# A Deep Signed Directional Distance Function for Object Shape Representation

arXiv: https://arxiv.org/abs/2107.11024 · HTML: https://mlsanity.com/paper/2107.11024/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 69 references that are in the map.
- First posted on arXiv 23 Jul 2021.

## Builds on (most cited first, 30 of 46)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [MVSNeRF: Fast Generalizable Radiance Field Reconstruction from Multi-View Stereo](https://mlsanity.com/paper/2103.15595/) (2021)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [IBRNet: Learning Multi-View Image-Based Rendering](https://mlsanity.com/paper/2102.13090/) (2021)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Learning Category-Specific Mesh Reconstruction from Image Collections](https://mlsanity.com/paper/1803.07549/) (2018)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)

## Built on by (most cited first, 10 of 10)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Representing 3D Shapes with Probabilistic Directed Distance Fields](https://mlsanity.com/paper/2112.05300/) (2021)
- [The Sky's the Limit: Re-lightable Outdoor Scenes via a Sky-pixel Constrained Illumination Prior and Outside-In Visibility](https://mlsanity.com/paper/2311.16937/) (2023)
- [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)
- [Multi-View Reconstruction using Signed Ray Distance Functions (SRDF)](https://mlsanity.com/paper/2209.00082/) (2022)
- [3D Neural Sculpting (3DNS): Editing Neural Signed Distance Functions](https://mlsanity.com/paper/2209.13971/) (2022)
- [TransPoser: Transformer as an Optimizer for Joint Object Shape and Pose Estimation](https://mlsanity.com/paper/2303.13477/) (2023)
- [Neural directional distance field object representation for uni-directional path-traced rendering](https://mlsanity.com/paper/2306.16142/) (2023)
- [Probabilistic Directed Distance Fields for Ray-Based Shape Representations](https://mlsanity.com/paper/2404.09081/) (2024)

## Abstract (arXiv)

Neural networks that map 3D coordinates to signed distance function (SDF) or occupancy values have enabled high-fidelity implicit representations of object shape. This paper develops a new shape model that allows synthesizing novel distance views by optimizing a continuous signed directional distance function (SDDF). Similar to deep SDF models, our SDDF formulation can represent whole categories of shapes and complete or interpolate across shapes from partial input data. Unlike an SDF, which measures distance to the nearest surface in any direction, an SDDF measures distance in a given direction. This allows training an SDDF model without 3D shape supervision, using only distance measurements, readily available from depth camera or Lidar sensors. Our model also removes post-processing steps like surface extraction or rendering by directly predicting distance at arbitrary locations and viewing directions. Unlike deep view-synthesis techniques, such as Neural Radiance Fields, which train high-capacity black-box models, our model encodes by construction the property that SDDF values decrease linearly along the viewing direction. This structure constraint not only results in dimensionality reduction but also provides analytical confidence about the accuracy of SDDF predictions, regardless of the distance to the object surface.