Iota (sub 1) and Iota (sub infinity) ODR Fitting of Geometric Elements
Abstract
We consider the fitting of geometric elements, such as lines, planes, circles, cones, and cylinders, in such a way that the sum of distances or the maximal distance from the element to the data points is minimized. We refer to this kind of distance based fitting as orthogonal distance regression or ODR. We present a separation of variables algorithm for iota(sub 1) and iota(sub infinity) ODR fitting of geometric elements. The algorithm is iterative and allows the element to be given in either implicit form f(chi, beta) = 0 or in parametric form chi = g(t, Beta) where Beta is the vector of shape parameters, chi is a 2- or 3-vector, and s is a vector of location parameters. The algorithm may even be applied in cases, such as with ellipses, in which a closed form expression for the distance is either not available or is difficult to compute. For iota(sub 1) and iota (sub infinity) fitting, the norm of the gradient is not available as a stopping criterion, as it is not continuous. We present a stopping criterion that handles both the iota(sub 1) and the iota(sub infinity) case, and is based on a suitable characterization of the stationary points.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 2001
- Accession Number
- ADP013727
Entities
People
- Daniel S. Zwick
- Hans-peter Helfrich
Organizations
- University of Bonn