Orthogonal distance least squares fitting: A novel approach

Abstract

Least squares is a common method of conic fitting that minimizes the squared sum of a distance measure between a set of points and a conic. Orthogonal distance, when used as the distance that is minimized, provides more accurate fits as it is the shortest distance between a point and a conic. The problem however lies in the calculation of the orthogonal distance for a general conic, which results in an unstable closed form solution. Existing methods avoid this closed form solution by using non-linear iterative procedures or incorporating conic specific information. This paper introduces a novel method to directly calculate the orthogonal distance for an arbitrary conic, thereby eliminating the need for iterative procedures and conic specific information. It further describes a least squares fitting algorithm that uses the orthogonal distance thus calculated, to fit general conics. This technique is then extended to fit quadrics to three dimensional data. © 2010 Springer-Verlag Berlin Heidelberg.