Over-parameterized method on variational surface for point-based reconstruction

This article tackles the problem of using varitional method for reconstructing 3D surface. We give an overview of over-parameterized method on variational surface when the 3D surface is represented by a point-based surface and a triangular mesh-based surface, and we detail the variational surface which embody used on surface reconstruction. In particular, we show how to rigorously account for efficiency in the surface reconstructing process. The key idea is to consider utilizing variational surface from a finite number of normals for surface reconstruction. We investigate the properties of the regularization functional and illustrate our technique by applying it to converge to the input shape as the number of measurements increases. In contrast to previous works our method can be considered on point-based surface and allows the use of over-parameterized scheme for 3D surface reconstruction. Experimental results show the proposed method is efficient.