Quantum-inspired Uncertainty Modeling for Point Cloud-based Large-scale Place Recognition

The existing works focus on extracting distinguishable features of a scene to enhance the performance of place recognition. However, the fact is ignored that the place recognition task is a process of probability learning, which still lacks comprehensive investigations. That is, the retrieved point cloud results may have multiple candidates. Therefore, in this paper, we formulate place recognition as an uncertainty probability problem. First, inspired by the uncertainty probability of quantum theory, we model point cloud-based place recognition in quantum states and propose Point Cloud Hilbert Space, which consists of six components including meta, point, point clouds, abstraction, combination, and positioning. This modeling endows Point Cloud Hilbert Space with the capability of uncertainty delivery from points to combinations, and then the uncertainty is eliminated by positioning measurement to generate the ultimate retrieved result. Second, to concretize this model for the place recognition task, we design a quantum-inspired framework, dubbed as QuantumPR, which includes point cloud embedding, point cloud mixture, and point cloud measurement. These three modules separately fulfill the quantum state embedding of point clouds, the mixture of quantum states, and the measurement of quantum states. The QuantumPR provides a feasible solution, which is also interpretable inheriting from the Point Cloud Hilbert Space. Third, to implement the above framework, we devise an instance network, where the amplitude-phase representation is adopted for initializing quantum states, and five QuantumPointConv blocks are established for exploring relations among points. Moreover, geometric-mean-pooling and half-output dimensions are adopted to lighten the network and get the combination. This network can be flexibly applied to other diverse methods. Finally, extensive experiments demonstrate the efficiency and generalizability of the proposed method for point cloud-based place recognition. By establishing the first bridge between quantum-theoretic uncertainty modeling and large-scale place recognition, we offer a mathematically interpretation and provide a reusable formalism for future uncertainty-aware place recognition.