Efficiently Computing Shortest Paths on Curved Surfaces with Newton's Method
Geodesics are important in the study of metric geometry. Although Euler–Lagrange equations are used to formulate geodesics, closed-form solutions are not available except in a few cases. Therefore, researchers have to seek for numerical methods instead of finding geodesics in computer vision and gra...
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| Veröffentlicht in: | Engineering letters 2023-02, Vol.31 (1), p.338 |
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| creator | Liu, Ruyuan Xiao, Fengyang Meng, Wenlong |
| description | Geodesics are important in the study of metric geometry. Although Euler–Lagrange equations are used to formulate geodesics, closed-form solutions are not available except in a few cases. Therefore, researchers have to seek for numerical methods instead of finding geodesics in computer vision and graphics. In this paper, we first formulate the computation of geodesics on a parametric surface into an optimizationdriven problem and then propose an efficient solution to the optimization problem with a second-order Newton iteration method. The comparative study shows that our algorithm is an order of magnitude faster than the existing approaches for the same level of accuracy. |
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Although Euler–Lagrange equations are used to formulate geodesics, closed-form solutions are not available except in a few cases. Therefore, researchers have to seek for numerical methods instead of finding geodesics in computer vision and graphics. In this paper, we first formulate the computation of geodesics on a parametric surface into an optimizationdriven problem and then propose an efficient solution to the optimization problem with a second-order Newton iteration method. 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Although Euler–Lagrange equations are used to formulate geodesics, closed-form solutions are not available except in a few cases. Therefore, researchers have to seek for numerical methods instead of finding geodesics in computer vision and graphics. In this paper, we first formulate the computation of geodesics on a parametric surface into an optimizationdriven problem and then propose an efficient solution to the optimization problem with a second-order Newton iteration method. The comparative study shows that our algorithm is an order of magnitude faster than the existing approaches for the same level of accuracy.</abstract><cop>Hong Kong</cop><pub>International Association of Engineers</pub></addata></record> |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Algorithms Comparative studies Computer vision Euler-Lagrange equation Geodesy Geometry Iterative methods Metric space Newton methods Numerical methods Optimization Shortest-path problems |
| title | Efficiently Computing Shortest Paths on Curved Surfaces with Newton's Method |
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