College of Information Science and Engineering, Northeastern University, Shenyang 110819, People's Republic of China.
Philos Trans A Math Phys Eng Sci. 2013 Apr 1;371(1990):20120148. doi: 10.1098/rsta.2012.0148. Print 2013 May 13.
A new class of fractional-order variational optical flow models, which generalizes the differential of optical flow from integer order to fractional order, is proposed for motion estimation in this paper. The corresponding Euler-Lagrange equations are derived by solving a typical fractional variational problem, and the numerical implementation based on the Grünwald-Letnikov fractional derivative definition is proposed to solve these complicated fractional partial differential equations. Theoretical analysis reveals that the proposed fractional-order variational optical flow model is the generalization of the typical Horn and Schunck (first-order) variational optical flow model and the second-order variational optical flow model, which provides a new idea for us to study the optical flow model and has an important theoretical implication in optical flow model research. The experiments demonstrate the validity of the generalization of differential order.
本文提出了一类新的分数阶变分光流模型，将光流的微分从整数阶推广到分数阶，用于运动估计。通过求解典型的分数变分问题，推导出相应的欧拉-拉格朗日方程，并提出了基于 Grunwald-Letnikov 分数导数定义的数值实现方法来求解这些复杂的分数偏微分方程。理论分析表明，所提出的分数阶变分光流模型是典型的 Horn 和 Schunck（一阶）变分光流模型和二阶变分光流模型的推广，为我们研究光流模型提供了新的思路，在光流模型研究中具有重要的理论意义。实验验证了微分阶数推广的有效性。
