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

arXiv: https://arxiv.org/abs/2111.13652 · HTML: https://mlsanity.com/paper/2111.13652/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 26 Nov 2021.

## Builds on (most cited first, 10 of 10)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [A Large Dataset of Object Scans](https://mlsanity.com/paper/1602.02481/) (2016)
- [RoutedFusion: Learning Real-time Depth Map Fusion](https://mlsanity.com/paper/2001.04388/) (2020)
- [NeuralFusion: Online Depth Fusion in Latent Space](https://mlsanity.com/paper/2011.14791/) (2020)
- [SurfelMeshing: Online Surfel-Based Mesh Reconstruction](https://mlsanity.com/paper/1810.00729/) (2018)

## Built on by (most cited first, 12 of 12)

- [Neural Vector Fields for Implicit Surface Representation and Inference](https://mlsanity.com/paper/2204.06552/) (2022)
- [FIRe: Fast Inverse Rendering using Directional and Signed Distance Functions](https://mlsanity.com/paper/2203.16284/) (2022)
- [4Deform: Neural Surface Deformation for Robust Shape Interpolation](https://mlsanity.com/paper/2502.20208/) (2025)
- [F-INR: Functional Tensor Decomposition for Implicit Neural Representations](https://mlsanity.com/paper/2503.21507/) (2025)
- [High-Quality RGB-D Reconstruction via Multi-View Uncalibrated Photometric Stereo and Gradient-SDF](https://mlsanity.com/paper/2210.12202/) (2022)
- [T4DT: Tensorizing Time for Learning Temporal 3D Visual Data](https://mlsanity.com/paper/2208.01421/) (2022)
- [Enhancing Surface Neural Implicits with Curvature-Guided Sampling and Uncertainty-Augmented Representations](https://mlsanity.com/paper/2306.02099/) (2023)
- [Cross-Dimensional Refined Learning for Real-Time 3D Visual Perception from Monocular Video](https://mlsanity.com/paper/2303.09248/) (2023)
- [OREN: Octree Residual Network for Real-Time Euclidean Signed Distance Mapping](https://mlsanity.com/paper/2510.18999/) (2025)
- [Coloring the Past: Neural Historical Buildings Reconstruction from Archival Photography](https://mlsanity.com/paper/2311.17810/) (2023)
- [TaylorGrid: Towards Fast and High-Quality Implicit Field Learning via Direct Taylor-based Grid Optimization](https://mlsanity.com/paper/2402.14415/) (2024)
- [Hermite-NGP: Gradient-Augmented Hash Encoding for Learning PDEs](https://mlsanity.com/paper/2605.24774/) (2026)

## Abstract (arXiv)

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.