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A higher‐order PDE‐based image registration approach
Author(s) -
Grimm Volker,
Henn Stefan,
Witsch Kristian
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.467
Subject(s) - mathematics , affine transformation , image registration , image warping , linear map , linear system , partial differential equation , algorithm , rotation (mathematics) , mathematical optimization , image (mathematics) , computer vision , computer science , mathematical analysis , geometry , pure mathematics
This paper addresses the problem of image registration with higher‐order partial differential equation (PDE) methods. From the study of existing affine‐linear and non‐linear methods, a new framework is proposed that unifies common image registration methods within a generic formulation. Currently image registration strategies are classified into either affine‐linear or non‐linear methods subject to the underlying transformations. The new approach combines both strategies to obtain proper approximations which are invariant under global geometrical distortion (shearing), anisotropic resolution (scale changes), as well as rotation and translation. To achieve this favourable property, a modified gradient flow approach is proposed which uses an operator with a kernel consisting of affine‐linear transformations. An approximation with finite differences leads to a large singular linear system. The pseudo‐inverse solution of this system can be computed efficiently by augmenting the singular system to a regular system. Numerical experiments show the improvements compared to unmodified gradient flow approaches. Copyright © 2005 John Wiley & Sons, Ltd.