Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection

Medical Image Analysis

Volumn 11, Issue 1, 2007, Pages 91-98

  Jennane, Rachid ^a   Harba, Rachid ^a   Lemineur, Gérald ^a   Bretteil, Stéphanie ^a   Estrade, Anne ^b   Benhamou, Claude Laurent ^c  

^a GDR ISIS   (France)

^b UNIVERSITÉ PARIS DESCARTES   (France)

^c CENTRE HOSPITALIER RÉGIONAL D ORLÉANS   (France)

Author keywords

Computed tomography; Fractal; Fractional Brownian motion; Osteoporosis; Self similarity; Trabecular bone; X ray images

Indexed keywords

BONE; BROWNIAN MOVEMENT; COMPUTER AIDED DIAGNOSIS; COMPUTER SIMULATION; COMPUTERIZED TOMOGRAPHY; IMAGE ANALYSIS; X RAYS;

FRACTIONAL BROWNIAN MOTION; OSTEOPOROSIS; TRABECULAR BONE;

MEDICAL IMAGING;

ARTICLE; BONE DENSITY; BONE RADIOGRAPHY; BONE STRUCTURE; COMPUTER ASSISTED TOMOGRAPHY; CONTROLLED STUDY; DIAGNOSTIC VALUE; DIGITAL IMAGING; EARLY DIAGNOSIS; FROZEN SECTION; HUMAN; HUMAN TISSUE; IMAGE ANALYSIS; IMAGE DISPLAY; IMAGE PROCESSING; MATHEMATICAL COMPUTING; MEDICAL ASSESSMENT; OSTEOPOROSIS; PRIORITY JOURNAL; QUANTITATIVE ANALYSIS; SIMULATION; THEORY; THREE DIMENSIONAL IMAGING; TRABECULAR BONE;

EID: 33846799343     PISSN: 13618415     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.media.2006.11.001     Document Type: Article

References (33)

