Continuous Global Optimization in Surface Reconstruction from an Oriented Point Cloud

TL;DR

This paper presents a continuous global optimization approach for surface reconstruction from noisy, oriented point clouds, improving accuracy and robustness over discrete methods by using a convex relaxation scheme.

Contribution

It introduces a novel convex relaxation-based continuous optimization method for surface reconstruction that handles noisy, weakly oriented point clouds more effectively than previous discrete approaches.

Findings

Robust to noise, holes, and non-uniform sampling

Reduces metrication errors at higher grid resolutions

Achieves globally optimal surface reconstructions

Abstract

We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based data-fit measures and a regularization term. A continuous convex relaxation scheme assures the global minima of the geometric surface functional. The reconstructed surface is implicitly represented by the binary segmentation of vertices of a 3D uniform grid and a triangulated surface can be obtained by extracting an appropriate isosurface. Unlike the discrete graph-cut solution, the continuous global optimization entails advantages like memory requirements, reduction of metrication errors for geometric quantities, allowing globally optimal surface reconstruction at higher grid resolutions. We demonstrate the performance of the proposed method on several oriented point clouds captured by laser scanners. Experimental results confirm that our approach is robust to noise, large holes and non-uniform sampling density under the condition of very coarse orientation information.