Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Generalized distances in digital geometry
Information Sciences: an International Journal
The t-cost distance in digital geometry
Information Sciences: an International Journal
Local distances for distance transformations in two and three dimensions
Pattern Recognition Letters
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
Fast computation of cross-sections of 3D objects from their Medical Axis Transforms
Pattern Recognition Letters
A note on a method for generating points uniformly on n-dimensional spheres
Communications of the ACM
Use of medial axis transforms for computing normals at boundary points
Pattern Recognition Letters
Weighted digital distance transforms in four dimensions
Discrete Applied Mathematics
Weighted distances based on neighbourhood sequences
Pattern Recognition Letters
Weighted distances based on neighborhood sequences for point-lattices
Discrete Applied Mathematics
On Euclidean norm approximations
Pattern Recognition
On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension
Pattern Recognition Letters
A Low Complexity Euclidean Norm Approximation
IEEE Transactions on Signal Processing
Comments on "On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension"
Pattern Recognition Letters
A quasi-Euclidean norm to speed up vector median filtering
IEEE Transactions on Image Processing
Hyperspheres of weighted distances in arbitrary dimension
Pattern Recognition Letters
Linear combination of weighted t-cost and chamfering weighted distances
Pattern Recognition Letters
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In the past, different distance functions and their combinations had been proposed as good approximators of Euclidean metrics. In particular in recent years, a few distance functions with their general forms in n-dimensional real and integer spaces were identified for their improved performances in approximating corresponding Euclidean metrics. In this paper, we have identified a linear combination of two such distance functions from the families of weighted distances (WD) and weighted t-cost distances (WtD), which provides significant improvement over the past results in the quality of approximation. Further, we discuss a special case of linear combination, convex combination of distances, and provide optimal combinations by minimizing mean square error (MSE). In this case also the proposed pair of norms perform superior to other reported combinations. In our study, we also present new results related to characterization of overestimated and underestimated norms of Euclidean norm by their hyperspheres. The analysis leads to new results on theoretical bounds of maximum relative error (MRE) of some of the existing distance functions, including their linear combinations.