Convective regularization for optical flow

We argue that the time derivative in a fixed coordinate frame may not be the most appropriate measure of time regularity of an optical flow field. Instead, for a given velocity field $v$ we consider the convective acceleration $v_t + \nabla v v$ which describes the acceleration of objects moving according to $v$. Consequently we investigate the suitability of the nonconvex functional $\|v_t + \nabla v v\|^2_{L^2}$ as a regularization term for optical flow. We demonstrate that this term acts as both a spatial and a temporal regularizer and has an intrinsic edge-preserving property. We incorporate it into a contrast invariant and time-regularized variant of the Horn-Schunck functional, prove existence of minimizers and verify experimentally that it addresses some of the problems of basic quadratic models. For the minimization we use an iterative scheme that approximates the original nonlinear problem with a sequence of linear ones. We believe that the convective acceleration may be gainfully introduced in a variety of optical flow models

Motion of Contact Line of a Crystal Over the Edge of Solid Mask in Epitaxial Lateral Overgrowth

Mathematical model that allows for direct tracking of the homoepitaxial crystal growth out of the window etched in the solid, pre-deposited layer on the substrate is described. The growth is governed by the normal (to the crystal-vapor interface) flux from the vapor phase and by the interface diffusion. The model accounts for possibly inhomogeneous energy of the mask surface and for strong anisotropies of crystal-vapor interfacial energy and kinetic mobility. Results demonstrate that the motion of the crystal-mask contact line slows down abruptly as radius of curvature of the mask edge approaches zero. Numerical procedure is suggested to overcome difficulties associated with ill-posedness of the evolution problem for the interface with strong energy anisotropy. Keywords: Thin films, epitaxy, MOCVD, surface diffusion, interface dynamics, contact lines, rough surfaces, wetting, regularization of ill-posed evolution problems.Comment: 21 pages, 11 figures; to appear in Computational Materials Scienc