Estimated topological surface for 3D reconstruction using variational scheme

Abstract

In this paper, we propose a novel variational scheme for three-dimensional (3D) reconstruction from point cloud using estimated topological surface. The scheme using estimated topological surface recovers the underlying 3D shape by integrating an estimated surface topology gradient field. The estimated gradient is usually non-integrable due to the presence of noise and outliers in the estimation process and inherent ambiguities. The method represents a continuum of surface reconstruction solutions of a given non-integrable gradient field. For an N×N point cloud, the subspace of all integrable gradient fields is of dimension N²−1. It can be applied to derive a range of meaningful surface reconstructions from this high dimensional space. We show that by using a progression of spatially varying anisotropic weights, significant improvements in surface reconstruction from point cloud can be achieved. Simulated surfaces are experimentally studied, and the results validate that the proposed approaches improve the reconstruction. The proposed method improves the reconstructing results significantly for the simulated data.

Keywords:

• variational scheme
• 3D reconstruction
• point cloud
• anisotropic weights

This research work is supported by the National Natural Science Foundation of China (nos. 60873130 and 60872115), the Shanghai’s Key Discipline Development Program (no. J50104) and the Shanghai University’s Graduate Student Innovative Fund (no. SHUCX101089).