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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Bibliographic Details
Published inEngineering letters Vol. 31; no. 1; p. 338
Main Authors Liu, Ruyuan, Xiao, Fengyang, Meng, Wenlong
Format Journal Article
LanguageEnglish
Published Hong Kong International Association of Engineers 23.02.2023
Subjects
Algorithms
Comparative studies
Computer vision
Euler-Lagrange equation
Geodesy
Geometry
Iterative methods
Metric space
Newton methods
Numerical methods
Optimization
Shortest-path problems
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Summary: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.
ISSN:1816-093X
1816-0948