title: Analytic regularization of uniform cubic B-spline deformation fields.
abstract: Image registration is inherently ill-posed, and lacks a unique solution. In the context of medical applications, it is desirable to avoid solutions that describe physically unsound deformations within the patient anatomy. Among the accepted methods of regularizing non-rigid image registration to provide solutions applicable to medical practice is the penalty of thin-plate bending energy. In this paper, we develop an exact, analytic method for computing the bending energy of a three-dimensional B-spline deformation field as a quadratic matrix operation on the spline coefficient values. Results presented on ten thoracic case studies indicate the analytic solution is between 61-1371x faster than a numerical central differencing solution.
authors.affiliation: Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA 02114, USA.
authors.forename: James A
authors.initials: JA
authors.lastname: Shackleford
authors.forename: Qi
authors.initials: Q
authors.lastname: Yang
authors.forename: Ana M
authors.initials: AM
authors.lastname: Lourenço
authors.forename: Nadya
authors.initials: N
authors.lastname: Shusharina
authors.forename: Nagarajan
authors.initials: N
authors.lastname: Kandasamy
authors.forename: Gregory C
authors.initials: GC
authors.lastname: Sharp
mesh_terms: D000465:Algorithms; D006801:Humans; D008168:Lung / Q000000981:diagnostic imaging*; D009716:Numerical Analysis, Computer-Assisted; D011856:Radiographic Image Enhancement / Q000379:methods; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D013902:Radiography, Thoracic / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique; D014057:Tomography, X-Ray Computed / Q000379:methods*