Surface creation on unstructured point sets using neural networks

Abstract

We present a new point set surfacing method based on a data-driven mapping between the parametric and geometric spaces. Our approach takes as input an unstructured and possibly noisy point set representing a two-manifold in R3. To facilitate parameterization, the set is first embedded in R2 using neighborhood-preserving locally linear embedding. A learning algorithm is then trained to learn a mapping between the embedded two-dimensional (2D) coordinates and the corresponding three-dimensional (3D) space coordinates. The trained learner is then used to generate a tessellation spanning the parametric space, thereby producing a surface in the geometric space. This approach enables the surfacing of noisy and non-uniformly distributed point sets. We discuss the advantages of the proposed method in relation to existing methods, and show its utility on a number of test models, as well as its applications to modeling in virtual reality environments.