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Manuscript Title: Hyper-Fractal Analysis v04: Implementation of a fuzzy box-counting algorithm for image analysis of artistic works
Authors: I.V. Grossu, S.A. El-Shamali
Program title: Hyper-Fractal Analysis v04
Catalogue identifier: AEEG_v4_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 184(2013)1812
Programming language: MS Visual Basic 6.0.
Computer: PC.
Operating system: MS Windows 98 or later.
RAM: 100M
Supplementary material: A copy of the original manuscript containing Figure 1 is available.
Keywords: Fuzzy fractal dimension, Craquelure.
Classification: 14.

Does the new version supersede the previous version?: Yes

Nature of problem:
Estimating the fractal dimension of images

Solution method:
Fuzzy box-counting algorithm

Reasons for new version:
Following the idea [2,3] of investigating old paintings by fractal analysis of craquelure [4,5], we were faced with significant difficulties involved by the band-pass filter limitations. Trying to find a smoother way of separating information from noise, we implemented a fuzzy box-counting algorithm [6-8].
The fractal dimension [9] can be defined as:

df = limr→0(logN(r)/log(1/r))     (1)

where N(r) represents the number of boxes, with length r, needed to cover the object. The main change considered is related to the significance of N(r). As opposed to the classical approach, where each box contributes to N(r) with either 1 (black), or 0 (white), in the fuzzy version (Fig.1) each box contributes to N(r) with a rational number p = 1 - color code /(total number of colors - 1).

Summary of revisions:
  1. Implementation of a fuzzy box-counting algorithm for estimating the fractal dimension of images
  2. Optimization of the file open procedure

Running time:
In a first approximation, the algorithm is linear [2].

References:
[1] I.V. Grossu, I. Grossu, D. Felea, C. Besliu, Al. Jipa, T. Esanu, C.C. Bordeianu, E. Stan, Computer Physics Communications, 184 (2013) 1344-1345
[2] I.V. Grossu, C. Besliu, M.V. Rusu, Al. Jipa, C. C. Bordeianu, D. Felea, Computer Physics Communications, 180 (2009) 1999-2001
[3] I.V. Grossu, M.V. Rusu, A. Teodosiu, Fractals in a particular process. Fractals in the investigation of artistic works, in National Conference of Physics, Romania, Constanta, 21-23 September 2000.
[4] A. Teodosiu, Din universul ascuns al operei de arta, Allfa, Romania (2001) pp. 113-122
[5] S Bucklow, Consensus in the Classification of Craquelure, Hamilton Kerr Institute Bulletin, number 3, ed. A Massing, Hamilton Kerr Institute, University of Cambridge 2000: pp. 61-73
[6] X. Zhuang, Q. Meng, Artificial Intelligence in Medicine (2004) 32, 29-36
[7] D. Dumitrescu, Hariton Costin, Retele Neuronale. Teorie si aplicatii, Teora, Bucuresti, 1996, pp. 228-262
[8] D. Dumitrescu, Fuzzy Measures and the entropy of fuzzy partitions, J. Math, Anal. Appl., 176 (1993b) 359-373
[9] R.H. Landau, M.J. Paez and C.C. Bordeianu, Computational physics : Problem solving with computers, Wiley-VCH-Verlag, Weinheim, 2007, pp. 293-306