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A Simple Regularizer for B-spline Nonrigid Image Registration That Encourages Local Invertibility

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2 Author(s)
Se Young Chun ; Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI ; Fessler, J.A.

Nonrigid image registration is an important task for many medical imaging applications. In particular, for radiation oncology it is desirable to track respiratory motion for thoracic cancer treatment. B-splines are convenient for modeling nonrigid deformations, but ensuring invertibility can be a challenge. This paper describes sufficient conditions for local invertibility of deformations based on B-spline bases. These sufficient conditions can be used with constrained optimization to enforce local invertibility. We also incorporate these conditions into nonrigid image registration methods based on a simple penalty approach that encourages diffeomorphic deformations. Traditional Jacobian penalty methods penalize negative Jacobian determinant values only at grid points. In contrast, our new method enforces a sufficient condition for invertibility directly on the deformation coefficients to encourage invertibility globally over a 3-D continuous domain. The proposed penalty approach requires substantially less compute time than Jacobian penalties per iteration.

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Selected Topics in Signal Processing, IEEE Journal of  (Volume:3 ,  Issue: 1 )