Mesh reconstruction by meshless denoising and parameterization

We present a new approach to simultaneously denoise and parameterize unorganized point cloud data. This is achieved by minimizing an appropriate energy function defined on the point cloud and its parameterization. An iterative algorithm to minimize the energy is described. The key ingredient of our approach is an "as-rigid-as-possible" meshless parameterization to map a point cloud with disk topology to the plane without building the connectivity of the point cloud. Then 2D triangulation method can be applied to the planar parameterization to provide triangle connectivity for the 2D points, which can be transferred back to the 3D point cloud to form a triangle mesh surface. We also show how to generalize the approach to meshes with closed topology of any genus. Experimental results have shown that our approach can effectively denoise the point cloud and our meshless parameterization can preserve local distances in the point cloud, resulting in a more regular 3D triangle mesh, compared to other methods.