Hyper-Fractal Analysis v04: Implementation of a fuzzy box-counting algorithm for image analysis of artistic works

Abstract

This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 4D objects (Grossu et al. 2013 [1]). Following our attempt of investigating artistic works by fractal analysis of craquelure, we encountered important difficulties in filtering real information from noise. In this context, trying to avoid a sharp delimitation of “black” and “white” pixels, we implemented a fuzzy box-counting algorithm. New version program summaryProgram title: Hyper-Fractal Analysis v04Catalogue identifier: AEEG_v4_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v4_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 745999No. of bytes in distributed program, including test data, etc.: 12844235Distribution format: tar.gzProgramming language: MS Visual Basic 6.0Computer: PCOperating system: MS Windows 98 or laterRAM: 100MClassification: 14Catalogue identifier of previous version: AEEG_v3_0Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 1344Does the new version supercede the previous version?: YesNature of problem: estimating the fractal dimension of imagesSolution method: fuzzy box-counting algorithmReasons for new version:Following the idea [2, 3] of investigating old paintings by fractal analysis of craquelure [4, 5], we 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: (1)df=limr→0logN(r)log(1/r) 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 images2.Optimization of the file open procedure. [Display omitted] Running time: In a first approximation, the algorithm is linear [2].