WSEAS Transactions on Biology and Biomedicine

Print ISSN: 1109-9518
E-ISSN: 2224-2902

Volume 14, 2017

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

On the Reliability of the Fractal Dimension as a Scalar Characteristic of the Medical Images’ Contours

AUTHORS: Elena Hadzieva, Dijana C. Bogatinoska, Marija Shuminoska, Risto Petroski

Download as PDF

ABSTRACT: Medical images typically have irregular and fragmented contours. This is a strong motivation to use fractal geometry, rather than Euclidian geometry, for their description and characterization. In this paper we analyse a set of 100 images of melanoma and non-melanoma moles. The moles have their contours extracted with several tools and then the contours have their fractal dimension computed with distinct estimators. We have used descriptive statistics to depict that the fractal dimension does not give clear classification or systematization of the moles. We have also applied the student’s t-test to show that in the considered cases the two sets of fractal dimensions of melanoma and non-melanoma moles are not statistically different.

KEYWORDS: moles, contours, medical diagnosing, fractal dimension, reliability, student’s t-tests


[1] E. Claridge, P.N. Hall, M. Keefe, J.P. Allen, Shape Analysis for Classification of Malignant Melanoma, JBE 14 (3), 1992, pp. 229-234.

[2] K. Klein, T. Maier, V.C. Hirschfeld-Warneken, J.P. Spatz, Marker-Free Phenotyping of Tumor Cells by Fractal Analysis of Reflection Interference Contrast Microscopy Images, NL, ACS Publications, American Chemical Society, | Nano Lett. 2013, 13, 2013, pp. 5474-5479.

[3] P. Y. Kim, K.M. Iftekharuddin, P.G. Davey, M. Toth, A. Garas, G. Hollo, E.A. Essock, Novel Fractal Feature-Based Multiclass Glaucoma Detection and Progression Prediction, BHI, IEEE Journal of, 17, no.2, March 2013, pp. 269-276, doi: 10.1109/TITB.2012.2218661.

[4] M. Mastrolonardo, E. Conte, J.P. Zbilut, 2006. A fractal analysis of skin pigmented lesions using the novel tool of the variogram technique, CSF, 28, 2006, pp. 1119-1135.

[5] A. Piantanelli, P. Maponi, L. Scalise, S. Serresi, A. Cialabrini, A. Basso, Fractal characterisation of boundary irregularity in skin pigmented lesions, MBEC. Jul; 43 (4), 2005, pp. 436-42.

[6] E. Zagrouba, W. Barhoumi, A preliminary approach for the automated recognition of malignant melanoma, IAS, 23, 2004, pp. 121-135.

[7] R. Dobrescu, M. Dobrescu, S. Mocanu and D. Popescu, Medical Images Classification for Skin Cancer Diagnosis Based on Combined Texture and Fractal Analysis, WSEAS Transactions on Biology and Biomedicine, 7, no. 3, 2010. pp. 223-232.

[8] R. Lopes, N. Betrouni, Fractal and multifractal analysis: A review, Medical Image Analysis, 13, 2009, pp. 634-649.

[9] S. Criscuoli, M.P. Ras, I. Ermolli and M. Centrone, On the reliability of the fractal dimension measure of solar magnetic features and on its variation with solar activity, AA, 461, 2007, pp. 331-338, DOI: 10.1051/0004-6361:20065951.

[10] H. Ahammer, T.T.J. DeVaney, The influence of edge detection algorithms on the estimation of the fractal dimension of binary digital images, C, 14(1), 2004, pp. 183-8.

[11] B. Braverman, M. Tambasco, Scale-Specific Multifractal Medical Image Analysis, CMMM, 2013, Hindawi Publishing Corporation, Article ID 262931, 2013, 11 pages,

[12] A. R. Martin, N. Sabathiel, H. Ahammer, Noise dependency of algorithms for calculating fractal dimensions in digital images, CSF, 78, 2015, pp. 39-46.

[13] B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, 1982.

[14] K. J. Falconer, Fractal Geometry. Mathematical foundations and Applications, John Wiley and Sons, England, 1990

[15] M. F. Barnsley, Fractals everywhere, Academic Press, USA, 1988.

[16] E. Hadzieva, D. C. Bogatinoska, Lj. Gjergjeska, M. Shuminoska, R. Petreski, Review of the Software Tools for Estimating the Fractal Dimension, S. Loshkovska, S. Koceski (Editors): ICT Innovations 2015, Web Proceedings, ISSN 1857-7288, 2015, p. 201-211.

[17] E. Hadzieva, D. C. Bogatinoska, R. Petroski, M. Shuminoska, Lj. Gjergjeska, A. Karadimce, V. Trajkova, Is the Fractal Dimension of Contour-lines a reliable Tool For Classification of Medical Images?, accepted for publishing for MATEC Web of Conferences.

[18] O. Zmeškal, M. Vesely, M. Nezadal, M. Buchniček, Fractal Analysis of Image Structures, HarFA - Harmonic and Fractal Image Analysis, 2001, pp. 3-5.

[19] M. E. Celebi, A. Aslandogan, W. V. Stoecker, Unsupervised Border Detection in Dermoscopy Images, SRT, 13(4), 2007, pp. 454–462.

[20] M. E. Celebi, H. Kingravi, H. Iyatomi, A. Aslandogan, W. V. Stoecker, R. H. Moss, Border Detection in Dermoscopy Images Using Statistical Region Merging, SRT, 14(3), 2008, pp. 347–353.

[21] M. E. Celebi, H. Iyatomi, G. Schaefer, W. V. Stoecker, Lesion Border Detection in Dermoscopy Images, CMIG, 33(2), 2009, pp. 148–153.

[22] M. E. Celebi, Q. Wen, S. Hwang, H. Iyatomi, G. Schaefer, Lesion Border Detection in Dermoscopy Images Using Ensembles of Thresholding Methods, Skin Research and Technology, 19(1), 2013, pp. e252–258.

[23] S. Angenent, E. Pichon, A. Tannenbaum, Mathematical Methods in Medical Image Processing, BAMS. 43, 2006, pp. 365-396.





[28] ml


WSEAS Transactions on Biology and Biomedicine, ISSN / E-ISSN: 1109-9518 / 2224-2902, Volume 14, 2017, Art. #4, pp. 19-28

Copyright © 2017 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

Bulletin Board


The editorial board is accepting papers.

WSEAS Main Site