Efficient surface reconstruction from scattered points through geometric data fusion

This paper describes a new method to reconstruct smooth surfaces from arbitrary triangulations of scattered 3D points. These points are considered to be noisy as a result of some sensory acquisition process. The reconstruction problem is transformed into one of surface approximation over irregular triangular meshes. The proposed formulation is based on weighted averages, a technique that has been widely used in homogeneous data fusion. Hence, the generated surfaces are the result of a geometric fusion process that considers topological relationships among control points. Moreover, an uncertainty factor can be associated with every point. This factor affects the final shape of the surface locally. The reconstructed surface is composed of a collection of triangular patches that join with C⁰ or G¹ geometric continuity and that can be computed independently. Since those patches are parametric functionals, arbitrary topologies of any genus can be represented. The aforementioned characteristics of this technique allow its utilization as an efficient surface modelling tool in diverse disciplines, including robotics, GIS and medical imaging