Optimal consensus set for digital Flake hyperspheres in nD

This paper presents a method for fitting digital hyperspheres to a given set of nD points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set. The digital Hyperspheres are defined using the k-Flake Digitization models [25]. We present an algorithm, that provides optimal fitting solutions for digital k-Flake hyperspheres within a time complexity O(((nk)2n−k)nNn+1log⁡N) for dimension n, N being the number of points. We have implemented this algorithm for the particular case of 3D 2-Flake spheres that corresponds to the classical so called Naive digital spheres.