# Level-Set Parameters: Novel Representation for 3D Shape Analysis

arXiv: https://arxiv.org/abs/2412.13502 · HTML: https://mlsanity.com/paper/2412.13502/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 62 of its 82 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Builds on (most cited first, 30 of 62)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (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)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [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)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)

## Abstract (arXiv)

3D shape analysis has been largely focused on traditional 3D representations of point clouds and meshes, but the discrete nature of these data makes the analysis susceptible to variations in input resolutions. Recent development of neural fields brings in level-set parameters from signed distance functions as a novel, continuous, and numerical representation of 3D shapes, where the shape surfaces are defined as zero-level-sets of those functions. This motivates us to extend shape analysis from the traditional 3D data to these novel parameter data. Since the level-set parameters are not Euclidean like point clouds, we establish correlations across different shapes by formulating them as a pseudo-normal distribution, and learn the distribution prior from the respective dataset. To further explore the level-set parameters with shape transformations, we propose to condition a subset of these parameters on rotations and translations, and generate them with a hypernetwork. This simplifies the pose-related shape analysis compared to using traditional data. We demonstrate the promise of the novel representations through applications in shape classification (arbitrary poses), retrieval, and 6D object pose estimation.