# Accession Number:

## ADP013727

# Title:

## Iota (sub 1) and Iota (sub infinity) ODR Fitting of Geometric Elements

# Descriptive Note:

## Conference paper

# Corporate Author:

## BONN UNIV (GERMANY) MATHEMATICS SEMINAR OF THE AGRICULTURAL FACULTY DEPT

# Personal Author(s):

# Report Date:

## 2001-07-01

# Pagination or Media Count:

## 7.0

# 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 iotasub 1 and iotasub infinity ODR fitting of geometric elements. The algorithm is iterative and allows the element to be given in either implicit form fchi, beta 0 or in parametric form chi gt, 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 iotasub 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 iotasub 1 and the iotasub infinity case, and is based on a suitable characterization of the stationary points.

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Test Facilities, Equipment and Methods
- Statistics and Probability