Robust fitting of 3D objects by affinely transformed superellipsoids using normalization

Abstract

We present an algorithm for the robust fitting of objects given as voxel data with affinely transformed superellipsoids. Superellipsoids cover a broad range of various forms and are widely used in many application fields. Our approach uses the method of normalization and a new separation of the affine transformation into a shearing, an anisotropic scale and a rotation. It extends our previous work for 2D fitting problems and for fitting rectangular boxes in 3D. Our technique can be used as a valuable tool for solving this fitting task for 3D data. If the exponents describing the superellipsoids to be fitted are known in advance, the method is extremely robust even against major distortions of the object to be fitted. © Springer-Verlag Berlin Heidelberg 2007.