Minimax ODR Fitting of Geometric Elements
by
Daniel S. Zwick
Double Star Research
Coauthors: Hans-Peter Helfrich (University of Bonn, Germany)

We consider the fitting of geometric elements, such as lines, planes, circles, cones, and cylinders, in such a way that 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 an algorithm for minimax ODR fitting of geometric elements. The algorithm is iterative and allows the element to be given in either implicit form f(x, b) = 0 or in parametric form x = f(s, b), where b is the vector of shape parameters, x 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.

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Date received: December 16, 1998