Signing the Unsigned: Robust Surface Reconstruction from Raw Pointsets

Abstract

We propose a modular framework for robust 3D reconstruction from unorganized, unoriented, noisy, and outlierridden geometric data. We gain robustness and scalability over previous methods through an unsigned distance approximation to the input data followed by a global stochastic signing of the function. An isosurface reconstruction is finally deduced via a sparse linear solve. We show with experiments on large, raw, geometric datasets that this approach is scalable while robust to noise, outliers, and holes. The modularity of our approach facilitates customization of the pipeline components to exploit specific idiosyncracies of datasets, while the simplicity of each component leads to a straightforward implementation.

Screened poisson surface reconstruction

“…Many techniques estimate a signed-distance function [Hoppe et al 1992; Bajaj et al 1995;Curless and Levoy 1996]. If the input points are unoriented, an important step is to correctly infer the sign of the resulting distance field [Mullen et al 2010].…”

An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes

“…Mullen et al [34] leveraged such distance functions and proposed a robust method to reconstruct smooth surfaces from raw point sets. Lipman and Daubechies [29], on the other hand, presented a solution for the transportation problem between conformal mass densities in order to determine similarities between 3D shapes.…”

SpringLS: A Deformable Model Representation to Provide Interoperability between Meshes and Level Sets

“…For large parametric deformations where the CFL number exceeds 1, it is usually faster to convert the unsigned level set to a signed level set [15,16] than to evolve the signed level set with active contour methods. We perform the conversion by growing the background region and then negating the unsigned level set in the foreground region.…”