Geometric Optimization Problems in Computer Vision & Medical Imaging: Multimodal

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Geometric Optimization Problems in Computer Vision & Medical Imaging by Seok Lee, Frank Chongwoo Park

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.

FORMAT
Paperback LANGUAGE
English CONDITION
Brand New Publisher Description

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.

Details ISBN3639032268 Author Frank Chongwoo Park Short Title GEOMETRIC OPTIMIZATION PROBLEM Pages 112 Language English ISBN-10 3639032268 ISBN-13 9783639032260 Media Book Format Paperback Year 2008 Subtitle Multimodal 3D Volume Registration, Discrete & Differential Pose Estimation DOI 10.1604/9783639032260 UK Release Date 2008-06-04 Imprint VDM Verlag Dr. Mueller E.K. Country of Publication Germany Illustrations black & white illustrations Publisher VDM Verlag Dr. Mueller E.K. Publication Date 2008-06-04 Audience General
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