Gradient-SDF: A Semi-Implicit Surface Representation for 3D Reconstruction

TL;DR

Gradient-SDF introduces a semi-implicit 3D surface representation combining signed distance and gradient fields, enabling efficient depth tracking, implicit optimization, and sharper reconstructions in 3D modeling.

Contribution

It proposes a novel semi-implicit surface representation that enhances implicit methods with explicit surface techniques for improved 3D reconstruction.

Findings

Allows direct SDF tracking from depth images

Enables photometric bundle adjustment in voxel space

Produces significantly sharper 3D reconstructions

Abstract

We present Gradient-SDF, a novel representation for 3D geometry that combines the advantages of implict and explicit representations. By storing at every voxel both the signed distance field as well as its gradient vector field, we enhance the capability of implicit representations with approaches originally formulated for explicit surfaces. As concrete examples, we show that (1) the Gradient-SDF allows us to perform direct SDF tracking from depth images, using efficient storage schemes like hash maps, and that (2) the Gradient-SDF representation enables us to perform photometric bundle adjustment directly in a voxel representation (without transforming into a point cloud or mesh), naturally a fully implicit optimization of geometry and camera poses and easy geometry upsampling. Experimental results confirm that this leads to significantly sharper reconstructions. Since the overall SDF voxel structure is still respected, the proposed Gradient-SDF is equally suited for (GPU) parallelization as related approaches.