural extension of the classical Radial Basis Function (RBF) approach. Experimental results show the superiority of our reconstruction algorithm to RBF and other methods in a variety of practical scenarios. I will also relate the distance function to a more general notion of indicator functions and discuss possible applications to learning and classification.
Joint work with Craig Gotsman and Roi Poranne, Technion.