A topological characterization of thinning
type: Item
instance of: scholarly article
title: A topological characterization of thinning
zbMATH Open document ID: 0622.68072
DOI: 10.1016/0304-3975(86)90164-7
author: Christian Ronse
published in: Theoretical Computer Science
publication date: 1986-01-01T00:00:00Z
review text: This is a very interesting and fundamental paper proving a basic assumption underlying almost all thinning algorithms. Namely, that to remove one set D from another set F, with the desire to preserve the topology of F, one can do so pixel by pixel, testing only if the number of connected components in figure and background change. The paper neatly proceeds from the notion of preservation of digital topology, to bijectivity of mappings between components, to removal of components preserving the bijectivity (called 'strong-deletability'), to removal of a single pixel satisfying the conservation of components in figure and background ('deletability'). Well written, concise, and highly readable. A problem in reading is that 'S is k-connected' is used in a double sense: in one sense it means 'S consists of components determined by the fact that points are k-connected', in the second sense it means 'S consists of 1 component whose points are k-connected'. In all theorems and derivations the second sense is used, in some definitions (1 and 2), examples and figures 1 and 2 the first sense is apparently used. This is confusing, since application of the theorems to the examples produces contradictions. One should read '(strongly) deletable' and 'componentwise (strongly) deletable' to resolve these problems. This intermediate step, removing a set component by component, ought to have been indicated more clearly.
Mathematics Subject Classification ID: 68T10
zbMATH DE Number: 4009848
zbMATH Keywords: binary images
zbMATH Keywords: skeleton
zbMATH Keywords: thinning
zbMATH Keywords: preservation
zbMATH Keywords: digital topology
zbMATH Keywords: removal of components
zbMATH Keywords: bijectivity
zbMATH Keywords: deletability
MaRDI profile type: Publication
full work available at URL: 0304-3975(86)90164-7
OpenAlex ID: W1974655611
cites work: Q5618910
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description: scientific article; zbMATH DE number 4009848