Approximate Euclidean shortest path in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Length Estimation in 3-D Using Cube Quantization
Journal of Mathematical Imaging and Vision
Rubber Band Algorithm for Estimating the Length of Digitized Space-Curves
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Least-squares smoothing of 3D digital curves
Real-Time Imaging - Special issue on multi-dimensional image processing
Analysis of the rubberband algorithm
Image and Vision Computing
Euclidean shortest paths in simple cube curves at a glance
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
An approximation algorithm for computing minimum-length polygons in 3D images
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part IV
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
Finding the shortest path between two points in a simple polygon by applying a rubberband algorithm
PSIVT'06 Proceedings of the First Pacific Rim conference on Advances in Image and Video Technology
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We consider simple digital curves in a 3D orthogonal grid as special polyhedrally bounded sets. These digital curves model digitized curves or arcs in three-dimensional Euclidean space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. So far, no algorithm was known for the calculation of such a shortest polygonal curve. This paper provides an iterative algorithmic solution for approximating the minimum-length polygon of a given simple digital space-curve. The theoretical foundations of this algorithm are presented as well as experimental results.