title: Topology preservation and regularity in estimated deformation fields.
abstract: A general formalism to impose topology preserving regularity on a given irregular deformation field is presented. The topology preservation conditions are derived with regard to the discrete approximations to the deformation field Jacobian in a two-dimensional image registration problem. The problem of enforcing topology preservation onto a given deformation field is formulated in terms of the deformation gradients, and solved using a cyclic projections approach. The generalization of the developed algorithm leads to a deformation field regularity control by limiting the per voxel volumetric change within a prescribed interval. Extension of the topology preservation conditions onto a three-dimensional registration problem is also presented, together with a comparative analysis of the proposed algorithm with respect to a Gaussian regularizer that enforces the same topology preservation conditions.
authors.affiliation: Section of Biomedical Image Analysis, Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104, USA.
authors.forename: Bilge
authors.initials: B
authors.lastname: Karaçali
authors.forename: Christos
authors.initials: C
authors.lastname: Davatzikos
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D003198:Computer Simulation; D004548:Elasticity; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008954:Models, Biological; D015233:Models, Statistical; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique