基于最优流,分割和最优控制的图像序列内插

介绍一种用最优控制论的方法解决图像序列内插问题,目的在于找到一个流场,使得第一个图像能够尽好地传输到第二个图像.对运输方程构建最优控制,通过正则化转化为求满足条件的最优的流场,并给出重整化解,及解的存在,唯一和稳定性.流场的散度有界和Sobolev空间的选择,使得问题不用强制满足莱布尼兹条件.在有界全变分框架下,罚项的弱下半连续得以保证,从而很好地将图像进行运输.最后将图像内插的最优控制方程与Chen-Vese的分割法相结合,用Landweber迭代法获得更快的迭代收敛速度.

Image Sequence Interpolation Based On Optimal Flow,Segmentation, and Optimal Control

This paper introduces a method using the optimal control theory to solve image sequence interpolation problem, i. e. we aim at finding a flow field which transport the first image as close as possible to the second image. We built optimal control model by transport equation, and using regularization into meet the condition of the optimal flow filed. Then the renormalized solution is giving, and we prove the existence of the renormalized, uniqueness and stability. Flow field divergence is bounded and the choice of Sobolev spaces makes the problem without forcing satisfy Lipschitz condition. In the framework of bounded total variation, penalty term is semi-- continuous, so the image transport is good. Finally, our approach is a combination of the optimal transport approach interpolation and the segmentation by the Chan--Vese approach, we get faster iteration speed of the Landweber iteration method.