Distances defined by neighborhood sequences
Pattern Recognition
Morphological structuring element decomposition
Computer Vision, Graphics, and Image Processing
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Some characterizations of city block distance
Pattern Recognition Letters
A contour characterization for multiply connected figures
Pattern Recognition Letters
Pipeline architectures for morphologic image analysis
Machine Vision and Applications
Knight's distance in digital geometry
Pattern Recognition Letters
A Multiscanning Approach Based on Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Spectrum and Multiscale Shape Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal Morphological Pattern Restoration from Noisy Binary Images
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)
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Journal of Mathematical Imaging and Vision
Distance transformation on two-dimensional irregular isothetic grids
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
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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A generalized distance transformation (GDT) of binary images and the related medial axis transformation (MAT) are discussed. These transformations are defined in a discrete space of arbitrary dimension and arbitrary grids. The GDT is based on successive morphological operations using alternatively N arbitrary structuring elements: N is called the period of the GDT. The GDT differs from the classical distance transformations based on a point-to-point distance. However, the well-known chessboard, city-block, and hexagonal distance transformations are special cases of the one-period GDT, whereas the octagonal distance transformation is a special case of the two-period GDT. In this paper, both one- and two-period GDTs are discussed. Different sequential algorithms are proposed for computing such GDTs. These algorithms need a maximum of two scannings of the image. The computation of the MAT is also discussed.