Classification and identification of algebraic surfaces from an unorganised cloud of points

Given an unorganised cloud of points in 3D resulting from sampling a collection of algebraic surfaces (with sampling errors), a novel probabilistic method for classification and identification of algebraic surfaces is introduced. The method detects the surfaces in O(k^2*A + k*n), where n is the number of points in the cloud, k is an upper bound on the number of surfaces expected to be detected and A is the minimal number of points sufficient to determine an algebraic surface of the highest degree. Algebraic surfaces are embedded in hyperplanes; the algorithm reduces the problem of reconstruction to the problem of defining a measure of "distance" and using clustering of hyperplanes in multidimensional space, and thereby produces effective results. The algorithm is robust and faster than most existing methods in most cases and there is no a priori knowledge on the number of surfaces involved. Non trivial examples of planar and quadric surfaces patches are given.