Neural Points: Point Cloud Representation with Neural Fields for Arbitrary Upsampling

Abstract: In this paper, we propose Neural Points, a novel point cloud representation and apply it to the arbitrary-factored upsampling task. Different from traditional point cloud representation where each point only represents a position or a local plane in the 3D space, each point in Neural Points represents a local continuous geometric shape via neural fields. Therefore, Neural Points contain more shape information and thus have a stronger representation ability. Neural Points is trained with surface containing rich geometric details, such that the trained model has enough expression ability for various shapes. Specifically, we extract deep local features on the points and construct neural fields through the local isomorphism between the 2D parametric domain and the 3D local patch. In the final, local neural fields are integrated together to form the global surface. Experimental results show that Neural Points has powerful representation ability and demonstrate excellent robustness and generalization ability. With Neural Points, we can resample point cloud with arbitrary resolutions, and it outperforms the state-of-the-art point cloud upsampling methods. Code is available at https://github.com/WanquanF/NeuralPoints.

• The paper presents Neural Points, a method that assigns neural fields to each point to represent continuous local surface patches, overcoming discrete limitations.
• The paper integrates local neural fields via mapping 3D coordinates to a 2D domain and skinned integration for a globally smooth, arbitrarily upsampled surface.
• The paper validates the approach with experiments showing lower Chamfer, Hausdorff, and point-to-surface errors compared to PU-Net, PU-GAN, and PU-GCN on diverse datasets.

Insights into Neural Points: Point Cloud Representation with Neural Fields

This paper introduces a novel representation for point clouds, a fundamental element in modeling 3D geometric data. Traditional approaches to point cloud representation are constrained by their resolution, with each point denoting merely a position and perhaps a local plane. Despite advancements in point cloud upsampling methods, they typically follow a discrete-to-discrete framework, which fundamentally limits their ability to enhance representation robustness and flexibility. The authors propose an innovative solution in the form of Neural Points, which employs neural fields to represent local continuous geometric shapes corresponding to each point. This approach enables arbitrary upsampling, offering significant improvements in representation ability over traditional methods.

Methodological Contributions

1. Neural Fields-Based Representation: Neural Points transcends conventional point cloud representation by assigning a neural field to each point, effectively encoding a local surface patch. This is achieved using a local isomorphism between the 2D parametric domain and the 3D local surface patch. This concept leverages the continuous nature of neural fields to represent more detailed shape information without being limited by finite resolution.
2. Integration of Local Neural Fields: The paper describes a method for integrating local neural fields into a coherent global surface. This integration is facilitated by mapping the 3D coordinates back to the 2D parametric domain and using a skinned integration strategy to achieve a globally smooth and continuous reshaping surface. This process not only covers the input surface but enables the extraction of point clouds at arbitrary resolutions.
3. Efficient Feature Extraction: The authors incorporate deep local features into the representation using a dynamic graph convolutional network (DGCNN). This method extracts robust features on local patches, which are integral to the effectiveness of the neural fields.

Experimental Validation

The authors conducted extensive experiments, demonstrating that Neural Points outperform existing state-of-the-art upsampling methods, such as PU-Net, PU-GAN, and PU-GCN, on both synthetic and real datasets. The results show superior accuracy as quantified by Chamfer Distance (CD), Hausdorff Distance (HD), and Point-to-Surface (P2F) metrics, with Neural Points consistently yielding lower error rates. Experiments also highlight the robustness of Neural Points against noise and its applicability to real-world data, including LiDAR scans and depth sensor data, showcasing excellent generalization capabilities.

The paper further validates the flexibility of Neural Points through arbitrary-factor upsampling, accommodating non-integer upscales with qualitative demonstrations. Additionally, ablation studies underscore the importance of critical components such as the local KNN structure in feature extraction and normal losses for training.

Theoretical and Practical Implications

The conceptual shift from discrete points to continuous neural fields represents a significant advancement in 3D data representation. It unlocks potential applications not only in 3D reconstruction but also in fields requiring precise control over resolution, such as virtual reality and autonomous navigation systems. By facilitating storage-efficient models that are agnostic to point density, this approach can serve as a foundation for future developments in real-time 3D processing and rendering.

Future Directions

While Neural Points offer a considerable improvement over traditional methods, the integration of other modalities like textures and global semantic structures may further enhance its representation capacity. Future work may also explore its application in dynamic environments and large-scale scene reconstruction, where real-time performance and integration with other forms of sensor data are crucial.

In summary, this paper provides a well-founded methodology and impressive experimental support for Neural Points, presenting a versatile and powerful tool for advanced 3D point cloud representation.