On shortest paths in polyhedral spaces
SIAM Journal on Computing
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Precision-sensitive Euclidean shortest path in 3-space (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Global Minimum for Active Contour Models: A Minimal Path Approach
International Journal of Computer Vision
Constructing approximate shortest path maps in three dimensions
Proceedings of the fourteenth annual symposium on Computational geometry
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Optimizing Ackermann's function by incrementalization
Proceedings of the 2003 ACM SIGPLAN workshop on Partial evaluation and semantics-based program manipulation
3D brain surface matching based on geodesics and local geometry
Computer Vision and Image Understanding - Special issue on nonrigid image registration
New results on shortest paths in three dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Rubberband Algorithms for Solving Various 2D or 3D Shortest Path Problems
ICCTA '07 Proceedings of the International Conference on Computing: Theory and Applications
Analysis of the rubberband algorithm
Image and Vision Computing
Flying over a polyhedral terrain
Information Processing Letters
New lower bound techniques for robot motion planning problems
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Approximate Euclidean shortest paths amid convex obstacles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Fast Object Segmentation by Growing Minimal Paths from a Single Point on 2D or 3D Images
Journal of Mathematical Imaging and Vision
Exact Geodesics and Shortest Paths on Polyhedral Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
The class of simple cube-curves whose MLPs cannot have vertices at grid points
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Visiting convex regions in a polygonal map
Robotics and Autonomous Systems
| Hi-index | 0.00 |
Since the pioneering work by (Cohen and Kimmel, 1997) on finding a contour as a minimal path between two end points, shortest paths in volume images have raised interest in computer vision and image analysis. This paper considers the calculation of a Euclidean shortest path (ESP) in a three-dimensional (3D) polyhedral space Π. We propose an approximate κ(ε) ċ O(M|V|) 3D ESP algorithm, not counting time for preprocessing. The preprocessing time complexity equals O(M|E|+|F|+|V|log|V|) for solving a special, but 'fairly general' case of the 3D ESP problem, where Π does not need to be convex. V and E are the sets of vertices and edges of Π, respectively, and F is the set of faces (triangles) of Π. M is the maximal number of vertices of a so-called critical polygon, and κ(ε) = (L0 - L)/ε where L0 is the length of an initial path and L is the true (i.e., optimum) path length. The given algorithm solves approximately three (previously known to be) NP-complete or NP-hard 3D ESP problems in time κ(ε)ċO(k), where k is the number of layers in a stack, which is introduced in this paper as being the problem environment. The proposed approximation method has straightforward applications for ESP problems when analyzing polyhedral objects (e.g., in 3D imaging), of for 'flying' over a polyhedral terrain.