Change The Spectral Flow Calculation Of The Mathematical Models And Numerical Methods

Optic flow is the speed of mode movement in images. Optic flow not only contains movement information of objects observed, but also carries abundant information of two-dimensional structure features. Although optic flow is only the projection of the true motion of the scene, it proves to be useful for a variety of different tasks, such as object segmentation, detection, tracking, robot navigation and information recovery and so on. Optic flow has become an important part in computer vision and related research fields.Optic flow field estimation is the foundation of image serials segmentation and object tracking. Compared with other optic flow calculation methods, variational methods has obvious advantages in modeling automation and accuracy and dense optic flow obtained, which can provide a unified description of the mathematical framework for different types of optic flow and can get more accurate optic flow. Thus, variational methods are among the best performing and the best understood techniques for computing the optic flow. The variational methods suggested by Horn and Schunck are typical one. Using this method, we can define energy functional with data item and smoothness item .Through variational methods, the Euler-Lagrange equation of optic flow computation is obtained and through differential method discrete solutions can be gotten. One research of this article is the mathematical models and numerical methods of optic flow based on the variational methods.Another research of this article is extension to the H-S model. First, we establish the data items of variational optic flow computation, which can effectively calculate optic flow under six cases, such as brightness constancy assumption, brightness gradient constancy assumption and brightness divergence constancy assumption and so on. Then, based on the image diffusion model, we derive five methods for designing smoothness item, including homogeneous diffusion, linear isotropic diffusion, linear anisotropic diffusion, nonlinear isotropic diffusion and nonlinear anisotropic diffusion, which is suitable for computation of discontinuous optic flow. Finally, we establish a general Euler-Lagrange equation based on the variational optic flow computation, and derive the corresponding semi-implicit difference scheme. In addition, we establish mathematical models optic flow computation for large displacement with typical data items and smoothness items.