Estimation of the asymptotoc fractal dimension of grey-scale images (bibtex)
by Rigaut, Jean Paul, Schoëvaërt-Brossault, Damien, Downs, Angela M, Vassy, Jany, Millot, Guy and Portet, Stéphanie
Abstract:
A new method using grey-scale functions, asymptotic fractals (Rigaut 1984) and the Minkowski (1901) dilation/erosion, produces two graph asymptotes, one having a slope of 1 and the other a slope of D(T)-D+1 (where D(T) is the topological dimension and D the fractal dimension).The method allows an evaluation of scaling properties of a grey-scale image, estimation of D without iteration and analysis of fractal texture models.Images from cultured MCF7 cells of cytoskeleton intermediate filaments serve as example.
Reference:
Estimation of the asymptotoc fractal dimension of grey-scale images (Rigaut, Jean Paul, Schoëvaërt-Brossault, Damien, Downs, Angela M, Vassy, Jany, Millot, Guy and Portet, Stéphanie), In Acta Stereologica, volume 16, 1997.
Bibtex Entry:
@ARTICLE{rigaut1997estimation,
  author = {Rigaut, Jean Paul and Scho{\"e}va{\"e}rt-Brossault, Damien and Downs,
	Angela M and Vassy, Jany and Millot, Guy and Portet, St{\'e}phanie},
  title = {Estimation of the asymptotoc fractal dimension of grey-scale images},
  journal = {Acta Stereologica},
  year = {1997},
  volume = {16},
  pages = {209-213},
  number = {3},
  abstract = {A new method using grey-scale functions, asymptotic fractals (Rigaut
	1984) and the Minkowski (1901) dilation/erosion, produces two graph
	asymptotes, one having a slope of 1 and the other a slope of D(T)-D+1
	(where D(T) is the topological dimension and D the fractal dimension).The
	method allows an evaluation of scaling properties of a grey-scale
	image, estimation of D without iteration and analysis of fractal
	texture models.Images from cultured MCF7 cells of cytoskeleton intermediate
	filaments serve as example.},
  keywords = {morphology; mathematics; asymptotic fractals; grey-scale images; Minkowski
	dilation/erosion}
}
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