Mid-Space-Independent Symmetric Data Term for Pairwise Deformable Image Registration
Aligning a pair of images in a mid-space is a common approach to ensuring that deformable image registration is symmetric – that it does not depend on the arbitrary ordering of the input images. The results are, however, generally dependent on the choice
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Martinos Center, Massachusetts General Hospital, Harvard Medical School, Boston, USA {iman,mreuter,msabuncu,fischl}@nmr.mgh.harvard.edu 2 Basque Center on Cognition, Brain and Language (BCBL), San Sebastian, Spain [email protected] 3 CSAIL, Massachusetts Institute of Technology, Cambridge, USA
Abstract. Aligning a pair of images in a mid-space is a common approach to ensuring that deformable image registration is symmetric – that it does not depend on the arbitrary ordering of the input images. The results are, however, generally dependent on the choice of the mid-space. In particular, the set of possible solutions is typically affected by the constraints that are enforced on the two transformations (that deform the two images), which are to prevent the mid-space from drifting too far from the native image spaces. The use of an implicit atlas has been proposed to define the mid-space for registration. In this work, by aligning the atlas to each image in the native image space, we make implicit-atlas-based pairwise registration independent of the mid-space, thereby eliminating the need for anti-drift constraints. We derive a new symmetric data term that only depends on a single transformation morphing one image to the other, and validate it through diffeomorphic registration experiments on brain MR images.
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Introduction
Image registration – i.e., computation of a set of dense spatial correspondences among images – is a central step in most population and longitudinal imaging studies. Since linear transformation is usually not sufficient to account for cross-subject variation and temporal changes in the anatomy, deformable image registration often becomes necessary. In pairwise deformable registration, the choice of the reference space in which the two images are compared affects the registration, making the resulting deformation field dependent on this choice, and leading to registration asymmetry [1-11]. Pairwise registration has been proposed to be symmetrized by minimizing the average of two cost functions, each using one input image as the reference space [1-4], yet integrating the mismatch measure non-uniformly in the native space of the interpolated image [11]. In a different approach to achieve symmetry, both images are deformed and compared in a mid-space, hence the invariance to the ordering of images [5-10]. Such approaches essentially minimize their cost functions with respect to two © Springer International Publishing Switzerland 2015 N. Navab et al. (Eds.): MICCAI 2015, Part II, LNCS 9350, pp. 263–271, 2015. DOI: 10.1007/978-3-319-24571-3_32
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transformations and that take the two input images to the mid-space. However, without additional constraints, this increases the degrees of freedom of the problem twofold, compared to the end result of pairwise registration that is the one transformation, = ∘ , taking the second input image to the first. Furthermore, if the images are compared in the mid-space (that depends on and ), the optimization algorithm is allowed to update the m
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