基于样条泛函的光流计算

吉林大学学报(工学版) ›› 2013, Vol. 43 ›› Issue (增刊1): 165-168.

基于样条泛函的光流计算

郭晓新^1,2, 杨光^1,2, 许志闻^1,2

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

收稿日期:2012-06-25 发布日期:2013-06-01
作者简介:郭晓新(1974-),男,副教授.研究方向:图像处理、机器视觉和计算机图形学.E-mail:guoxx@jlu.edu.cn
基金资助:
国家自然科学基金资助项目(60905022).

Optical flow computation based on spline functionals

GUO Xiao-xin^1,2, YANG Guang^1,2, XU Zhi-wen^1,2

1. College of Computer Science and Technology, Jilin University, Changchun 130012, China;
2. Key Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education, Jilin University, Changchun 130012, China

Received:2012-06-25 Published:2013-06-01

摘要/Abstract

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。

关键词: 光流, 样条泛函, 偏微分方程, 光滑约束

Abstract:

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.

Key words: optical flow, spline functionals, partial deferential equation (PDE), smooth constraint

中图分类号:

TP391.41

郭晓新, 杨光, 许志闻. 基于样条泛函的光流计算[J]. 吉林大学学报(工学版), 2013, 43(增刊1): 165-168.

GUO Xiao-xin, YANG Guang, XU Zhi-wen. Optical flow computation based on spline functionals[J]. 吉林大学学报(工学版), 2013, 43(增刊1): 165-168.

参考文献

[1] Aubert G,Kornprobst P.Mathematical Problems in Image Processing [M].Berlin:Springer,2002.

[2] Barron J L,Fleet D J,Beauchemin S S.Performance of optical flow techniques [J].International Journal of Computer Vision,1994,12(1):43-77.

[3] Horn B,Schunck B.Determining optical flow [J].Artificial Intelligence,1981,17:185-203.

[4] Lucas B,Kanade T.An iterative image registration technique with application to stereo vision [C]//Proc DARPA Image Understanding Workshop,1981:121-130.

[5] Fleet D J,Jepson A D.Computation of component image velocity from local phase information [J].International Journal Computer Vision,1990,5(1):77-104.

[6] Black M J,Fleet D J.Probabilistic detection and tracking of motion boundaries [J].International Journal Computer Vision,2000,38(3):231-245.

[7] Brox T,Bruhn A,Papenberg N,et al.High Accuracy optical flow estimation based on a theory for warping [C]//Proc 8th European Conf Computer Vision,2004,4:25-36.

[8] Anandan P.A computational framework and an algorithm for the measurement of visual motion [J].International Journal Computer Vision,1989,2:283-310.

[9] Black M J,Anandan P.The robust estimation of multiple motions:parametric and piecewise smooth flow fields [J].Computer Vision and Image Understanding,1996,63:75-104.

[10] Memin E,Perez P.A Multigrid approach for hierarchical motion estimation [C]//Proc 6th Int Conf Computer Vision,1998:933-938.

[11] Terzopoulos D.Regularization of inverse visual problems involving discontinuities [J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1986,8:413-424.

[12] Terzopoulos D.Multilevel Reconstruction of Visual Surfaces:Variational Principles and Finite Element Representations [M].Multiresolution Image Processing and Analysis,New York:Springer Verlag,1984:273-310.

[13] Grimson W E L.From Images to Surfaces:a Computational Study of the Human Early Visual System [M].Cambridge,MA:MIT Press,1981.

[14] Karayiannis N B,Venetsanopoulos A N.Regularization theory in image restoration:The stabilizing functional approach [J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1990,38(7):1155-1179.

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