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

Michael Keane, K. Károly, and Boris Solomyak. "The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition." Fundamenta Mathematicae 180.3 (2003): 279-292. <http://eudml.org/doc/282630>.

@article{MichaelKeane2003,
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.},
author = {Michael Keane, K. Károly, Boris Solomyak},
journal = {Fundamenta Mathematicae},
keywords = {graph directed iterated function systems; self-affine fractals; fractal image compression; Hausdorff dimension; iterated function system},
language = {eng},
number = {3},
pages = {279-292},
title = {The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition},
url = {http://eudml.org/doc/282630},
volume = {180},
year = {2003},
}

TY - JOUR
AU - Michael Keane
AU - K. Károly
AU - Boris Solomyak
TI - The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition
JO - Fundamenta Mathematicae
PY - 2003
VL - 180
IS - 3
SP - 279
EP - 292
AB - 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.
LA - eng
KW - graph directed iterated function systems; self-affine fractals; fractal image compression; Hausdorff dimension; iterated function system
UR - http://eudml.org/doc/282630
ER -