Skip to main content
SpringerLink
Log in

Fractal characterisation of boundary irregularity in skin pigmented lesions

  • Published:
Medical and Biological Engineering and Computing Aims and scope Submit manuscript

Abstract

A growing literature shows researcher's interest in fractal analysis, arising from its ability to describe and characterise quantitatively the complexity of several tumour profiles. The aim of the work was to investigate the fractal properties of skin pigmented lesion boundaries. Although melanoma is one of the most aggressive tumours, early detection and a high rate of diagnostic accuracy, followed by timely excision, can allow complete recovery in melanoma patients. A modified approach to fractal dimension estimation was performed that was able to consider, in a data fit procedure, the range in which lesions show fractal properties. Identification of this zone is the most important step towards a correct fractal analysis procedure. The method was checked against a known fractal dimension object (Koch's curve) with an error of 0.007. The fractal dimension was estimated in 110 skin pigmented lesions and showed a significantly increasing linear regression (p<0.05), from common naevi to naevi with dysplasia to melanomas. This result is important for screening, as it can inform the decision to excise precociously malignant lesions or to avoid unnecessary removal of benign ones. The limitations of the method are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Argenziano, G., Fabbrocini, G., Carli, P., de Giorgi, V., Sammarco, E., andDelfino, M. (1998): ‘Epiluminescence microscopy for the diagnosis of doubtful melanocytic skin lesions. Comparison of the ABCD rule of dermatoscopy and a new 7-point checklist based on pattern analysis’,Arch. Dermatol.,134, pp. 1563–1570

    Article  Google Scholar 

  • Argenziano, G.,et al. (2003): ‘Dermoscopy of pigmented skin lesions: Results of a consensus meeting via the Internet’,J. Am. Acad. Dermatol.,48, pp. 679–693

    Article  Google Scholar 

  • Baish, J. W., andJain, R. K. (2000): ‘Fractals and cancer’,Cancer Res.,60, pp. 3683–3688

    Google Scholar 

  • Baumann, G., Barth, A., andNonnenmacher, T. F. (1994): ‘Measuring fractal dimensions of cell contours: practical approaches and their limitations’, inNonnenmacher, T.F., Losa, G.A., andWeibel, E.R. (Eds): ‘Fractals in biology and medicine’ (Birkhauser-Verlag Press, Basel, 1994), pp. 182–189.

    Google Scholar 

  • Brown, J. H., Gupta, V. K., Li, B. L., Milne, B. T., Restrepo, C., andWest, G. B. (2002): ‘The fractal nature of nature: power laws, ecological complexity and biodiversity’,Philos. Trans. R. Soc. Lond. B. Biol. Sci.,357, pp. 619–626

    Google Scholar 

  • Claridge, E., Hall, P. N., Keefe, M., andAllen, J. P. (1992): ‘Shape analysis for classification of malignant melanoma’,J. Biomed. Eng.,14, pp. 229–234.

    Google Scholar 

  • Cross, S. S., andCotton, D. W. K. (1992): ‘The fractal dimension may be a useful morphometric discriminant in histopatholy’,J. Pathol.,166, pp. 409–411

    Article  Google Scholar 

  • Cross, S. S., McDonagh, A. J. G., Stephenson, T. J., Cotton, D. W. K., andUnderwood, J. C. E. (1995): ‘Fractal and integer-dimensional geometric analysis of pigmented skin lesions’,Am. J. Dermatopathol.,17, pp. 374–378

    Google Scholar 

  • Cross, S. S. (1997): ‘Fractals in pathology’,J. Pathol.,182, pp. 1–8

    Article  Google Scholar 

  • Goldberger, A. L., Peng, C. K., andLipsitz, L. A. (2002): ‘What is physiologic complexity and how does it change with aging and disease?’,Neurobiol. Aging,23, pp. 23–26

    Article  Google Scholar 

  • Grana, C., Pellacani, G., Cucchiara, R., andSeidenari, S. (2003): ‘A new algorithm for border description of polarized light surface microscopic images of pigmented skin lesions’,IEEE Trans. Med. Imag.,22, pp. 959–964

