ConvPoint: Continuous Convolutions for Point Cloud Processing (1904.02375v5)

Abstract: Point clouds are unstructured and unordered data, as opposed to images. Thus, most machine learning approach developed for image cannot be directly transferred to point clouds. In this paper, we propose a generalization of discrete convolutional neural networks (CNNs) in order to deal with point clouds by replacing discrete kernels by continuous ones. This formulation is simple, allows arbitrary point cloud sizes and can easily be used for designing neural networks similarly to 2D CNNs. We present experimental results with various architectures, highlighting the flexibility of the proposed approach. We obtain competitive results compared to the state-of-the-art on shape classification, part segmentation and semantic segmentation for large-scale point clouds.

• The paper presents a continuous convolution formulation that enables CNNs to directly process unstructured point clouds.
• It integrates continuous convolutions into hierarchical network architectures, achieving 92.5% accuracy on ModelNet40 and 83.4% mcIoU on ShapeNet.
• The approach offers efficient and robust processing for 3D tasks such as shape classification, segmentation, and real-time mapping.

ConvPoint: Continuous Convolutions for Point Cloud Processing

The paper "ConvPoint: Continuous Convolutions for Point Cloud Processing" introduces a novel approach to applying convolutional neural networks (CNNs) to point clouds, which are inherently unstructured and unordered data sets. Traditional CNNs rely on grid-like data structures, such as those found in images, where discrete convolution operations are naturally defined. However, point clouds, central to applications such as autonomous driving and historical preservation, cannot be processed in the same manner because of their lack of inherent spatial structure. The authors propose a generalization of CNNs by adapting them to employ continuous convolutional operations instead of discrete ones, thereby addressing the unique characteristics of point clouds.

Main Contributions

The paper's primary contributions are twofold:

1. Continuous Convolution Formulation: The authors present a continuous convolution framework designed specifically for unstructured data such as point clouds. This approach replaces the traditional grid-dependent kernel operations with continuous kernels, capable of processing the data structure inherent in point clouds. This allows the convolution operation to be applied directly on the point cloud without a need for transformation into intermediary structures like voxel grids.
2. Implementation in Neural Networks: The paper demonstrates that continuous convolutions can be seamlessly integrated into network architectures similar to those used for image processing. The approach employs a hierarchical representation of data through a search tree, capable of efficiently computing the necessary convolutions.

Numerical and Empirical Results

The proposed approach is empirically validated through a series of experiments in three key application areas: shape classification, part segmentation, and semantic segmentation of large-scale point clouds. The experiments demonstrate that ConvPoint achieves competitive performance relative to existing state-of-the-art methods across various datasets. Notably:

• On the ModelNet40 dataset for 3D object classification, ConvPoint achieves an overall accuracy of 92.5%, which is comparable to or exceeds many contemporary methods.
• In the ShapeNet part segmentation task, the method delivers a mean class intersection over union (mcIoU) of 83.4%, positioning it favorably among other leading algorithms.
• For the Semantic8 and Paris-Lille 3D datasets, ConvPoint's approach demonstrates robustness and efficacy, often surpassing established techniques in terms of accuracy and computational efficiency.

Implications and Future Work

The continuous convolution formulation is promising for the field of geometric deep learning and paves the way for various practical applications involving lidar data, 3D scans, and more. The approach's robustness to unordered data and its ability to efficiently handle varying point cloud sizes suggest that it might further impact real-time processing, critical for applications like autonomous vehicle navigation and real-time 3D mapping.

Future developments could explore alternative network architectures, potentially incorporating precomputed geometric features such as curvature or normal vectors as inputs, to enhance performance further. Another avenue for research may involve adaptive approaches to manage varying point densities without predefined neighborhood sizes.

In conclusion, the ConvPoint framework represents a significant step forward in adapting deep learning architecture for point cloud processing. It opens up new opportunities for efficiently leveraging CNNs in domains where spatial data does not conform to regular grids, fostering continued advancement in both theoretical and practical aspects of point cloud analysis.