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. 2013 Dec 23:7:39.
doi: 10.3389/fninf.2013.00039. eCollection 2013.

Explicit B-spline regularization in diffeomorphic image registration

Nicholas J Tustison  1 , Brian B Avants  2
Affiliations

Explicit B-spline regularization in diffeomorphic image registration

Nicholas J Tustison et al. Front Neuroinform. .

Abstract

Diffeomorphic mappings are central to image registration due largely to their topological properties and success in providing biologically plausible solutions to deformation and morphological estimation problems. Popular diffeomorphic image registration algorithms include those characterized by time-varying and constant velocity fields, and symmetrical considerations. Prior information in the form of regularization is used to enforce transform plausibility taking the form of physics-based constraints or through some approximation thereof, e.g., Gaussian smoothing of the vector fields [a la Thirion's Demons (Thirion, 1998)]. In the context of the original Demons' framework, the so-called directly manipulated free-form deformation (DMFFD) (Tustison et al., 2009) can be viewed as a smoothing alternative in which explicit regularization is achieved through fast B-spline approximation. This characterization can be used to provide B-spline "flavored" diffeomorphic image registration solutions with several advantages. Implementation is open source and available through the Insight Toolkit and our Advanced Normalization Tools (ANTs) repository. A thorough comparative evaluation with the well-known SyN algorithm (Avants et al., 2008), implemented within the same framework, and its B-spline analog is performed using open labeled brain data and open source evaluation tools.

Keywords: Advanced normalization tools; Insight Toolkit; diffeomorphisms; directly manipulated free-form deformation; spatial normalization.

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Figures

Figure 1
Figure 1
Illustration of the greedy SyN formulation. Given images IA and IB, the symmetric set-up requires finding the two transform pairs (ϕ1, ϕ−11) (ϕ2, ϕ−12) which map to/from the respective images to the midway point. During optimization, the update field at each iteration is determined from the metric field gradient taken at the midway point, i.e., ∇ Π~ (I ◦ ϕ1(0.5), J ◦ ϕ2(0.5)). The full forward and inverse transforms are found through composition, i.e., ϕ = ϕ1 ◦ ϕ−12 and ϕ−1 = ϕ2 ◦ ϕ−11.
Listing 1
Listing 1
Representative script containing antsRegistration and antsApplyTransforms command calls used for evaluation.
Figure 2
Figure 2
Canonical views for each of the five cohort-specific templates generated using the ANTs tools as described in Avants et al. (2010). The pseudo-geodesic transform between subjects is created from the composition of transforms to/from the relevant template.
Figure 3
Figure 3
Illustration of generating a pseudo-geodesic for any two subjects within the MGH10 cohort. Once the transforms between the template and each subject are calculated, the mapping between any two subjects is found by composition of forward and inverse transforms. For example, in the MGH data set, the pseudo-geodesic transform to map Subject g4 to Subject g7 is found by composing the forward transform from g4 to the template with the inverse transform from the template to g7 (green dashed lines).
Figure 4
Figure 4
Axial views of sample labelings for a member of each data set. The second row consists of the original labelings with the third row being refined versions of those labelings using the MALF algorithm (Wang et al., 2013). These refinements provide more consistency between labelings and improved comparative assessments between algorithms.
Figure 5
Figure 5
Dice results for both algorithms for each subject warped to every other subject using the pseudo- geodesic transform. Each row corresponds to one of the five data sets used for evaluation. For each data set we include a plotting of all individual label Dice results by volume and a combined label box plotting. The left and right halves show the respective results for original and MALF-derived labelings. The black dashed regression line (y ~ x3) illustrates how performance difference varies with label volume for each cohort.
Figure 6
Figure 6
Violin plots of the range of log Jacobian values (95th%—5th%) for all deformable transforms from each subject to its corresponding template. B-spline SyN demonstrates a tendency to produce a much greater range of log Jacobian values.
Figure 7
Figure 7
Randomly selected axial slices showing qualitative differences between SyN and B-spline SyN. Crosshairs indicate regions of maximal Jacobian difference.
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