用李群统一建模视频中的平移与旋转，让动态场景更真实连贯。
Lie Flow: Video Dynamic Fields Modeling and Predicting with Lie Algebra as Geometric Physics Principle
- 基于SE(3)李群构建运动场，统一处理平移与旋转
- 在合成与真实数据上显著提升画面质量与物理合理性
- 适合做动态4D场景建模的研究者和开发者
建模4D场景需同时捕捉空间结构与时间运动，但复杂刚体与非刚体运动的物理一致性难以保证。现有方法多依赖平移位移，难以准确表示旋转与关节运动，常导致空间不一致和物理上不合理的运动。本文提出LieFlow，一种基于SE(3)李群的动态辐射场框架，显式建模运动，实现平移与旋转在统一几何空间中的协同学习。SE(3)变换场施加物理启发的约束，确保运动连续性与几何一致性。评估包含一个具有刚体轨迹的合成数据集及两个真实世界数据集（含自然光照与遮挡）。在所有数据集上，LieFlow均显著优于基于NeRF的基线，在视图合成保真度、时间连贯性和物理真实性方面表现更优。结果表明，基于SE(3)的运动建模为动态4D场景提供了稳健且物理基础牢固的表达框架。
原文摘要 · Abstract (English)
Modeling 4D scenes requires capturing both spatial structure and temporal motion, which is challenging due to the need for physically consistent representations of complex rigid and non-rigid motions. Existing approaches mainly rely on translational displacements, which struggle to represent rotations, articulated transformations, often leading to spatial inconsistency and physically implausible motion. LieFlow, a dynamic radiance representation framework that explicitly models motion within the SE(3) Lie group, enabling coherent learning of translation and rotation in a unified geometric space. The SE(3) transformation field enforces physically inspired constraints to maintain motion continuity and geometric consistency. The evaluation includes a synthetic dataset with rigid-body trajectories and two real-world datasets capturing complex motion under natural lighting and occlusions. Across all datasets, LieFlow consistently improves view-synthesis fidelity, temporal coherence, and physical realism over NeRF-based baselines. These results confirm that SE(3)-based motion modeling offers a robust and physically grounded framework for representing dynamic 4D scenes.
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