Optimal control approach to data set alignment

A mathematical problem arising from data set alignment is studied. For two given real-valued functions defined on two (2D or 3D) domains, separately, find a transformation between the two domains that optimizes a similarity functional between the functions. Our approach is based on optimal control w...

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Bibliographic Details
Published inApplied mathematics letters Vol. 21; no. 9; pp. 898 - 905
Main Authors Liao, Guojun G., Cai, Xianxin, Fleitas, Dion, Luo, Xiaonan, Wang, Jianmin, Xue, Jiaxing
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.09.2008
Elsevier
Subjects
Calculus of variations and optimal control
Data set alignment
Deformation method
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Optimal control
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Real functions
Sciences and techniques of general use
Data set alignment
Optimal control
Deformation method
Real function
Applied mathematics
Partial differential equation
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Summary:A mathematical problem arising from data set alignment is studied. For two given real-valued functions defined on two (2D or 3D) domains, separately, find a transformation between the two domains that optimizes a similarity functional between the functions. Our approach is based on optimal control with PDE (partial differential equation) constraints. Numerical examples are provided to demonstrate the effectiveness of the method.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2007.09.011