# Toward Robust Neural Reconstruction from Sparse Point Sets

arXiv: https://arxiv.org/abs/2412.16361 · HTML: https://mlsanity.com/paper/2412.16361/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 94 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## Builds on (most cited first, 30 of 63)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [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)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [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)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Zero-Shot Text-Guided Object Generation with Dream Fields](https://mlsanity.com/paper/2112.01455/) (2021)
- [BlendedMVS: A Large-scale Dataset for Generalized Multi-view Stereo Networks](https://mlsanity.com/paper/1911.10127/) (2019)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Neural Point-Based Graphics](https://mlsanity.com/paper/1906.08240/) (2019)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Visual Geometry Grounded Deep Structure From Motion](https://mlsanity.com/paper/2312.04563/) (2023)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [SemanticPOSS: A Point Cloud Dataset with Large Quantity of Dynamic Instances](https://mlsanity.com/paper/2002.09147/) (2020)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)

## Built on by (most cited first, 5 of 5)

- [Sparfels: Fast Reconstruction from Sparse Unposed Imagery](https://mlsanity.com/paper/2505.02178/) (2025)
- [SparSplat: Fast Multi-View Reconstruction with Generalizable 2D Gaussian Splatting](https://mlsanity.com/paper/2505.02175/) (2025)
- [Anti-Aliased 2D Gaussian Splatting](https://mlsanity.com/paper/2506.11252/) (2025)
- [TextureSplat: Per-Primitive Texture Mapping for Reflective Gaussian Splatting](https://mlsanity.com/paper/2506.13348/) (2025)
- [Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2512.12550/) (2025)

## Abstract (arXiv)

We consider the challenging problem of learning Signed Distance Functions (SDF) from sparse and noisy 3D point clouds. In contrast to recent methods that depend on smoothness priors, our method, rooted in a distributionally robust optimization (DRO) framework, incorporates a regularization term that leverages samples from the uncertainty regions of the model to improve the learned SDFs. Thanks to tractable dual formulations, we show that this framework enables a stable and efficient optimization of SDFs in the absence of ground truth supervision. Using a variety of synthetic and real data evaluations from different modalities, we show that our DRO based learning framework can improve SDF learning with respect to baselines and the state-of-the-art methods.