Equivariance-Based Markov Decision Process for Unsupervised Point Cloud Registration

Unsupervised point cloud registration is crucial in 3D computer vision. However, most unsupervised methods struggle to construct effective optimization objectives and reliable unsupervised signals to enhance the performance of the model. To address these issues, with the observation of the significant alignment between the registration process and the Markov Decision Process (MDP), we model point cloud registration as MDP, which can provide more reliable unsupervised signals through the reward. We propose a colored noise based cross-entropy method, which introduces colored noise into sampling process, regulating the power spectral density of the action sequence and expanding the search space, improving the registration effect. Particularly, to strengthen constraints on MDP and training in the transformation space, we utilize equivariance theory to construct transformation equivariant constraint as a new optimization objective and derive equivariant constraint solutions for optimization, providing more reliable unsupervised signals. Extensive experiments demonstrate the superior performance of our method on benchmark datasets.