Adaptivity and group invariance in mathematical morphology

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Abstract

The standard morphological operators are (i) defined on Euclidean space, (ii) based on structuring elements, and (iii) invariant with respect to translation. There are several ways to generalise this. One way is to make the operators adaptive by letting the size or shape of structuring elements depend on image location or on image features. Another one is to extend translation invariance to more general invariance groups, where the shape of the structuring element spatially adapts in such a way that global group invariance is maintained. We review group-invariant morphology, discuss the relations with adaptive morphology, point out some pitfalls, and show that there is no inherent incompatibility between a spatially adaptive structuring element and global translation invariance of the corresponding morphological operators.
Original languageEnglish
Title of host publication2009 16TH IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOLS 1-6
Place of PublicationNEW YORK
PublisherIEEE (The Institute of Electrical and Electronics Engineers)
Pages2229-2232
Number of pages4
ISBN (Electronic)9781424456550
ISBN (Print)978-1-4244-5653-6
Publication statusPublished - 2009
Event16th IEEE International Conference on Image Processing - , Egypt
Duration: 7-Nov-200910-Nov-2009

Other

Other16th IEEE International Conference on Image Processing
Country/TerritoryEgypt
Period07/11/200910/11/2009

Keywords

  • Group morphology
  • adaptive morphology
  • space-variant structuring elements
  • THEORETICAL FOUNDATIONS
  • IMAGES

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