Dynamic scene rendering has taken a leap forward with the rise of 4D Gaussian Splatting, but there's still one elusive challenge: how to make 3D Gaussians move through time as naturally as they would in the real world, all while keeping the motion smooth and consistent. In this paper, we unveil a fresh approach that blends state-space modeling with Wasserstein geometry, paving the way for a more fluid and coherent representation of dynamic scenes.
We introduce a State Consistency Filter that merges prior predictions with the current observations, enabling Gaussians to stay true to their way over time. We also employ Wasserstein distance regularization to ensure smooth, consistent updates of Gaussian parameters, reducing motion artifacts. Lastly, we leverage Wasserstein geometry to capture both translational motion and shape deformations, creating a more physically plausible model for dynamic scenes.
Our approach guides Gaussians along their natural way in the Wasserstein space, achieving smoother, more realistic motion and stronger temporal coherence.
Our framework integrates three key components for dynamic scene rendering. First, a state-space updating mechanism with neural Gaussian deformation estimates motion patterns. Second, Wasserstein distance regularization ensures smooth parameter updates. Third, we model Gaussian dynamics under Wasserstein geometry for accurate motion prediction with intrinsic physical plausibility.
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