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This paper explores the problem of task-oriented downsampling over 3D pointclouds, which aims to downsample a point cloud while maintaining theperformance of subsequent applications applied to the downsampled sparse pointsas much as possible. Designing from the perspective of matrix optimization, wepropose MOPS-Net, a novel interpretable deep learning-based method, which isfundamentally different from the existing deep learning-based methods due toits interpretable feature. The optimization problem is challenging due to itsdiscrete and combinatorial nature. We tackle the challenges by relaxing thebinary constraint of the variables, and formulate a constrained anddifferentiable matrix optimization problem. We then design a deep neuralnetwork to mimic the matrix optimization by exploring both the local and globalstructures of the input data. MOPS-Net can be end-to-end trained with a tasknetwork and is permutation-invariant, making it robust to the input. We alsoextend MOPS-Net such that a single network after one-time training is capableof handling arbitrary downsampling ratios. Extensive experimental results showthat MOPS-Net can achieve favorable performance against state-of-the-art deeplearning-based methods over various tasks, including classification,reconstruction, and registration. Besides, we validate the robustness ofMOPS-Net on noisy data.

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