Properties of Ridges and Cores for TwoDimensional Images
 James Damon
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Pizer and Eberly introduced the “core” as the analogue of the medial axis for greyscale images. For twodimensional images, it is obtained as the “ridge” of a “medial function” defined on 2 + 1dimensional scale space. The medial function is defined using Gaussian blurring and measures the extent to which a point is in the center of the object measured at a scale. Numerical calculations indicate the core has properties quite different from the medial axis. In this paper we give the generic properties of ridges and cores for twodimensional images and explain the discrepancy between core and medial axis properties. We place cores in a larger “relative critical set structure”, which coherently relates disjoint pieces of core. We also give the generic transitions which occur for sequences of images varying with a parameter such as time. The genericity implies the stability of the full structure in any compact viewing area of scale space under sufficiently small L2 perturbations of the image intensity function. We indicate consequences for finding cores and also for adding “markings” to completely determine the structure of the medial function.
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 Title
 Properties of Ridges and Cores for TwoDimensional Images
 Journal

Journal of Mathematical Imaging and Vision
Volume 10, Issue 2 , pp 163174
 Cover Date
 19990301
 DOI
 10.1023/A:1008379107611
 Print ISSN
 09249907
 Online ISSN
 15737683
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 ridges and cores
 relative critical set
 Gaussian blurring
 medial functions
 genericity
 Industry Sectors
 Authors

 James Damon ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599, USA