Computing Optimal Beams in Two and Three Dimensions
Identifieur interne : 007A84 ( Main/Exploration ); précédent : 007A83; suivant : 007A85Computing Optimal Beams in Two and Three Dimensions
Auteurs : Danny Z. Chen [États-Unis] ; Xiaobo Sharon Hu [États-Unis] ; Jinhui Xu [États-Unis]Source :
- Journal of Combinatorial Optimization [ 1382-6905 ] ; 2003-06-01.
English descriptors
Abstract
Abstract: The problem of computing an optimal beam among weighted regions (called the optimal beam problem) arises in several applied areas such as radiation therapy, stereotactic brain surgery, medical surgery, geological exploration, manufacturing, and environmental engineering. In this paper, we present computational geometry techniques that enable us to develop efficient algorithms for solving various optimal beam problems among weighted regions in two and three dimensional spaces. In particular, we consider two types of problems: the covering problems (seeking an optimal beam to contain a specified target region), and the piercing problems (seeking an optimal beam of a fixed shape to pierce the target region). We investigate several versions of these problems, with a variety of beam shapes and target region shapes in 2-D and 3-D. Our algorithms are based on interesting combinations of computational geometry techniques and optimization methods, and transform the optimal beam problems to solving a collection of instances of certain special non-linear optimization problems. Our approach makes use of interesting geometric observations, such as utilizing some new features of Minkowski sums.
Url:
DOI: 10.1023/A:1024484412699
Affiliations:
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In this paper, we present computational geometry techniques that enable us to develop efficient algorithms for solving various optimal beam problems among weighted regions in two and three dimensional spaces. In particular, we consider two types of problems: the covering problems (seeking an optimal beam to contain a specified target region), and the piercing problems (seeking an optimal beam of a fixed shape to pierce the target region). We investigate several versions of these problems, with a variety of beam shapes and target region shapes in 2-D and 3-D. Our algorithms are based on interesting combinations of computational geometry techniques and optimization methods, and transform the optimal beam problems to solving a collection of instances of certain special non-linear optimization problems. Our approach makes use of interesting geometric observations, such as utilizing some new features of Minkowski sums.</div></front></TEI><affiliations><list><country><li>États-Unis</li></country><region><li>Indiana</li><li>État de New York</li></region></list><tree><country name="États-Unis"><region name="Indiana"><name sortKey="Chen, Danny Z" sort="Chen, Danny Z" uniqKey="Chen D" first="Danny Z." last="Chen">Danny Z. Chen</name></region><name sortKey="Chen, Danny Z" sort="Chen, Danny Z" uniqKey="Chen D" first="Danny Z." last="Chen">Danny Z. Chen</name><name sortKey="Hu, Xiaobo Sharon" sort="Hu, Xiaobo Sharon" uniqKey="Hu X" first="Xiaobo Sharon" last="Hu">Xiaobo Sharon Hu</name><name sortKey="Hu, Xiaobo Sharon" sort="Hu, Xiaobo Sharon" uniqKey="Hu X" first="Xiaobo Sharon" last="Hu">Xiaobo Sharon Hu</name><name sortKey="Xu, Jinhui" sort="Xu, Jinhui" uniqKey="Xu J" first="Jinhui" last="Xu">Jinhui Xu</name><name sortKey="Xu, Jinhui" sort="Xu, Jinhui" uniqKey="Xu J" first="Jinhui" last="Xu">Jinhui Xu</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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