title: A simple regularizer for B-spline nonrigid image registration that encourages local invertibility.
abstract: 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 3D continuous domain. The proposed penalty approach requires substantially less compute time than Jacobian penalties per iteration.
authors.affiliation: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, 48109 USA.
authors.forename: Se Young
authors.initials: SY
authors.lastname: Chun
authors.forename: Jeffrey A
authors.initials: JA
authors.lastname: Fessler