title: 3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization.
abstract: This paper deals with topology preservation in three-dimensional (3-D) deformable image registration. This work is a nontrivial extension of, which addresses the case of two-dimensional (2-D) topology preserving mappings. In both cases, the deformation map is modeled as a hierarchical displacement field, decomposed on a multiresolution B-spline basis. Topology preservation is enforced by controlling the Jacobian of the transformation. Finding the optimal displacement parameters amounts to solving a constrained optimization problem: The residual energy between the target image and the deformed source image is minimized under constraints on the Jacobian. Unlike the 2-D case, in which simple linear constraints are derived, the 3-D B-spline-based deformable mapping yields a difficult (until now, unsolved) optimization problem. In this paper, we tackle the problem by resorting to interval analysis optimization techniques. Care is taken to keep the computational burden as low as possible. Results on multipatient 3-D MRI registration illustrate the ability of the method to preserve topology on the continuous image domain.
authors.affiliation: Université Louis Pasteur (ULP), 67085 Strasbourg, France. vincent.noblet@ensps.u-strasbg.fr
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; D001185:Artificial Intelligence; D001921:Brain / Q000033:anatomy & histology*; D003198:Computer Simulation; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D008279:Magnetic Resonance Imaging; D008954:Models, Biological; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique