Greed for the Spheres: A Signed Distance Interpolation Method

TL;DR

This paper introduces a novel greedy algorithm for interpolating Signed Distance Functions (SDFs) that guarantees consistency with input data, enabling improved surface reconstruction and data repair.

Contribution

It presents a new geometric constraint-based interpolation method for SDFs, ensuring consistency and validity, with GPU acceleration for efficiency.

Findings

The method guarantees SDF consistency with input data.

It improves surface detail reconstruction from coarse SDFs.

It effectively repairs pseudo-SDFs from various pipelines.

Abstract

We propose a method to interpolate Signed Distance Function (SDF) data from a discrete set of samples. Unlike prior work, our approach ensures that the new SDF data values are fully consistent with the input and each other, such that the augmented data still corresponds to a geometrically realizable surface. We express the theoretical properties of SDFs as hard geometric constraints, and construct an efficient greedy algorithm for consistent SDF interpolation that is made even faster with powerful parallelized GPU preprocessing. We exemplify the usefulness of our method by evaluating it on three practical applications: global SDF refinement, in which the SDF data is upsampled without knowledge of the ground truth; mesh reconstruction, where our method can reconstruct highly detailed surfaces using global information from coarse input SDFs; and repair of pseudo-SDFs, which result from many pipelines such as CSG Boolean operations and must be turned into valid SDFs for downstream processing tasks. Our refined SDFs are guaranteed to be consistent with the input, where previous methods have no such guarantee.