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A PRIMAL-DUAL LEVEL SET METHOD FOR COMPUTING GEODESIC DISTANCES
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DOI：10.1137/24M1721086.png)
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Abstract
En 中文
The numerical computation of shortest paths or geodesics on surfaces, along with the associated geodesic distance, has a wide range of applications. Compared to Euclidean distance computation, these tasks are more complex due to the influence of surface geometry on the behavior of shortest paths. This paper introduces a primal-dual level set method for computing geodesic distances. A key insight is that the underlying surface can be implicitly represented as a zero level set, allowing us to formulate a constraint minimization problem. We employ the primal-dual methodology, along with regularization and acceleration techniques, to develop our algorithm. This approach is robust, efficient, and easy to implement. We establish a convergence result for the high resolution PDE system, and numerical evidence suggests that the method converges to a geodesic in the limit of refinement.
Keywords:
geodesic
primal-dual
level set
convergence
Journal
IF:
2.9
Papers:
29
Citations:
1.5W