# Learning Continuous Implicit Field with Local Distance Indicator for Arbitrary-Scale Point Cloud Upsampling

arXiv: https://arxiv.org/abs/2312.15133 · HTML: https://mlsanity.com/paper/2312.15133/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 23 Dec 2023.

## Builds on (most cited first, 27 of 27)

- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [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)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Patch-based Progressive 3D Point Set Upsampling](https://mlsanity.com/paper/1811.11286/) (2018)
- [PU-GCN: Point Cloud Upsampling using Graph Convolutional Networks](https://mlsanity.com/paper/1912.03264/) (2019)
- [Point Cloud Upsampling via Disentangled Refinement](https://mlsanity.com/paper/2106.04779/) (2021)
- [PUGeo-Net: A Geometry-centric Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2002.10277/) (2020)
- [Neural Point Cloud Rendering via Multi-Plane Projection](https://mlsanity.com/paper/1912.04645/) (2019)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [Neural Points: Point Cloud Representation with Neural Fields for Arbitrary Upsampling](https://mlsanity.com/paper/2112.04148/) (2021)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [Grad-PU: Arbitrary-Scale Point Cloud Upsampling via Gradient Descent with Learned Distance Functions](https://mlsanity.com/paper/2304.11846/) (2023)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Fast Learning Radiance Fields by Shooting Much Fewer Rays](https://mlsanity.com/paper/2208.06821/) (2022)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [Meta-PU: An Arbitrary-Scale Upsampling Network for Point Cloud](https://mlsanity.com/paper/2102.04317/) (2021)
- [Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priors](https://mlsanity.com/paper/2303.14505/) (2023)
- [SPU-Net: Self-Supervised Point Cloud Upsampling by Coarse-to-Fine Reconstruction with Self-Projection Optimization](https://mlsanity.com/paper/2012.04439/) (2020)
- [Self-Supervised Arbitrary-Scale Point Clouds Upsampling via Implicit Neural Representation](https://mlsanity.com/paper/2204.08196/) (2022)
- [PU-EVA: An Edge Vector based Approximation Solution for Flexible-scale Point Cloud Upsampling](https://mlsanity.com/paper/2204.10750/) (2022)
- [PC2-PU: Patch Correlation and Point Correlation for Effective Point Cloud Upsampling](https://mlsanity.com/paper/2109.09337/) (2021)
- [Arbitrary Point Cloud Upsampling with Spherical Mixture of Gaussians](https://mlsanity.com/paper/2208.05274/) (2022)

## Built on by (most cited first, 19 of 19)

- [DiffGS: Functional Gaussian Splatting Diffusion](https://mlsanity.com/paper/2410.19657/) (2024)
- [Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set](https://mlsanity.com/paper/2410.14189/) (2024)
- [Binocular-Guided 3D Gaussian Splatting with View Consistency for Sparse View Synthesis](https://mlsanity.com/paper/2410.18822/) (2024)
- [Zero-Shot Scene Reconstruction from Single Images with Deep Prior Assembly](https://mlsanity.com/paper/2410.15971/) (2024)
- [UDiFF: Generating Conditional Unsigned Distance Fields with Optimal Wavelet Diffusion](https://mlsanity.com/paper/2404.06851/) (2024)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [MonoInstance: Enhancing Monocular Priors via Multi-view Instance Alignment for Neural Rendering and Reconstruction](https://mlsanity.com/paper/2503.18363/) (2025)
- [NeRFPrior: Learning Neural Radiance Field as a Prior for Indoor Scene Reconstruction](https://mlsanity.com/paper/2503.18361/) (2025)
- [Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation](https://mlsanity.com/paper/2503.23670/) (2025)
- [GAP: Gaussianize Any Point Clouds with Text Guidance](https://mlsanity.com/paper/2508.05631/) (2025)
- [Deep Learning for 3D Point Cloud Enhancement: A Survey](https://mlsanity.com/paper/2411.00857/) (2024)
- [Fourier Decomposition for Explicit Representation of 3D Point Cloud Attributes](https://mlsanity.com/paper/2503.10055/) (2025)
- [U-CAN: Unsupervised Point Cloud Denoising with Consistency-Aware Noise2Noise Matching](https://mlsanity.com/paper/2510.25210/) (2025)
- [3D-WAG: Hierarchical Wavelet-Guided Autoregressive Generation for High-Fidelity 3D Shapes](https://mlsanity.com/paper/2411.19037/) (2024)
- [MBPU: A Plug-and-Play State Space Model for Point Cloud Upsamping with Fast Point Rendering](https://mlsanity.com/paper/2410.15941/) (2024)
- [PLATYPUS: Progressive Local Surface Estimator for Arbitrary-Scale Point Cloud Upsampling](https://mlsanity.com/paper/2411.00432/) (2024)
- [SPU-IMR: Self-supervised Arbitrary-scale Point Cloud Upsampling via Iterative Mask-recovery Network](https://mlsanity.com/paper/2502.19452/) (2025)
- [PU-Gaussian: Point Cloud Upsampling using 3D Gaussian Representation](https://mlsanity.com/paper/2509.20207/) (2025)
- [2D Representation for Unguided Single-View 3D Super-Resolution in Real-Time](https://mlsanity.com/paper/2511.08224/) (2025)

## Abstract (arXiv)

Point cloud upsampling aims to generate dense and uniformly distributed point sets from a sparse point cloud, which plays a critical role in 3D computer vision. Previous methods typically split a sparse point cloud into several local patches, upsample patch points, and merge all upsampled patches. However, these methods often produce holes, outliers or nonuniformity due to the splitting and merging process which does not maintain consistency among local patches. To address these issues, we propose a novel approach that learns an unsigned distance field guided by local priors for point cloud upsampling. Specifically, we train a local distance indicator (LDI) that predicts the unsigned distance from a query point to a local implicit surface. Utilizing the learned LDI, we learn an unsigned distance field to represent the sparse point cloud with patch consistency. At inference time, we randomly sample queries around the sparse point cloud, and project these query points onto the zero-level set of the learned implicit field to generate a dense point cloud. We justify that the implicit field is naturally continuous, which inherently enables the application of arbitrary-scale upsampling without necessarily retraining for various scales. We conduct comprehensive experiments on both synthetic data and real scans, and report state-of-the-art results under widely used benchmarks.