Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Length Estimation in 3-D Using Cube Quantization
Journal of Mathematical Imaging and Vision
Static and kinetic geometric spanners with applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Digital Curves in 3D Space and a Linear-Time Length Estimation Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Segmentation and Length Estimation of 3D Discrete Curves
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Approximation of 3D Shortest Polygons in Simple Cube Curves
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Minimum-Length Polygons in Simple Cube-Curves
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Rubber Band Algorithm for Estimating the Length of Digitized Space-Curves
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Convex Optimization
Analysis of the rubberband algorithm
Image and Vision Computing
New lower bound techniques for robot motion planning problems
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Minimum-length polygons of first-class simple cube-curves
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
Minimum-Length polygon of a simple cube-curve in 3d space
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
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
Shortest paths in a cuboidal world
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Automated DNA fragments recognition and sizing through AFM image processing
IEEE Transactions on Information Technology in Biomedicine
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Length measurements in 3D images have raised interest in image geometry for a long time. This paper discusses the Euclidean shortest path (ESP) to be calculated in a loop of face-connected grid cubes in the 3D orthogonal grid, which are defined by minimum-length polygonal (MLP) curves. We propose a new approximation algorithm for computing such an MLP. It is much simpler and easier to understand and to implement than previously published algorithms by Li and Klette. It also has a straightforward application for finding an approximate minimumlength polygonal arc (MLA), a generalization of the MLP problem. We also propose two heuristic algorithms for computing a simple cube-arc within a 3D image component, with a minimum number of cubes between two cubes in this component. This may be interpreted as being an approximate solution to the general ESP problem in 3D (which is known as being NP-hard) assuming a regular subdivision of the 3D space into cubes of uniform size.