# Learning Modified Indicator Functions for Surface Reconstruction

arXiv: https://arxiv.org/abs/2111.09526 · HTML: https://mlsanity.com/paper/2111.09526/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 18 Nov 2021.

## Builds on (most cited first, 17 of 17)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Scan2Mesh: From Unstructured Range Scans to 3D Meshes](https://mlsanity.com/paper/1811.10464/) (2018)
- [Sign-Agnostic Implicit Learning of Surface Self-Similarities for Shape Modeling and Reconstruction from Raw Point Clouds](https://mlsanity.com/paper/2012.07498/) (2020)

## Built on by (most cited first, 2 of 2)

- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation](https://mlsanity.com/paper/2209.15619/) (2022)

## Abstract (arXiv)

Surface reconstruction is a fundamental problem in 3D graphics. In this paper, we propose a learning-based approach for implicit surface reconstruction from raw point clouds without normals. Our method is inspired by Gauss Lemma in potential energy theory, which gives an explicit integral formula for the indicator functions. We design a novel deep neural network to perform surface integral and learn the modified indicator functions from un-oriented and noisy point clouds. We concatenate features with different scales for accurate point-wise contributions to the integral. Moreover, we propose a novel Surface Element Feature Extractor to learn local shape properties. Experiments show that our method generates smooth surfaces with high normal consistency from point clouds with different noise scales and achieves state-of-the-art reconstruction performance compared with current data-driven and non-data-driven approaches.