Efficient Point Cloud Analysis Using Hilbert Curve

Some previous state-of-the-art research on analyzing point cloud rely on the voxelization quantization because it keeps the better spatial locality and geometry. However, these 3D voxelization methods and subsequent 3D convolution networks often bring the large computational overhead and GPU occupation. A straightforward alternative is to flatten 3D voxelization into 2D structure or utilize the pillar representation to perform the dimension reduction, while all of them would inevitably alter the spatial locality and 3D geometric information. In this way, we propose the HilbertNet to maintain the locality advantage of voxel-based methods while significantly reducing the computational cost. Here the key component is a new flattening mechanism based on Hilbert curve, which is a famous locality and geometry preserving function. Namely, if flattening 3D voxels using Hilbert curve encoding, the resulting structure will have similar spatial topology compared with original voxels. Through the Hilbert flattening, we can not only use 2D convolution (more lightweight than 3D convolution) to process voxels, but also incorporate technologies suitable in 2D space, such as transformer, to boost the performance. Our proposed HilbertNet achieves state-of-the-art performance on ShapeNet, ModelNet40 and S3DIS datasets with smaller cost and GPU occupation.