Digital geometry PDF20151118-30219-H9TALP

Title	Digital geometry
Author	Reinhard Klette
Pages	5
File Size	62.2 KB
File Type	PDF20151118-30219-H9TALP
Total Downloads	105
Total Views	354

Summary

Information Sciences 148 (2002) 123–127 www.elsevier.com/locate/ins Digital geometry a,* b Azriel Rosenfeld , Reinhard Klette a Institute for Advanced Computer Studies, Center for Automation Research, University of Maryland, College Park, MD 20742-3275, USA b Information Technology, Tamaki Campus, U...

Description

Digital geometry Azriel Rosenfeld a,*, Reinhard Klette b a Institute for Advanced Computer Studies, Center for Automation Research, University of Maryland, College Park, MD 20742-3275, USA b Information Technology, Tamaki Campus, University of Auckland, Auckland, New Zealand Received 30 December 2001; accepted 18May 2002 Abstract Digital geometry is the study of geometrical properties of subsets of digital images. If the digitization is su ciently ne-grained, such properties can be regarded as approx- imations to the corresponding properties of the ''real'' sets that gave rise, by digitization to the digital sets; but it is also important to de ne how the properties can be computed for the digital sets themselves. Questions of particular interest include how images and image subsets are digitized; how geometric properties are de ned for digitized sets; the computational complexity ofcomputing them––in particular, whetherthey can be computed using simple (e.g., local)operations; characterizing image operations that preserve them; and characterizing digital objects that could be the digitizations of real objectsthat have given geometric properties. Conceptsthat have been extensively studied include topological properties (connected components, boundaries); curves and surfaces; straightness, curvature, convexity, and elongatedness; distance, extent, length area, surface area, volume, and moments; shape description, similarity, symmetry, and relative position; shape simpli cation and skeletonization. Ó 2002 Elsevier Science Inc. All rights reserved. Digital geometry emerged with the rise of computer technologies in the second half of the 20th century as an application-oriented eld, in uenced by the new possibilities in computer graphics and digital image analysis. It has its mathematical roots in graph theory and discrete topology; it deals with sets of Information Sciences 148(2002) 123–127 www.elsevier.com/locate/ins * Corresponding author. Tel.: +1-301-405-4526; fax: +1-301-314-9115. E-mail address: [email protected] (A. Rosenfeld). 0020-0255/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 0 - 0 2 5 5 ( 0 2 ) 0 0 2 84 - 0...