Task-Oriented Compact Representation of 3D Point Clouds via A Matrix Optimization-Driven Network

This paper explores the task-oriented compact representation of 3D point clouds, which should maintain the performance of subsequent applications applied to such compact point clouds as much as possible. Designing from the perspective of matrix optimization, we propose MOPS-Net, a novel deep learning-based method that is distinguishable from existing approaches due to its interpretability and flexibility. The matrix optimization problem is challenging due to the discrete and combinatorial nature of the sampling matrix. Therefore, we tackle the challenges by relaxing the binary constraint of the sampling matrix and formulating a constrained and differentiable 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.