ELF-Nets: Deep learning on point clouds using extended laplacian filter

We propose a deep learning framework for various 3D vision tasks, which takes a point cloud as input. The convolution is a basic operator for feature extraction in deep learning. However, it is not directly applicable to a point cloud, which is an irregular, unordered point set. This makes deep learning on point clouds challenging. To address this issue, we propose the extended Laplacian filter (ELF) for point clouds, which adopts the design principles of discrete Laplacian filters in 2D image processing. In other words, ELF extends the Laplacian filters and has the following two properties: 1) it is a two-state filter using two filter matrices (one for a center point and the other for neighboring points), and 2) it employs a scalar weighting function to predict the relative importance of the neighboring points. Then, we develop ELF-Nets, which consist of ELF convolution layers and fully connected layers. Experimental results demonstrate that the proposed ELF-Nets are capable of recognizing the 3D shape of a point cloud effectively and efficiently. In particular, ELF-Nets provide better or comparable performances than the state-of-the-art techniques in both object classification and part segmentation tasks.