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Fractal-based image texture analysis of trabecular bone architecture

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Abstract

Fractal-based image analysis methods are investigated to extract textural features related to the anisotropic structure of trabecular bone from the X-ray images of cubic bone specimens. Three methods are used to quantify image textural features: power spectrum, Minkowski dimension and mean intercept length. The global fractal dimension is used to describe the overall roughness of the image texture. The anisotropic features formed by the trabeculae are characterised by a fabric ellipse, whose orientation and eccentricity reflect the textural anisotropy of the image. Tests of these methods with synthetic images of known fractal dimension show that the Minkowski dimension provides a more accurate and consistent estimation of global fractal dimension. Tests on bone x-ray (eccentricity range 0.25–0.80) images indicate that the Minkowski dimension is more sensitive to the changes in textural orientation. The results suggest that the Minkowski dimension is a better measure for characterising trabecular bone anisotropy in the x-ray images of thick specimens.

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References

  • Acharya, R. S., LeBlanc, A., Shackelford, L., Swarnarkar, V., Krishnamurthy, R., Hausman, E., andLin, C. (1995). ‘Fractal analysis of bone structure with application to osteoporosis and microgravity effects’,Proc SPIE,2433, pp. 388–403

    Article  Google Scholar 

  • Anguiano, E., Pancorbo, M., andAguilar, M. (1993): ‘Fractal characterisation by frequency analysis. 1. Surfaces’,J. Microscopy,172, pp. 223–232

    Google Scholar 

  • Benhamou, C. L., Lespessailles, E., Jacquet, G., Harba, R., Jennane, R., Loussot, T., Tourliere, D., andOhley, W. (1994): ‘Fractal organisation of trabecular bone images, on calcaneus radiographs,’J. Bone Min. Res.,9, pp. 1909–1918

    Article  Google Scholar 

  • Bentzen, S. M., Hvid, I., andJorgensen, J. (1987): ‘Mechanical strength of tibial trabecular bone evaluation by X-ray computed tomography,’J. Biomech.,20, pp. 743–752

    Article  Google Scholar 

  • Berry, J. L., Webber, R. L., andJerome, C. (1994): ‘Change in trabecular architecture as measured by fractal dimension,’Proc. SPIE,2168, pp. 432–439

    Article  Google Scholar 

  • Carter, D. R., andHayes, W. C. (1977): ‘The compressive behaviour of bone as a two-phase porous structure,’J. Bone Joint Surg.,59-A, pp. 954–962

    Google Scholar 

  • Haralick, R. M., Sternberg, S. R., andZhuang X. (1987): ‘Image analysis using mathematical morphology,’IEEE Trans.,PAMI-9, pp. 532–550

    Google Scholar 

  • Harrigan, T. P., andMann, R. W. (1984): ‘Characterisation of microstructural anisotropy in orthotropic material using a second rank tensor,’J. Mat. Sci.,19, pp. 761–767

    Article  Google Scholar 

  • Hvid, I., Bentzen, S. M., Linde, F., Mosekilde, L., andPongsoipetch, B. (1989): ‘X-ray quantitative computed tomography: the relations,to physical properties of proximal tibial trabecular bone specimens,’J. Biomech.,22, pp. 837–844

    Article  Google Scholar 

  • Jiang, C. (1997): ‘Assessment of trabecular bone quality using quantitative image analysis’, PhD thesis, Cornell University, Ithaca, New York, USA

    Google Scholar 

  • Keaveny, T. M., Brochers, R. E., Gibson, L. J., andHayes, W. C. (1993): ‘Trabecular bone modulus and strength can depend on specimen geometry’,J. Biomech.,26, pp. 991–1000

    Article  Google Scholar 

  • Maragos, P. (1994): ‘Fractal signal analysis using mathematical morphology,’Adv. Electron. Electron. Phys.,88, pp. 199–246

    Google Scholar 

  • Mundinger, A., Wiesmeier, B., Dinkel, E., Helwig, A., Beck, A., andMoenting, J. S. (1993): ‘Quantitative image analysis of vertebral body architecture improved diagnosis in osteoporosis based on high-resolution computed tomography,’Br. J. Radiol.,66, pp. 209–213

    Article  Google Scholar 

  • Oxnard, C. E. (1993): ‘Bone and bones, architecture and stress, fossils and osteoporosis,’J. Biomech.,26, pp. 63–79

    Article  Google Scholar 

  • Riggs, B. L., Wahner, H. W., Dunn, W. L., Mazess, R. B., Offord, K. P., andMelton, L. J. (1981): ‘Differential changes in bone mineral density of the appendicular and axial skeleton with ageing,’J. Clin. Invest.,67, pp. 328–335

    Article  Google Scholar 

  • Ruttiman, U. E., Webber, R. L., andHazelrig, J. B. (1992): ‘Fractal dimension from radiographs of peridental alveolar bone: a possible diagnostic indicator of osteoporosis,’Oral Surg. Oral Med. Oral Pathol.,74, pp. 98–110

    Article  Google Scholar 

  • Samarabandu, J., Acharya, R., Hausmann, E., andAllen, K. (1993): ‘Analysis of bone X-rays using morphological fractals,’IEEE Trans. Med. Imag,12, pp. 466–470

    Article  Google Scholar 

  • Saupe, D. (1988): ‘Algorithms for random fractals,’inPeitgen, H. O., andSaupe, D. (Eds.): ‘The science of fractal dimension’ (Springer-Verlag, NY) pp. 71–113

    Google Scholar 

  • Serra, J. (1982): ‘Image analysis and mathematical morphology’, (Academic Press, London)

    MATH  Google Scholar 

  • Snyder, B. D., Piazza, S., Edwards, W. T., andHayes, W. C. (1993): ‘Role of trabecular morphology in the etiology of agerelated vertebral fracture,’Calcif. Tissue Int.,53, (Suppl 1), pp. S14-S22

    Article  Google Scholar 

  • Southard, T. E., Southard, K. A., Jakobsen, J. R., Hillis, S. L., andNajim, C. A. (1996): ‘Fractal dimension in radiographic analysis of alveolar process bone,’Oral Surg. Oral Med. Oral Pathol.,82, pp. 569–576

    Google Scholar 

  • Voss, R. F. (1985): ‘Random fractals forgeries,’,inEarnshaw, R. A. (Ed.): ‘Fundamental algorithms for computer graphics’ (Springer-Verlag, Berlin) pp. 805–835

    Google Scholar 

  • Voss, R. F. (1988): ‘Fractals in nature,’inPeitgen, H. O., andSaupe, D. (Eds.): ‘The science of fractal dimension’ (Springer-Verlag, NY) pp. 1–70

    Google Scholar 

  • Whitehouse, W. J. (1974): ‘The quantitative morphology of anisotropic trabecular bone,’J. Microscopy,101, pp. 153–168

    Google Scholar 

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Jiang, C., Pitt, R.E., Bertram, J.E.A. et al. Fractal-based image texture analysis of trabecular bone architecture. Med. Biol. Eng. Comput. 37, 413–418 (1999). https://doi.org/10.1007/BF02513322

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