Reconstruction of visual surfaces from sparse data using parametric triangular approximants

This paper presents the application of a recently proposed geometrical modelling technique to computer vision in order to reconstruct smooth surfaces from arbitrary triangulations of scattered 3D points. These points are considered to be noisy as a result of a sensory acquisition process. The reconstruction problem is transformed into one of surface approximation over arbitrary triangular meshes. 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 these patches are parametric functionals, arbitrary topologies of any genus can be represented. This method is efficient and easily parallelizable. Affine invariance, locality and other valuable properties are analysed and some examples are finally shown to illustrate the behaviour of this technique in reconstructing real complex objects