基于样条泛函的光流计算  

Optical flow computation based on spline functionals

作　　者：郭晓新[1,2] 杨光[1,2] 许志闻[1,2] 

机构地区：[1]吉林大学计算机科学与技术学院,长春130012 [2]吉林大学符号计算与知识工程教育部重点实验室,长春130012

出　　处：《吉林大学学报（工学版）》2013年第S1期165-168,共4页Journal of Jilin University:Engineering and Technology Edition

基　　金：国家自然科学基金资助项目(60905022)

摘　　要：给出了以样条泛函作为光滑约束的数学模型,并且给出了光流计算最小化问题解的必要条件。该模型包含了二阶和四阶偏微分方程以约束这两个特例。该模型从方法学角度为光流计算的形式化表示和数值计算提供了依据。采用该数学模型的意义还在于它能将光流计算的方程组简化为线性代数方程组。这种转换便于光流方程的离散化表示,同时也从代数方程的角度验证了光滑约束的使用能确保解的存在性和唯一性。A mathematical model using the spline functional as smooth constraints was presented.The second-and fourth-order partial differential equations constraints were two special cases in the model.The necessary condition for optical flow minimization problem solution was also presented.This model provided a basis for formal representation and numerical computation of optical flow from a methodological point of view.The significance of this mathematical model lay in the simplification of the equations for optical flow computation into linear algebraic equations.The simplification can contribute to discrete representation of the optical flow equation,and also verify that the use of smoothness constraints can ensure the existence and uniqueness of the solution from the view of the algebraic equations.

关 键 词：光流 样条泛函 偏微分方程 光滑约束 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]