Geometric fit of a point set by generalized circles

摘要

In our paper we approximate a set of given points by a general circle. More precisely, given two norms k_1 and k_2 and a set of points in the plane, we consider the problem of locating and scaling the unit circle of norm k such that the sum of weighted distances between the circumference of the circle and the given points is minimized, where the distance is measured by a norm k_2. We present results for the general case. In the case that k and k_2 are both polyhedral norms, we are able to solve the problem by investigating a finite candidate set.