title: Geometric direct search algorithms for image registration.
abstract: A widely used approach to image registration involves finding the general linear transformation that maximizes the mutual information between two images, with the transformation being rigid-body [i.e., belonging to SE(3)] or volume-preserving [i.e., belonging to SL(3)]. In this paper, we present coordinate-invariant, geometric versions of the Nelder-Mead optimization algorithm on the groups SL(3), SE(3), and their various subgroups, that are applicable to a wide class of image registration problems. Because the algorithms respect the geometric structure of the underlying groups, they are numerically more stable, and exhibit better convergence properties than existing local coordinate-based algorithms. Experimental results demonstrate the improved convergence properties of our geometric algorithms.
authors.affiliation: Seoul National University, Seoul, Korea. lee.seok@gmail.com
authors.forename: Seok
authors.initials: S
authors.lastname: Lee
authors.forename: Minseok
authors.initials: M
authors.lastname: Choi
authors.forename: Hyungmin
authors.initials: H
authors.lastname: Kim
authors.forename: Frank Chongwoo
authors.initials: FC
authors.lastname: Park
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique