ReynoldsFlow: Physics-Inspired Spatiotemporal Flow Representation for Video Understanding

Video understanding has largely relied on deep spatiotem-poral architectures, including 3D convolutional networks and opticalflow (OF) based models. While effective, these methods are often com-putationally expensive and depend on heuristic motion representationsthat are sensitive to illumination, scale, and structural changes. To ad-dress these limitations, we propose ReynoldsFlow, a physics-inspiredrepresentation grounded in the Reynolds transport theorem (RTT) andHelmholtz-Hodge decomposition (HHD). ReynoldsFlow decomposes mo-tion into curl-free (CF) and divergence-free (DF) components, providinga principled and interpretable characterization of scene dynamics. Bycoupling intensity information with decomposed motion cues, it producesdynamics-aware, texture-preserving features that boost downstream taskssuch as pose estimation, action recognition, and tiny object detection.Lightweight and modular, ReynoldsFlow can be readily integrated intoexisting architectures. Experiments across diverse benchmarks show thatReynoldsFlow consistently matches or surpasses existing approaches, of-fering improved generalizability and computational efficiency.