Fractal properties from 2D curvature on multiple scales
by , , ,
Abstract:
Basic properties of 2-D-nonlinear scale-space representations of images are considered. First, local-energy filters are used to estimate the Hausdorff dimension, DH, of images. A new fractal dimension, DN, defined as a property of 2-D-curvature representations on multiple scales, is introduced as a natural extension of traditional fractal dimensions, and it is shown that the two types of fractal dimensions can give a less ambiguous description of fractal image structure. Since fractal analysis is just one (limited) aspect of scale-space analysis, some more general properties of curvature representations on multiple scales are considered. Simulations are used to analyze the stability of curvature maxima across scale and to illustrate that spurious resolution can be avoided by extracting 2-D-curvature features.
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PDF URL: http://dx.doi.org/10.1117/12.146648
Reference:
Fractal properties from 2D curvature on multiple scales (Erhardt Barth, Christoph Zetzsche, Mario Ferraro, Ingo Rentschler), In Geometric Methods in Computer Vision II (Baba C. Vemuri, ed.), SPIE-Intl Soc Optical Eng, 1993.
Bibtex Entry:
@InProceedings{Barth1993a,
  author    = {Erhardt Barth and Christoph Zetzsche and Mario Ferraro and Ingo Rentschler},
  title     = {Fractal properties from {2D} curvature on multiple scales},
  booktitle = {Geometric Methods in Computer Vision {II}},
  year      = {1993},
  editor    = {Baba C. Vemuri},
  pages     = {87-99},
  month     = {jun},
  publisher = {{SPIE}-Intl Soc Optical Eng},
  abstract  = {Basic properties of 2-D-nonlinear scale-space representations of images are considered. First, local-energy filters are used to estimate the Hausdorff dimension, DH, of images. A new fractal dimension, DN, defined as a property of 2-D-curvature representations on multiple scales, is introduced as a natural extension of traditional fractal dimensions, and it is shown that the two types of fractal dimensions can give a less ambiguous description of fractal image structure. Since fractal analysis is just one (limited) aspect of scale-space analysis, some more general properties of curvature representations on multiple scales are considered. Simulations are used to analyze the stability of curvature maxima across scale and to illustrate that spurious resolution can be avoided by extracting 2-D-curvature features.},
  doi       = {10.1117/12.146648},
  url       = {10.1117/12.146648">http://dx.doi.org/10.1117/12.146648},
}