    Google Scholar 

  • Kenet, R. O., Kang, S., Kenet, B. J., Fitzpatrick, T. B., Sober, A. J., andBarnhill, R. L. (1993): ‘Clinical diagnosis of pigmented lesions using digital epiluminescence microscopy’,Arch. Dermatol.,129, pp. 157–174

    Article  Google Scholar 

  • Kopf, A. W., Gross, D. F., Rogers, G. S., Rigel, D. S., Hellman, L. J., Levenstein, M., Welkovich, B., Friedman, R. J., Roses, D. F., andBart, R. S. (1987): ‘Prognostic index for malignant melanoma’,Cancer,59, pp. 1236–1241

    Google Scholar 

  • Landini, G., Misson, G. P., andMurray, P. I. (1993): ‘Fractal analysis of the normal human retinal fluorescein angiogram’,Curr. Eye Res.,12, pp. 23–27

    Google Scholar 

  • Landini, G. (1998): ‘Complexity in tumour growth patterns’, inLosa, G. A., Merlini, D., Nonnenmacher, T. F., andWeibel, E. R. (Eds): ‘Fractals in biology and medicine’ (Birkhauser-Verlag Press, Basel, 1998), pp. 268–283

    Google Scholar 

  • Lee, T. K., McLean, D. I., andAtkins, M. S. (2003): ‘Irregularity index: a new border irregularity measure for cutaneous melanocytic lesions’,Med. Image Anal.,7, pp. 47–64

    Article  Google Scholar 

  • Libertini, G., Cesini, G., Paroncini, M., andCodagnone, G. (1997): ‘Evaluation and realization of the lighting conditions for early diagnosis of melanoma’.Proc. LUX Europa, 8th European Lighting Conf., 11–14 May, Amsterdam

  • Losa, G. A. (1995): ‘Fractals in pathology: are they really useful?’,Pathologica,87, pp. 310–317

    Google Scholar 

  • Losa, G. A., andNonnenmacher, T. F. (1996): ‘Self-similarity and fractal irregularity in pathologic tissues’,Mod. Pathol.,9, pp. 174–182

    Google Scholar 

  • Losa, G. A. (2002): ‘Fractal morphometry of cell complexity’,Riv. Biol.,95, pp. 239–258

    Google Scholar 

  • Mandelbrot, B. B. (1983): ‘The fractal geometry of nature’ (W.H Freeman, and Co, San Francisco, 1983)

    Google Scholar 

  • Miracco, C., Bianciardi, G., Perrone, A., Bruni, A., Lazzi, S., andLuzi, P. (1998): ‘Fractal dimension of epithelial-connective tissue interface in basal cell carcinoma of the skin’ inLosa, G. A., Merlini, D., Nonnenmacher, T. F., andWeibel, E. R. (Eds): ‘Fractals in biology and medicine’ (Birkhauser-Verlag Press, Basel, 1998), pp. 284–293

    Google Scholar 

  • Piantanelli, A., Libertini, G., Rossolini, G., Basso, A., Bertoni-Freddari, C., andPiantanelli, L. (1998): ‘Measuring fractal dimension in biology and medicine: analysis of image contour’,J. Biol. Res.,74, pp. 57–60

    Google Scholar 

  • Piantanelli, A., Serresi, S., Giacchetti, A., Libertini, G., Ricotti, G., Rossolini, G., Zaia, A., Basso, A., andPiantanelli, L. (2000): ‘Estimation of image contour fractal dimension of human pigmented skin lesions’,Riv. Biol.,93, pp. 341–343

    Google Scholar 

  • Piantanelli, L., Rossolini, G., Basso, A., Piantanelli, A., Malavolta, M., andZaia, A. (2001): ‘Use of mathematical models of survivorship in the study of biomarkers of aging: the role of heterogeneity’,Mech. Ageing Dev.,122, pp. 1461–1475

    Google Scholar 

  • Piantanelli, A., Zaia, A., Serresi, S., Pasquali, C., Ricotti, G., Rossolini, G., Balietti, M., Basso, A., andMurri, R. (2002a): ‘Fractal dimension as a parameter for measuring complexity: an application on skin pigmented lesion images’. Proc. 3rd European Congress of Biogerontology,Biogerontology,3, pp. 94–95

