A nonlinear variational problem for image matching
SIAM Journal on Scientific Computing
Deformations incorporating rigid structures
Computer Vision and Image Understanding
Journal of Mathematical Imaging and Vision
Multigrid
Insight into Images: Principles and Practice for Segmentation, Registration, and Image Analysis
Insight into Images: Principles and Practice for Segmentation, Registration, and Image Analysis
Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity
Journal of Mathematical Imaging and Vision
A Multilevel Method for Image Registration
SIAM Journal on Scientific Computing
Image Registration with Guaranteed Displacement Regularity
International Journal of Computer Vision
Variational image registration with local properties
WBIR'06 Proceedings of the Third international conference on Biomedical Image Registration
Generalized Rigid and Generalized Affine Image Registration and Interpolation by Geometric Multigrid
Journal of Mathematical Imaging and Vision
Computers and Electrical Engineering
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Registration is a technique nowadays commonly used in medical imaging. A drawback of most of the current registration schemes is that all tissue is being considered as non-rigid (Staring et al., Proceedings of the SPIE 2006, vol. 6144, pp. 1---10, 2006). Therefore, rigid objects in an image, such as bony structures or surgical instruments, may be transformed non-rigidly. In this paper, we integrate the concept of local rigidity to the FLexible Image Registration Toolbox (FLIRT) (Haber and Modersitzki, in SIAM J. Sci. Comput. 27(5):1594---1607, 2006; Modersitzki, Numerical Methods for Image Registration, 2004). The idea is to add a penalty for local non-rigidity to the cost function and thus to penalize non-rigid transformations of rigid objects. As our examples show, the new approach allows the maintenance of local rigidity in the desired fashion. For example, the new scheme can keep bony structures rigid during registration. We show, how the concept of local rigidity can be integrated in the FLIRT approach and present the variational backbone, a proper discretization, and a multilevel optimization scheme. We compare the FLIRT approach to the B-spline approach. As expected from the more general setting of the FLIRT approach, our examples demonstrate that the FLIRT results are superior: much smoother, smaller deformations, visually much more pleasing.