# Deep Level Sets: Implicit Surface Representations for 3D Shape Inference

arXiv: https://arxiv.org/abs/1901.06802 · HTML: https://mlsanity.com/paper/1901.06802/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2019.

## Built on by (most cited first, 30 of 53)

- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [SNARF: Differentiable Forward Skinning for Animating Non-Rigid Neural Implicit Shapes](https://mlsanity.com/paper/2104.03953/) (2021)
- [H-NeRF: Neural Radiance Fields for Rendering and Temporal Reconstruction of Humans in Motion](https://mlsanity.com/paper/2110.13746/) (2021)
- [imGHUM: Implicit Generative Models of 3D Human Shape and Articulated Pose](https://mlsanity.com/paper/2108.10842/) (2021)
- [3DILG: Irregular Latent Grids for 3D Generative Modeling](https://mlsanity.com/paper/2205.13914/) (2022)
- [NPMs: Neural Parametric Models for 3D Deformable Shapes](https://mlsanity.com/paper/2104.00702/) (2021)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [Towards High-Fidelity Single-view Holistic Reconstruction of Indoor Scenes](https://mlsanity.com/paper/2207.08656/) (2022)
- [NeUDF: Leaning Neural Unsigned Distance Fields with Volume Rendering](https://mlsanity.com/paper/2304.10080/) (2023)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Multiresolution Deep Implicit Functions for 3D Shape Representation](https://mlsanity.com/paper/2109.05591/) (2021)
- [HVTR: Hybrid Volumetric-Textural Rendering for Human Avatars](https://mlsanity.com/paper/2112.10203/) (2021)
- [Uncertainty-Aware Deep Multi-View Photometric Stereo](https://mlsanity.com/paper/2202.13071/) (2022)
- [State of the Art in Dense Monocular Non-Rigid 3D Reconstruction](https://mlsanity.com/paper/2210.15664/) (2022)
- [Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priors](https://mlsanity.com/paper/2303.14505/) (2023)
- [Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2306.01405/) (2023)
- [Unsupervised Learning of Fine Structure Generation for 3D Point Clouds by 2D Projection Matching](https://mlsanity.com/paper/2108.03746/) (2021)
- [Latent Partition Implicit with Surface Codes for 3D Representation](https://mlsanity.com/paper/2207.08631/) (2022)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [Zero-shot Pose Transfer for Unrigged Stylized 3D Characters](https://mlsanity.com/paper/2306.00200/) (2023)
- [Learning Visibility Field for Detailed 3D Human Reconstruction and Relighting](https://mlsanity.com/paper/2304.11900/) (2023)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [Shape of my heart: Cardiac models through learned signed distance functions](https://mlsanity.com/paper/2308.16568/) (2023)
- [LATO: 3D Mesh Flow Matching with Structured TOpology Preserving LAtents](https://mlsanity.com/paper/2603.06357/) (2026)
- [DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling](https://mlsanity.com/paper/2402.08876/) (2024)
- [SurMo: Surface-based 4D Motion Modeling for Dynamic Human Rendering](https://mlsanity.com/paper/2404.01225/) (2024)
- [SinGRAV: Learning a Generative Radiance Volume from a Single Natural Scene](https://mlsanity.com/paper/2210.01202/) (2022)
- [p-Poisson surface reconstruction in curl-free flow from point clouds](https://mlsanity.com/paper/2310.20095/) (2023)
- [LightSAL: Lightweight Sign Agnostic Learning for Implicit Surface Representation](https://mlsanity.com/paper/2103.14273/) (2021)
- [DiViNeT: 3D Reconstruction from Disparate Views via Neural Template Regularization](https://mlsanity.com/paper/2306.04699/) (2023)

## Abstract (arXiv)

Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract 3D surface meshes. To overcome this limitation, we propose an end-to-end trainable model that directly predicts implicit surface representations of arbitrary topology by optimising a novel geometric loss function. Specifically, we propose to represent the output as an oriented level set of a continuous embedding function, and incorporate this in a deep end-to-end learning framework by introducing a variational shape inference formulation. We investigate the benefits of our approach on the task of 3D surface prediction and demonstrate its ability to produce a more accurate reconstruction compared to voxel-based representations. We further show that our model is flexible and can be applied to a variety of shape inference problems.