Neural Gas for Surface Reconstruction

In this paper we present an adaptation of Neural Gas (NG) for reconstructing 3D-surfaces from point clouds. NG is based on online adaptation according to given data points and constitutes a neural clustering algorithm that is robust with respect to noisy data and efficient, because the runtime depends solely on the accuracy of the surface reconstruction and is independent of the size of the input data. NG is a mathematically well founded method with guaranteed convergence that provably induces a valid Delaunay triangulation of a given surface of arbitrary genus provided the sampling of the surface is sufficiently dense. To apply NG to surface reconstruction, we extend the basic model by techniques that reconstruct surface triangles from the NG neighbourhood graph and repair possible topological defects of the mesh. Moreover, we extend NG by a growing strategy which introduces a dynamic adaptation to the problem complexity such that a fast initial adaptation to the general global shape of the target model is achieved after which the finer details can be extracted.