# Learning Occupancy Function from Point Clouds for Surface Reconstruction

arXiv: https://arxiv.org/abs/2010.11378 · HTML: https://mlsanity.com/paper/2010.11378/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 13 of 13)

- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [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)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [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)
- [DeepMend: Learning Occupancy Functions to Represent Shape for Repair](https://mlsanity.com/paper/2210.05728/) (2022)
- [Registered and Segmented Deformable Object Reconstruction from a Single View Point Cloud](https://mlsanity.com/paper/2311.07357/) (2023)
- [DeepJoin: Learning a Joint Occupancy, Signed Distance, and Normal Field Function for Shape Repair](https://mlsanity.com/paper/2211.12400/) (2022)
- [A Review on Organ Deformation Modeling Approaches for Reliable Surgical Navigation using Augmented Reality](https://mlsanity.com/paper/2408.02713/) (2024)
- [Occupancy-Based Dual Contouring](https://mlsanity.com/paper/2409.13418/) (2024)

## Abstract (arXiv)

Implicit function based surface reconstruction has been studied for a long time to recover 3D shapes from point clouds sampled from surfaces. Recently, Signed Distance Functions (SDFs) and Occupany Functions are adopted in learning-based shape reconstruction methods as implicit 3D shape representation. This paper proposes a novel method for learning occupancy functions from sparse point clouds and achieves better performance on challenging surface reconstruction tasks. Unlike the previous methods, which predict point occupancy with fully-connected multi-layer networks, we adapt the point cloud deep learning architecture, Point Convolution Neural Network (PCNN), to build our learning model. Specifically, we create a sampling operator and insert it into PCNN to continuously sample the feature space at the points where occupancy states need to be predicted. This method natively obtains point cloud data's geometric nature, and it's invariant to point permutation. Our occupancy function learning can be easily fit into procedures of point cloud up-sampling and surface reconstruction. Our experiments show state-of-the-art performance for reconstructing With ShapeNet dataset and demonstrate this method's well-generalization by testing it with McGill 3D dataset citesiddiqi2008retrieving. Moreover, we find the learned occupancy function is relatively more rotation invariant than previous shape learning methods.