# SALD: Sign Agnostic Learning with Derivatives

arXiv: https://arxiv.org/abs/2006.05400 · HTML: https://mlsanity.com/paper/2006.05400/

## Key facts

- Cited by 115 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 30 of 115)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [iSDF: Real-Time Neural Signed Distance Fields for Robot Perception](https://mlsanity.com/paper/2204.02296/) (2022)
- [LEAP: Learning Articulated Occupancy of People](https://mlsanity.com/paper/2104.06849/) (2021)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [Generative Models as Distributions of Functions](https://mlsanity.com/paper/2102.04776/) (2021)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations](https://mlsanity.com/paper/2205.02825/) (2022)
- [ALSO: Automotive Lidar Self-supervision by Occupancy estimation](https://mlsanity.com/paper/2212.05867/) (2022)
- [LISA: Learning Implicit Shape and Appearance of Hands](https://mlsanity.com/paper/2204.01695/) (2022)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [SA-ConvONet: Sign-Agnostic Optimization of Convolutional Occupancy Networks](https://mlsanity.com/paper/2105.03582/) (2021)
- [Neural Fields as Learnable Kernels for 3D Reconstruction](https://mlsanity.com/paper/2111.13674/) (2021)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [GIFS: Neural Implicit Function for General Shape Representation](https://mlsanity.com/paper/2204.07126/) (2022)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [DrapeNet: Garment Generation and Self-Supervised Draping](https://mlsanity.com/paper/2211.11277/) (2022)
- [Deep Implicit Surface Point Prediction Networks](https://mlsanity.com/paper/2106.05779/) (2021)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Phase Transitions, Distance Functions, and Implicit Neural Representations](https://mlsanity.com/paper/2106.07689/) (2021)
- [Learning Anchored Unsigned Distance Functions with Gradient Direction Alignment for Single-view Garment Reconstruction](https://mlsanity.com/paper/2108.08478/) (2021)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [GenSDF: Two-Stage Learning of Generalizable Signed Distance Functions](https://mlsanity.com/paper/2206.02780/) (2022)
- [Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priors](https://mlsanity.com/paper/2303.14505/) (2023)
- [Facial Geometric Detail Recovery via Implicit Representation](https://mlsanity.com/paper/2203.09692/) (2022)
- [Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2306.01405/) (2023)
- [Few 'Zero Level Set'-Shot Learning of Shape Signed Distance Functions in Feature Space](https://mlsanity.com/paper/2207.04161/) (2022)

## Abstract (arXiv)

Learning 3D geometry directly from raw data, such as point clouds, triangle soups, or unoriented meshes is still a challenging task that feeds many downstream computer vision and graphics applications. In this paper, we introduce SALD: a method for learning implicit neural representations of shapes directly from raw data. We generalize sign agnostic learning (SAL) to include derivatives: given an unsigned distance function to the input raw data, we advocate a novel sign agnostic regression loss, incorporating both pointwise values and gradients of the unsigned distance function. Optimizing this loss leads to a signed implicit function solution, the zero level set of which is a high quality and valid manifold approximation to the input 3D data. The motivation behind SALD is that incorporating derivatives in a regression loss leads to a lower sample complexity, and consequently better fitting. In addition, we prove that SAL enjoys a minimal length property in 2D, favoring minimal length solutions. More importantly, we are able to show that this property still holds for SALD, i.e., with derivatives included. We demonstrate the efficacy of SALD for shape space learning on two challenging datasets: ShapeNet that contains inconsistent orientation and non-manifold meshes, and D-Faust that contains raw 3D scans (triangle soups). On both these datasets, we present state-of-the-art results.