# Iso-Points: Optimizing Neural Implicit Surfaces with Hybrid Representations

arXiv: https://arxiv.org/abs/2012.06434 · HTML: https://mlsanity.com/paper/2012.06434/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2020.

## Built on by (most cited first, 30 of 39)

- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Towards Implicit Text-Guided 3D Shape Generation](https://mlsanity.com/paper/2203.14622/) (2022)
- [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)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [Aug-NeRF: Training Stronger Neural Radiance Fields with Triple-Level Physically-Grounded Augmentations](https://mlsanity.com/paper/2207.01164/) (2022)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian](https://mlsanity.com/paper/2309.01793/) (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)
- [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)
- [VaxNeRF: Revisiting the Classic for Voxel-Accelerated Neural Radiance Field](https://mlsanity.com/paper/2111.13112/) (2021)
- [NTO3D: Neural Target Object 3D Reconstruction with Segment Anything](https://mlsanity.com/paper/2309.12790/) (2023)
- [Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction](https://mlsanity.com/paper/2109.04398/) (2021)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature](https://mlsanity.com/paper/2404.13420/) (2024)
- [Spelunking the Deep: Guaranteed Queries on General Neural Implicit Surfaces via Range Analysis](https://mlsanity.com/paper/2202.02444/) (2022)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation](https://mlsanity.com/paper/2405.13745/) (2024)
- [1-Lipschitz Neural Distance Fields](https://mlsanity.com/paper/2407.09505/) (2024)
- [Neural Poisson: Indicator Functions for Neural Fields](https://mlsanity.com/paper/2211.14249/) (2022)
- [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)
- [Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation](https://mlsanity.com/paper/2503.23670/) (2025)
- [Sphere-Guided Training of Neural Implicit Surfaces](https://mlsanity.com/paper/2209.15511/) (2022)

## Abstract (arXiv)

Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the parameters for accurate and robust reconstructions remains a challenge, especially when the input data is noisy or incomplete. In this work, we develop a hybrid neural surface representation that allows us to impose geometry-aware sampling and regularization, which significantly improves the fidelity of reconstructions. We propose to use iso-points as an explicit representation for a neural implicit function. These points are computed and updated on-the-fly during training to capture important geometric features and impose geometric constraints on the optimization. We demonstrate that our method can be adopted to improve state-of-the-art techniques for reconstructing neural implicit surfaces from multi-view images or point clouds. Quantitative and qualitative evaluations show that, compared with existing sampling and optimization methods, our approach allows faster convergence, better generalization, and accurate recovery of details and topology.