Symplectic Dual-Path Decoupling 3D Gaussian Splatting for Motion Deblurring

To address the above issues, a symplectic geometry dual path decoupling 3D Gaussian splashing method for motion deblurring is proposed. This method introduces the Hamiltonian dynamics framework to model the camera motion as a dual evolution of position momentum in phase space, and then uses a symplectic geometric differential equation solver to ensure that the phase flow satisfies symplectic preservation properties, physically ensuring the continuity of the camera motion trajectory; On this basis, a dual path adaptive motion decoupling framework that combines physical priors and residual refinement is proposed.

The camera motion is decomposed into a rigid body motion branch that provides a global pose baseline and a residual refinement branch that compensates for subtle motion deviations and integral approximation errors. The two branches are combined adaptively to achieve stable expression of complex non-uniform motion; The results were validated on the Deblur NeRF synthetic/real dataset and the ExBluRF extreme fuzzy dataset.

Compared with mainstream methods, the performance indicators reached the best on both the real dataset and the ExBluRF dataset, and the PSNR and LPIPS reached the best on the synthetic dataset. Among them, the PSNR was improved by 0.12 dB, 1.75 dB, and 1.87 dB compared to the suboptimal method on the three datasets, and the advantage was particularly obvious in complex non-uniform motion scenes. Conclusion: The experimental results show that the proposed method effectively improves the quality of 3D reconstruction in motion blurred scenes through symplectic geometry modeling and dual path decoupling strategy.