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

About

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.

Christiane Sommer, Lu Sang, David Schubert, Daniel Cremers · 2021

Related benchmarks

Task	Dataset	Result
Visual SLAM	TUM RGB-D fr1 desk	ATE RMSE (cm)0.056	24
Visual SLAM	TUM RGB-D fr1/desk2	ATE RMSE0.066	7
Camera Tracking	TUM RGB-D fr1 xyz	ATE RMSE (cm)2	4
Camera Tracking	TUM RGB-D fr1 rpy	ATE RMSE (cm)4.9	4
Camera Tracking	TUM RGB-D fr1 plant	ATE RMSE (cm)11.2	4
Camera Tracking	TUM RGB-D fr1 teddy	ATE RMSE (cm)11.3	4
Camera Tracking	TUM RGB-D fr3 household	ATE RMSE (cm)5.2	4