Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Fast erosion and dilation by contour processing and thresholding of distance maps
Pattern Recognition Letters
The Euclidean distance transform in arbitrary dimensions
Pattern Recognition Letters
Graphical Models and Image Processing
SIAM Review
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
SIAM Journal on Numerical Analysis
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Image filtering using morphological amoebas
Image and Vision Computing
2D Euclidean distance transform algorithms: A comparative survey
ACM Computing Surveys (CSUR)
Theoretical Foundations of Spatially-Variant Mathematical Morphology Part I: Binary Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Theoretical Foundations of Spatially-Variant Mathematical Morphology Part II: Gray-Level Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spatially-Variant Morpho-Hessian Filter: Efficient Implementation and Application
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
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We present an attribute weighted distance transform (AWDT) in which the distance metric is differentially weighted by an attribute of an associated labeled foreground object. Both external and internal transforms are presented. Foreground objects in a binary image are labeled, their attributes computed and a weighting function derived from the attribute values. The weighting function is then integrated into Ragnemalm's (1992) contour processing algorithm for computing the Euclidean distance transform. A threshold of the AWDT can be thought of as a dilation or erosion with a disk whose radius is spatially varying, according to attributes of nearby objects. We compare our method with that of Rosin and West (1995). Our method can be seen as an extension of this method. The usefulness of the method is illustrated in various examples.