The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition

Michael Keane, K. Simon, Boris Solomyak

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.

Original languageEnglish
Pages (from-to)279-292
Number of pages14
JournalFundamenta Mathematicae
Volume180
Issue number3
Publication statusPublished - 2003

Fingerprint

Image Recognition
Directed Graph
Attractor
Overlap
Fractal
Self-affine
Iterated Function System
Line
Contraction
Open Problems
Restriction
Partial
Similarity

Keywords

  • Fractal image recognition
  • Fractals with overlapping cylinders
  • Graph directed IFS
  • Self-affine fractals

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition. / Keane, Michael; Simon, K.; Solomyak, Boris.

In: Fundamenta Mathematicae, Vol. 180, No. 3, 2003, p. 279-292.

Research output: Contribution to journalArticle

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