1. Aggarwal N.D., Singh G.D., and Aggarwall R. A survey of osteoporosis using the calcaneum as an index. Int. Orthop. 10 (1986) 147-153
2. Barnsley M.F., Devaney R.L., Mandelbrot B.B., Peitgen H.O., Saupe D., and Voss R.F. The Science of Fractal Images (1988), Springer Verlag, New York
3. Benhamou L., Lespessailles E., Jacquet G., Harba R., Jennane R., Loussot T., Tourliere D., and Ohley W.J. Fractal organization of the trabecular bone images on calcaneus radiographs. J. Bone. Miner. Res. 9 (1994) 1909-1918
4. Bonami A., and Estrade A. Anisotropic analysis of some Gaussian models. J. Fourier Anal. Appl. 9 (2003) 215-236
5. Consensus Development Conference. Diagnosis, prophylaxis and treatment of osteoporosis. Am. J. Med. (1991) 107-110
6. Croucher P.I., Garrahan N.J., and Compton J.E. Assessment of cancellous bone structure: comparison of strut analysis, trabecular bone pattern factor, and narrow space star volume. J. Bone Miner. Res. 11 (1996) 955-961
7. Falconer K.J. The Geometry of Fractal Sets (1985), Cambridge University Press, Cambridge
8. Faulkner K.G., Gluer C.C., Majumdar S., Lang P., Engelke K., and Genant H.K. Noninvasive measurements of bone mass, structure and strength: current methods and experimental techniques. AJR 157 (1991) 1229-1237
9. Feder J. Fractals (1988), Plenum Press, New York and London
10. Goldstein S.A. The mechanical properties of trabecular bone: dependence on anatomic location and function. J. Biomech. 20 (1987) 1055-1061
11. Goulet R.W., Goldstein S.A., Ciarelli M.J., Kuhn J.L., Brown M.B., and Feldkampt L.A. The relation between the structural and orthogonal compressive properties of trabecular bone. J. Biomech. 27 (1994) 375-389
12. Guggenbuhl P., Bodic F., Hamel L., Basle M.F., and Chappard D. Texture analysis of X-ray radiographs of iliac bone is correlated with bone micro-CT. Osteoporos. Int. 17 3 (2006) 447-457
13. Harba R., Jacquet G., Jennane R., Loussot T., Benhamou C.L., Lespessailes E., and Tourlière D. Determination of fractal scaleson trabecular bone X-ray images. Fractals 2 3 (1994) 451-456
14. Jennane, R., Harba, R., Jacquet, G., 1996. Quality of synthesis and analysis methods for fractional Brownian motion. IEEE Digital Signal Processing WorkShop, Loen, Norway, pp. 307-310.
15. Jennane R., Harba R., and Jacquet G. Méthodes d'analyse du mouvement Brownien fractionnaire: théorie et résultats comparatifs. Traitement du Signal 18 5-6 (2001) 419-436
16. Jennane, R., Harba, R., Perrin, E., Bonami, A., Estrade, A., 2001. Analyse de champs Browniens fractionnaires anisotropes. In: GRETSI 2001, pp. 99-102.
17. Jennane R., Ohley W.J., Majumdar S., and Lemineur G. Fractal analysis of bone X-ray tomographic microscopy projections. IEEE Tans. Med. Imag. 20 5 (2001) 443-449
18. Kaplan L.M., and Kuo J.C.C. Extending self-similarity for fractional Brownian motion. IEEE Trans. Signal Proc. 42 12 (1994) 3526-3550
19. Lespessailles E., Jullien A., Eynard E., Harba R., Jacquet G., Ildefonse J.P., Ohley W., and Benhamou C.L. Biomechanical properties of human os calcanei: relationships with bone density and fractal evaluation of bone microarchitecture. J. Biomech. 31 (1998) 817-824
20. Lundhal T., Ohley W.J., Kay S.M., and Siffert R. Fractional Brownian motion: a maximum likelihood estimator and its application to image Texture. IEEE Trans. Med. Imaging 5 (1986) 152-161
21. Majumdar S., Link T.M., Ouyang X., Milard J., Lin J.C., and Tsag D. Fractal analysis of radiographs: comparison of techniques and correlation with bmd and biomechanics. J. Bone Miner. Res. 12 (1997) T652
22. Majumdar S., Link T.M., Millard J., Lin J.C., Augat P., Newitt D., Lane N., and Genant H.K. In vivo assessment of trabecular bone structure using fractal analysis of distal radius radiographs. Med. Phys. 27 11 (2000) 2594-2599
23. Mandelbrot B.B. The Fractal Geometry of Nature (1982), W.H. Freeman, San-Fransisco
24. Mandelbrot B.B., and Van Ness J. Fractional Brownian motion, fractional noise and applications. SIAM 10 (1968) 422-438
25. Parfitt A.M. Implications of architecture for the pathogenesis and prevention of vertebral fractural. Bone 13 Suppl. 2 (1992) 41-77
26. Pentland A.P. Fractal-based description of natural scenes. IEEE Trans. Patt. Mach. Int. PAMI-6 6 (1984) 661-674
27. Perrin E., Harba R., Jennane R., and Iribarren I. Piecewise fractional Brownian motion. IEEE Trans. Signal Process. 53 3 (2005) 1211-1215
28. Pothuaud L., Lespessailles E., Harba R., Jennane R., Royant V., Eynard E., and Benhamou C.L. Fractal analysis of trabecular bone texture on radiographs: discriminant value in post menopausal osteoporosis. Osteoporos. Int. 8 (1998) 618-625
29. Pothuaud L., Benhamou C.L., Poirion P., Lespessailles E., Harba R., and Levitz P. Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture. J. Bone Miner. Res. 15 4 (2000) 691-699
30. Prouteau S., Ducher G., Nanyan P., Lemineur G., Benhamou L., and Courteix D. Fractal analysis of bone texture: a screening tool for stress fracture risk?. Eur. J. Clin. Invest. 34 2 (2004) 137-142
31. Reed S., Lee P., and Truong T.K. Spectral representation of fractional Brownian motion in n dimensions and its properties. IEEE Trans. Inf. Theory 41 5 (1995) 1439-1451
32. Rockoff S.D., Scandrett J., and Zacher R. Quantitation of relevant image information: automated radiographic bone trabecular characterization. Radiology 101 (1971) 435-439
33. Tricot C., Quiniou J.F., Wehbi D., Roques-Carmes C., and Dubuc B. Evaluation de la dimension fractale d'un graphe. Revue Phys. Appl. 23 (1988) 111-124