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A Generalized Framework for Analytic Regularization of Uniform Cubic B-Spline Deformation Fields

K Shah1, J Shackleford1, N Kandasamy1, G Sharp2*, (1) Drexel University, Philadelphia, PA, (2) Massachusetts General Hospital, Boston, MA


(Sunday, 7/12/2020) 4:30 PM - 5:30 PM [Eastern Time (GMT-4)]

Room: Track 2

Purpose: Deformable image registration is an inherently ill-posed problem. As such, one must bias the registration to physically meaningful transforms by regularizing it via an appropriate penalty term. This regularization penalty is usually a function of vector field derivatives that can be calculated either analytically or numerically. A numerical approach, however, is computationally expensive depending on the image size, and therefore a computationally efficient analytical framework has been developed.

Methods: Cubic B-splines were used as the registration transform. A generalized framework was developed for five distinct regularizers: diffusion, curvature, linear elastic, third-order and total displacement. The approach was validated and benchmarked by testing the accuracy and speed-up achieved by each regularizer with their numerical counterpart. Ten thoracic 4DCT images from the DIR-Lab dataset were used for these experiments.

Results: The maximum relative difference between the analytical and numerical solutions was 7.4%. Analytic regularization ran significantly faster -- up to two orders of magnitude -- than central-differencing based numerical solutions. For example, for a volume of 512 * 512 *512 voxels with a control-point spacing of 30 mm, the analytical form of the curvature regularizer executes in 1.1 secs, whereas the numerical counterpart requires 137.1 secs. OpenMP-based implementations further reduce the single-threaded execution time linearly with the number of CPU cores.

Conclusion: A fast and general framework that supports five different regularizers for deformable image registration has been developed. The computation time is almost negligible when compared to the time required for a numerical gradient computation. This new approach is superior to numeric calculation for most registration problems.

Funding Support, Disclosures, and Conflict of Interest: This material is based upon work supported by the National Science Foundation under Grant Nos. 1553436, 1642345 and 1642380.


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