Radial basis function methods for 3D applications: Fast evaluation of 3D polyharmonic splines
by
Rick Beatson
Department of Mathematics and Statistics, University of Canterbury

The energy minimisation characterisations of polyharmonic splines, fitted by interpolation or spline smoothing, make them ideally suited to many 3D data fitting problems. For example they have recently been used to fit surfaces to laser scans of statues and lidar scans of mines and filmsets. However, there are obstacles to tackling such problems as the datasets are typically huge, with hundreds of thousands to millions of points, and the data density is typically highly non uniform.

The first part of the talk will outline some of these recent applications and some of the algorithmic techniques/fragments which in combination make the computations tractable. Much of the work of this section is joint with Jonathan Carr, Tim Mitchell, Rick Fright, Bruce McCallum and others at ARANZ.

Amongst the algorithmic techniques employed one of the most important is fast evaluation of 3D polyharmonic splines. In the body of the talk the function theory underlying such fast evaluation code will be presented.

Date received: February 11, 2002