Restricted range approximation with RBFs
by
Tim McLennan and Tim Mitchell
Applied Research Associates NZ Ltd.
Coauthors: Jon Cherrie

A new approach is formulated for reconstructing surfaces from noisy range data using Radial Basis Functions (RBFs). This approach, called the smoothest restricted range fit, results in the smoothest surface within a specified tolerance of each data point, and as such, is a more appropriate method for modeling real world data than direct interpolation. The technique falls naturally into a quadratic programming framework and can typically be used in place of other data reduction techniques. Coupled with fast direct interpolation methods for RBFs this allows the reconstruction of large sets. An implementation of the restricted range approximation method is demonstrated by reconstructing surfaces from real world LIDAR scans comprising millions of points.

Date received: February 14, 2002