Image Registration with Local Rigidity Constraints Jan Modersitzki Institute of Mathematics, University of L¨ ubeck, Wallstraße 40, D-23560 L¨ ubeck Email: modersitzki@math.uni-luebeck.de Abstract. Registration is a technique nowadays commonly used in med- ical imaging. A drawback of most of the current registration schemes is that all tissue is being considered as non-rigid. 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 lo- cal rigidity to the FLexible Image Registration Toolbox (FLIRT). 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 exam- ples show, the new approach allows the maintenance of local rigidity in the desired fashion. For example, the new scheme is able to keep bony structures rigid during registration. 1 Introduction The incorporation of pre-knowledge in registration is a key for getting meaningful results. For many registration tasks, the images inhibits an classification of soft and hard tissue. It thus seems to be natural to ask for transformations keeping hard tissue rigid. However, current registration schemes consider all parts of the tissue as non-rigid [1]. As a consequence rigid objects, such as bony structures or surgical instruments, can be transformed non-rigidly. Other consequences are that tumor growth between follow-up images may be concealed, or that struc- tures containing contrast material in only one of the images may be compressed by the registration scheme. Starting with the variational framework of the FLexible Image Registration Toolbox (FLIRT) [2, 3], we integrate the concept of local rigidity in terms of an additional penalty term. For a transformation, rigidity is measured by linearity, orthogonality, and orientation preservation. We also compared our approach to the non-rigidity penalized but B-spline based scheme in [1]. As it turned out, the FLIRT approach gives visually more pleasing results: a perfect match (i.e. transformed template equals reference) is achieved with a much more regular transformation; see, e.g., Figure 1. 2 State of the art and new contribution There are currently two main numerical approaches to image registration. The first one is based on an expansion of the wanted transformation in terms of