Abstract
This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03)Catalogue identifier: AEEG_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_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.: 745761No. of bytes in distributed program, including test data, etc.: 12544491Distribution format: tar.gzProgramming language: MS Visual Basic 6.0Computer: PCOperating system: MS Windows 98 or laterRAM: 100MClassification: 14Catalogue identifier of previous version: AEEG_v2_0Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831–832Does the new version supersede the previous version? YesNature of problem: Estimating the fractal dimension of 4D images.Solution method: Optimized implementation of the 4D box-counting algorithm.Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images.Summary of revisions:1.The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files.2.A new form was added for generating 2D, 3D, and 4D test data.Additional comments:1.The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1).2.The algorithm could be extended, with minimum effort, to higher number of dimensions.3.Easy integration with other applications by using the very simple comma separated values file format for storing multi-dimensional images.4.Implementation of χ2 test as a criterion for deciding whether an object is fractal or not.5.User friendly graphical interface. [Display omitted] Running time: In a first approximation, the algorithm is linear [2].
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