title: Accurate inversion of 3-D transformation fields.
abstract: This correspondence addresses the inversion of 3-D transformation fields, which is a problem that typically arises in image warping problems. A topology preserving parametric B-spline-based representation of the deformation field is considered. Topology preservation ensures that the transformation is a one-to-one mapping and consequently that it is invertible. Inverting such transformation fields amounts to solving a system of nonlinear equations. To tackle this problem, we rely on interval analysis techniques. The proposed algorithm yields a solution whose accuracy is user-controlled. This method may be extended to any dense transformation field and also to deformations defined on a grid of points, by considering a projection in the space of topology preserving B-spline-based deformation fields. The performance of the algorithm is illustrated on transformation fields coming from intersubject brain registration.
authors.forename: Vincent
authors.initials: V
authors.lastname: Noblet
authors.forename: Christian
authors.initials: C
authors.lastname: Heinrich
authors.forename: Fabrice
authors.initials: F
authors.lastname: Heitz
authors.forename: Jean-Paul
authors.initials: JP
authors.lastname: Armspach
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity