Avoiding symmetry-breaking spatial non-uniformity in deformable image registration via a quasi-volume-preserving constraint

Intermediate Deformable Image Registration via Windowed Cross-Correlation

In population and longitudinal imaging studies that employ deformable image registration, more accurate results can be achieved by initializing deformable registration with the results of affine registration where global misalignments have been considerably reduced. Such affine registration, however, is limited to linear transformations and it cannot account for large nonlinear anatomical variations, such as those between pre- and post-operative images or across different subject anatomies. In this work, we introduce a new intermediate deformable image registration (IDIR) technique that recovers large deformations via windowed cross-correlation, and provide an efficient implementation based on the fast Fourier transform. We evaluate our method on 2D X-ray and 3D magnetic resonance images, demonstrating its ability to align substantial nonlinear anatomical variations within a few iterations.

Infant FreeSurfer: An automated segmentation and surface extraction pipeline for T1-weighted neuroimaging data of infants 0-2 years

The development of automated tools for brain morphometric analysis in infants has lagged significantly behind analogous tools for adults. This gap reflects the greater challenges in this domain due to: 1) a smaller-scaled region of interest, 2) increased motion corruption, 3) regional changes in geometry due to heterochronous growth, and 4) regional variations in contrast properties corresponding to ongoing myelination and other maturation processes. Nevertheless, there is a great need for automated image-processing tools to quantify differences between infant groups and other individuals, because aberrant cortical morphologic measurements (including volume, thickness, surface area, and curvature) have been associated with neuropsychiatric, neurologic, and developmental disorders in children. In this paper we present an automated segmentation and surface extraction pipeline designed to accommodate clinical MRI studies of infant brains in a population 0-2 year-olds. The algorithm relies on a single channel of T1-weighted MR images to achieve automated segmentation of cortical and subcortical brain areas, producing volumes of subcortical structures and surface models of the cerebral cortex. We evaluated the algorithm both qualitatively and quantitatively using manually labeled datasets, relevant comparator software solutions cited in the literature, and expert evaluations. The computational tools and atlases described in this paper will be distributed to the research community as part of the FreeSurfer image analysis package.

Multimodal Image Registration through Simultaneous Segmentation

Multimodal image registration facilitates the combination of complementary information from images acquired with different modalities. Most existing methods require computation of the joint histogram of the images, while some perform joint segmentation and registration in alternate iterations. In this work, we introduce a new non-information-theoretical method for pairwise multimodal image registration, in which the error of segmentation - using both images - is considered as the registration cost function. We empirically evaluate our method via rigid registration of multi-contrast brain magnetic resonance images, and demonstrate an often higher registration accuracy in the results produced by the proposed technique, compared to those by several existing methods.

Mid-space-independent deformable image registration

Aligning 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 mathematical definition of the mid-space. In particular, the set of possible solutions is typically restricted by the constraints that are enforced on the transformations to prevent the mid-space from drifting too far from the native image spaces. The use of an implicit atlas has been proposed as an approach to mid-space image registration. In this work, we show that when the atlas is aligned to each image in the native image space, the data term of implicit-atlas-based deformable registration is inherently independent of the mid-space. In addition, we show that the regularization term can be reformulated independently of the mid-space as well. We derive a new symmetric cost function that only depends on the transformation morphing the images to each other, rather than to the atlas. This eliminates the need for anti-drift constraints, thereby expanding the space of allowable deformations. We provide an implementation scheme for the proposed framework, and validate it through diffeomorphic registration experiments on brain magnetic resonance images.

Constrained H1-regularization schemes for diffeomorphic image registration

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov regularization ensures well-posedness. Our scheme augments standard smoothness regularization operators based on H1- and H2-seminorms with a constraint on the divergence of the velocity field, which resembles variational formulations for Stokes incompressible flows. In our formulation, we invert for a stationary velocity field and a mass source map. This allows us to explicitly control the compressibility of the deformation map and by that the determinant of the deformation gradient. We also introduce a new regularization scheme that allows us to control shear. We use a globalized, preconditioned, matrix-free, reduced space (Gauss-)Newton-Krylov scheme for numerical optimization. We exploit variable elimination techniques to reduce the number of unknowns of our system; we only iterate on the reduced space of the velocity field. Our current implementation is limited to the two-dimensional case. The numerical experiments demonstrate that we can control the determinant of the deformation gradient without compromising registration quality. This additional control allows us to avoid oversmoothing of the deformation map. We also demonstrate that we can promote or penalize shear whilst controlling the determinant of the deformation gradient.

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 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 pairwise registration. In this work, we show that by aligning the atlas to each image in the native image space, implicit-atlas-based pairwise registration can be made independent of the mid-space, thereby eliminating the need for anti-drift constraints. We derive a new symmetric cost function that only depends on a single transformation morphing one image to the other, and validate it through diffeomorphic registration experiments on brain magnetic resonance images.