MOPS-Net: A Matrix Optimization-driven Network forTask-Oriented 3D Point Cloud Downsampling

This paper explores the problem of task-oriented downsampling over 3D point clouds, which aims to downsample a point cloud while maintaining the performance of subsequent applications applied to the downsampled sparse points as much as possible. Designing from the perspective of matrix optimization, we propose MOPS-Net, a novel interpretable deep learning-based method, which is fundamentally different from the existing deep learning-based methods due to its interpretable feature. The optimization problem is challenging due to its discrete and combinatorial nature. We tackle the challenges by relaxing the binary constraint of the variables, and formulate a constrained and differentiable matrix optimization problem. We then design a deep neural network to mimic the matrix optimization by exploring both the local and global structures of the input data. MOPS-Net can be end-to-end trained with a task network and is permutation-invariant, making it robust to the input. We also extend MOPS-Net such that a single network after one-time training is capable of handling arbitrary downsampling ratios. Extensive experimental results show that MOPS-Net can achieve favorable performance against state-of-the-art deep learning-based methods over various tasks, including classification, reconstruction, and registration. Besides, we validate the robustness of MOPS-Net on noisy data.