    Google Scholar 

  • Piantanelli, A., Serresi, S., Ricotti, G., Rossolini, G., Zaia, A., Basso, A., andPiantanelli, L. (2002b): ‘Color-based method for fractal dimension estimation of pigmented skin lesion contour’, inLosa, G. A., Merlini, D., Nonnenmacher, T. F. andWeibel, E. R. (Eds): ‘Fractals in Biology and Medicine’ (Birkhauser-Verlag Press, Basel, 2002), pp. 127–136

    Google Scholar 

  • Piccolo, D., Smolle, J., Argenziano, G., Wolf, I. H., Braun, R., Cerroni, L., Ferrari, A., Hofmann-Wellenhof, R., Kenet, R. O., Magrini, F., Mazzocchetti, G., Pizzichetta, M. A., Schaeppi, H., Stolz, W., Tanaka, M., Kerl, H., Chimenti, S., andSoyer, H. P. (2000): ‘Teledermoscopy results of a multicentre study on 43 pigmented skin lesions’,J. Telemed. Telecare,6, pp. 132–137

    Article  Google Scholar 

  • Piccolo, D., Ferrari, A., Peris, K., Diadone, R., Ruggeri, B., andChimenti, S. (2002): ‘Dermoscopic diagnosis by a trained clinician vs. a clinician with minimal dermoscopy training vs. computeraided diagnosis of 341 pigmented skin lesions: a comparative study’,Br. J. Dermatol.,147, pp. 481–486

    Article  Google Scholar 

  • Sedivy, R., Windischberger, C. H., Svozil, K., Moser, E., andBreitenecker, G. (1999): ‘Fractal analysis: an objective method for identifying a typical nuclei in dysplastic lesions of the cervix uteri’,Gynecol. Oncol.,75, pp. 78–83

    Article  Google Scholar 

  • Seidenari, S., Burroni, M., Dell'eva, G., Pepe, P., andBelletti, B. (1995): ‘Computerized evaluation of pigmented skin lesion images recorded by a videomicroscope: comparison between polarizing mode observation and oil/slide mode observation’,Skin Res. Technol.,1, pp. 187–191

    Google Scholar 

  • Soyer, HP., Argenziano, G., Chimenti, S., andRuocco, V. (2001): ‘Dermoscopy of pigmented skin lesions’,Eur. J. Dermatol.,11, pp. 270–277

    Google Scholar 

  • Stolz, W., Riemann, A., Cognetta, A. B.,et al. (1994): ‘ABCD rule of dermatoscopy: a new practical method for early recognition of malignant melanoma’,Eur. J. Dermatol.,4, pp. 521–527

    Google Scholar 

  • Stolz, W., Braun-Falco, O., Bilek, P., Landthaler, M., Burgdorf, W. H. C., andCognetta, A. B. (2002): ‘Color atlas of dermatoscopy’ (Blackwell Publishing, Berlin, 2002)

    Google Scholar 

  • Vilela, M. J., Martins, M. L., andBoschetti, S. R. (1995): ‘Fractal patterns for cells in culture’,J. Pathol.,177, pp. 103–107

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center of Biochemistry, INRCA, Ancona, Italy

    A. Piantanelli & A. Basso

  2. Unit of Dermatology, INRCA, Ancona, Italy

    A. Piantanelli & S. Serresi

  3. Department of Mathematics, Università di Camerino, Camerino, Italy

    P. Maponi & A. Cialabrini

  4. Department of Mechanics, Università Politecnica delle Marche, Ancona, Italy

    L. Scalise

Authors
  1. A. Piantanelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Maponi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Scalise
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Serresi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Cialabrini
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. A. Basso
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Scalise.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Piantanelli, A., Maponi, P., Scalise, L. et al. Fractal characterisation of boundary irregularity in skin pigmented lesions. Med. Biol. Eng. Comput. 43, 436–442 (2005). https://doi.org/10.1007/BF02344723

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02344723

Keywords

Search

Navigation