Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Generalized distances in digital geometry
Information Sciences: an International Journal
Distance functions in digital geometry
Information Sciences: an International Journal
Octagonal distances for digital pictures
Information Sciences: an International Journal
The t-cost distance in digital geometry
Information Sciences: an International Journal
Best simple octagonal distances in digital geometry
Journal of Approximation Theory
On digital distance transforms in three dimensions
Computer Vision and Image Understanding
On approximating Euclidean metrics by digital distances in 2D and 3D
Pattern Recognition Letters
Distance transforms for three-dimensional grids with non-cubic voxels
Computer Vision and Image Understanding
Distances based on neighbourhood sequences in non-standard three-dimensional grids
Discrete Applied Mathematics
Weighted distances based on neighbourhood sequences
Pattern Recognition Letters
General neighborhood sequences in Zn
Discrete Applied Mathematics
Distance with generalized neighbourhood sequences in nD and ∞D
Discrete Applied Mathematics
Weighted neighborhood sequences in non-standard three-dimensional grids: parameter optimization
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Generating distance maps with neighbourhood sequences
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Comments on "On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension"
Pattern Recognition Letters
Hyperspheres of weighted distances in arbitrary dimension
Pattern Recognition Letters
Linear combination of norms in improving approximation of Euclidean norm
Pattern Recognition Letters
Linear combination of weighted t-cost and chamfering weighted distances
Pattern Recognition Letters
| Hi-index | 0.10 |
In this work, we propose a new class of distance functions called weighted t-cost distances. This function maximizes the weighted contribution of different t-cost norms in n-dimensional space. With proper weight assignment, this class of function also generalizes m-neighbor and octagonal distances. A non-strict upper bound (denoted as R"u in this work) of its relative error with respect to Euclidean norm is derived and an optimal weight assignment by minimizing R"u is obtained. However, it is observed that the strict upper bound of weighted t-cost norm may be significantly lower than R"u. For example, an inverse square root weight assignment leads to a good approximation of Euclidean norm in arbitrary dimension.