An Efficient Uniform Cost Algorithm Applied to Distance Transforms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance
Journal of the ACM (JACM)
Weighted distances based on neighbourhood sequences
Pattern Recognition Letters
Medial axis lookup table and test neighborhood computation for 3D chamfer norms
Pattern Recognition
Path-based distance with varying weights and neighborhood sequences
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Minimal-delay distance transform for neighborhood-sequence distances in 2D and 3D
Computer Vision and Image Understanding
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In recent years, the theory behind distance functions defined by neighbourhood sequences has been developed in the digital geometry community. A neighbourhood sequence is a sequence of integers, where each element defines a neighbourhood. In this paper, we establish the equivalence between the representation of convex digital disks as an intersection of half-planes ($\mathcal{H}$-representation) and the expression of the distance as a maximum of non-decreasing functions. Both forms can be deduced one from the other by taking advantage of the Lambek-Moser inverse of integer sequences. Examples with finite sequences, cumulative sequences of periodic sequences and (almost) Beatty sequences are given. In each case, closed-form expressions are given for the distance function and $\mathcal{H}$-representation of disks. The results can be used to compute the pair-wise distance between points in constant time and to find optimal parameters for neighbourhood sequences.