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. Experimental results show significant improvements in rendering quality and efficiency, outperforming current state-of-the-art techniques.
动态场景渲染随着4D高斯散射的兴起取得了显著进展，但仍有一个难以攻克的挑战：如何让3D高斯在时间中自然移动，就像真实世界中的表现一样，同时保持运动的平滑性和一致性。 在本文中，我们提出了一种全新的方法，将状态空间建模与Wasserstein几何相结合，为动态场景提供更流畅且连贯的表示。我们引入了一种状态一致性滤波器（State Consistency Filter），将先验预测与当前观测融合，使高斯能够在时间维度上保持其自然轨迹。 我们还采用Wasserstein距离正则化，确保高斯参数的更新平滑且一致，从而减少运动伪影。此外，通过Wasserstein几何捕捉平移运动和形状变形，构建了一个更符合物理规律的动态场景模型。 我们的方法引导高斯在Wasserstein空间中沿其自然路径移动，实现更平滑、更真实的运动以及更强的时间连贯性。实验结果表明，该方法在渲染质量和效率方面均取得了显著改进，优于当前最先进的技术。