Geometric Optimization Problems in Computer Vision & Medical Imaging

ISBN-13: 9783639032260 / Angielski / Miękka / 2008 / 112 str.

Seok Lee; Frank Chongwoo Park

Opis

We explore various optimization problems which appear in computer vision and image processing. By exploiting the geometric structure of the underlying search spaces, we develop more efficient and robust ways to find optimal solutions. We present the Nelder-Mead algorithms on Lie groups and describe its application to medical image registration. A widely used approach to image registration involves finding the transformation that maximizes the mutual information between two images, with the transformation restricted to be either rigid-body (i.e., belonging to SE(3)) or volume-preserving (i.e., belonging to SL(3)). We present coordinate-invariant, geometric versions of the Nelder-Mead optimization algorithm on the transformation groups SL(3), SE(3), and its various subgroups, that are applicable to a wide class of image registration problems. Because the algorithms respect the geometric structure of the underlying transformation 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 geometrics algorithm.

O autorze

Lee, Seok Seok Lee, PhD: Studied Robotics at Seoul National University. R&D Staff Member at Samsung Advanced Institute of Technology, Korea. Frank Chongwoo Park, PhD: Studied Applied Mathematics at Harvard University. Professor at Seoul National University, Korea Chongwoo Park, Frank Seok Lee, PhD: Studied Robotics at Seoul National University. R&D Staff Member at Samsung Advanced Institute of Technology, Korea. Frank Chongwoo Park, PhD: Studied Applied Mathematics at Harvard University. Professor at Seoul National University, Korea