Image data simplification using spherical and ellipsoidal primitives

This paper discusses the problem of approximating data points in n-dimensional Euclidean space, using spherical and ellipsoidal surfaces. For the specific cases of n = 2 and n = 3, the problem is of fundamental importance id computer vision and robotics. A closed form solution is provided for spherical approximation, while an efficient, globally optimal solution for the ellipsoidal problem is proposed in terms of semidefinite programming (SDP). The paper also presents a result for robust fitting in the presence of outliers, and illustrates the theory with several numerical examples