# Few 'Zero Level Set'-Shot Learning of Shape Signed Distance Functions in Feature Space

arXiv: https://arxiv.org/abs/2207.04161 · HTML: https://mlsanity.com/paper/2207.04161/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 82 references that are in the map.
- First posted on arXiv 9 Jul 2022.

## Builds on (most cited first, 30 of 64)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [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)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [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)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)

## Built on by (most cited first, 22 of 22)

- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [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)
- [SparseCraft: Few-Shot Neural Reconstruction through Stereopsis Guided Geometric Linearization](https://mlsanity.com/paper/2407.14257/) (2024)
- [Unsupervised Occupancy Learning from Sparse Point Cloud](https://mlsanity.com/paper/2404.02759/) (2024)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [Neural Mesh-Based Graphics](https://mlsanity.com/paper/2208.05785/) (2022)
- [Mixing-Denoising Generalizable Occupancy Networks](https://mlsanity.com/paper/2311.12125/) (2023)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [Learning Generalizable Light Field Networks from Few Images](https://mlsanity.com/paper/2207.11757/) (2022)
- [Robustifying Generalizable Implicit Shape Networks with a Tunable Non-Parametric Model](https://mlsanity.com/paper/2311.12967/) (2023)
- [SCoDA: Domain Adaptive Shape Completion for Real Scans](https://mlsanity.com/paper/2304.10179/) (2023)
- [Sparfels: Fast Reconstruction from Sparse Unposed Imagery](https://mlsanity.com/paper/2505.02178/) (2025)
- [Inferring Neural Signed Distance Functions by Overfitting on Single Noisy Point Clouds through Finetuning Data-Driven based Priors](https://mlsanity.com/paper/2410.19680/) (2024)
- [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)
- [GeoTransfer : Generalizable Few-Shot Multi-View Reconstruction via Transfer Learning](https://mlsanity.com/paper/2408.14724/) (2024)
- [Few-Shot Unsupervised Implicit Neural Shape Representation Learning with Spatial Adversaries](https://mlsanity.com/paper/2408.15114/) (2024)
- [Toward Robust Neural Reconstruction from Sparse Point Sets](https://mlsanity.com/paper/2412.16361/) (2024)
- [TextureSplat: Per-Primitive Texture Mapping for Reflective Gaussian Splatting](https://mlsanity.com/paper/2506.13348/) (2025)
- [APC2Mesh: Bridging the gap from occluded building faccades to full 3D models](https://mlsanity.com/paper/2404.02391/) (2024)
- [HYVE: Hybrid Vertex Encoder for Neural Distance Fields](https://mlsanity.com/paper/2310.06644/) (2023)

## Abstract (arXiv)

We explore a new idea for learning based shape reconstruction from a point cloud, based on the recently popularized implicit neural shape representations. We cast the problem as a few-shot learning of implicit neural signed distance functions in feature space, that we approach using gradient based meta-learning. We use a convolutional encoder to build a feature space given the input point cloud. An implicit decoder learns to predict signed distance values given points represented in this feature space. Setting the input point cloud, i.e. samples from the target shape function's zero level set, as the support (i.e. context) in few-shot learning terms, we train the decoder such that it can adapt its weights to the underlying shape of this context with a few (5) tuning steps. We thus combine two types of implicit neural network conditioning mechanisms simultaneously for the first time, namely feature encoding and meta-learning. Our numerical and qualitative evaluation shows that in the context of implicit reconstruction from a sparse point cloud, our proposed strategy, i.e. meta-learning in feature space, outperforms existing alternatives, namely standard supervised learning in feature space, and meta-learning in euclidean space, while still providing fast inference.