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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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
Anguiano, E., Pancorbo, M., andAguilar, M. (1993): ‘Fractal characterisation by frequency analysis. 1. Surfaces’,J. Microscopy,172, pp. 223–232
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
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
Berry, J. L., Webber, R. L., andJerome, C. (1994): ‘Change in trabecular architecture as measured by fractal dimension,’Proc. SPIE,2168, pp. 432–439
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
Haralick, R. M., Sternberg, S. R., andZhuang X. (1987): ‘Image analysis using mathematical morphology,’IEEE Trans.,PAMI-9, pp. 532–550
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
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
Jiang, C. (1997): ‘Assessment of trabecular bone quality using quantitative image analysis’, PhD thesis, Cornell University, Ithaca, New York, USA
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
Maragos, P. (1994): ‘Fractal signal analysis using mathematical morphology,’Adv. Electron. Electron. Phys.,88, pp. 199–246
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
Oxnard, C. E. (1993): ‘Bone and bones, architecture and stress, fossils and osteoporosis,’J. Biomech.,26, pp. 63–79
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
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
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
Saupe, D. (1988): ‘Algorithms for random fractals,’inPeitgen, H. O., andSaupe, D. (Eds.): ‘The science of fractal dimension’ (Springer-Verlag, NY) pp. 71–113
Serra, J. (1982): ‘Image analysis and mathematical morphology’, (Academic Press, London)
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
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
Voss, R. F. (1985): ‘Random fractals forgeries,’,inEarnshaw, R. A. (Ed.): ‘Fundamental algorithms for computer graphics’ (Springer-Verlag, Berlin) pp. 805–835
Voss, R. F. (1988): ‘Fractals in nature,’inPeitgen, H. O., andSaupe, D. (Eds.): ‘The science of fractal dimension’ (Springer-Verlag, NY) pp. 1–70
Whitehouse, W. J. (1974): ‘The quantitative morphology of anisotropic trabecular bone,’J. Microscopy,101, pp. 153–168
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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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DOI: https://doi.org/10.1007/BF02513322