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A New Method for 3D Thinning of Hybrid Shaped Porous Media Using Artificial Intelligence. Application to Trabecular Bone

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Abstract

Curve and surface thinning are widely-used skeletonization techniques for modeling objects in three dimensions. In the case of disordered porous media analysis, however, neither is really efficient since the internal geometry of the object is usually composed of both rod and plate shapes. This paper presents an alternative to compute a hybrid shape-dependant skeleton and its application to porous media. The resulting skeleton combines 2D surfaces and 1D curves to represent respectively the plate-shaped and rod-shaped parts of the object. For this purpose, a new technique based on neural networks is proposed: cascade combinations of complex wavelet transform (CWT) and complex-valued artificial neural network (CVANN). The ability of the skeleton to characterize hybrid shaped porous media is demonstrated on a trabecular bone sample. Results show that the proposed method achieves high accuracy rates about 99.78%–99.97%. Especially, CWT (2nd level)-CVANN structure converges to optimum results as high accuracy rate—minimum time consumption.

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References

  1. di Baja, G. S., and Thiel, E., Computing and comparing distance-driven skeletons. World Scientific, Aspects of Visual Form Processing, pp. 465–486, 1994.

  2. Malandain, G., and Fern’andez-Vidal, S., Euclidean skeletons. Image Vis. Comput. 16(5):317–327, 1998.

    Article  Google Scholar 

  3. Kong, T. Y., and Rosenfeld, A., Digital topology: introduction and survey. Comput. Vis. Graph. Image Process. 48(3):357–393, 1989.

    Article  Google Scholar 

  4. Lam, L., Lee, S.-W., and Suen, C., Thinning methodologies-a comprehensive survey. IEEE Trans. Pattern Anal. Mach. Intell. 14:869–885, 1992.

    Article  Google Scholar 

  5. Ma, C. M., and Sonka, M., A fully parallel 3d thinning algorithm and its applications. Comp. Vis. Image Underst. 64(3):420–433, 1996.

    Article  Google Scholar 

  6. Palagyi, K., and Kuba, A., A 3D 6-subiteration thinning algorithm for extracting medial lines. Pattern Recogn. Lett. 19(7):613–627, 1998.

    Article  MATH  Google Scholar 

  7. Bertrand, G., A parallel thinning algorithm for medial surfaces. Pattern Recogn. Lett. 16:979–996, 1995.

    Article  Google Scholar 

  8. Gong, W., and Bertrand, G., A simple parallel 3D thinning algorithm. in International Conference on Pattern Recognition (ICPR), pp. 188–190, 1990.

  9. Ma, C. M., and Wan, S. Y., A medial-surface oriented 3D two-subfield thinning algorithm. Pattern Recogn. Lett. 2(13):1439–1446, 2001.

    Article  Google Scholar 

  10. Manzanera, A., Bernard, T., Preteux, F., and Longuet, B., Medial faces from a concise 3D thinning algorithm. in IEEE International Conference on Computer Visions (ICCV‘99), pp. 337–343, 1999.

  11. Palagyi, K., A 3-subiteration 3D thinning algorithm for extracting medial surfaces. Pattern Recogn. Lett. 23:663–675, 2002.

    Article  MATH  Google Scholar 

  12. Tsao, Y. F., and Fu, K. S., A parallel thinning algorithm for 3D pictures". Comp. Graph. Image Process. 17(4):315–331, 1981.

    Article  Google Scholar 

  13. Mukherjee, J., Chatterji, B. N., and Das, P. P., Thinning of 3D images using the safe point thinning algorithm (SPTA). Pattern Recogn. Lett. 10(3):167–173, 1989.

    Article  MATH  Google Scholar 

  14. Mukherjee, J., Das, P. P., and Chatterji, B. N., On connectivity issues of ESPTA. Pat. Recogn. Lett. 11(9):643–648, 1990.

    Article  MATH  Google Scholar 

  15. Aufort, G., Jennane, R., and Harba, R., Hybrid skeleton graph analysis of disordered porous media. Application to trabecular bone. In Proc. IEEE Int. Conf. Acou. Spee. Sig. Proc. 2007, pp. II 781–784, May 2006, Toulouse, France.

  16. Aufort, G., Jennane, R., Harba, R., Gasser, A., Soulat, D., and Benhamou, C. L., Nouvelle approche de modélisation de milieux poreux. Application à l’os trabéculaire. In GRETSI’05, pp. 429–432, Louvain-la-Neuve, Belgium, September 2005.

  17. Ceylan, M., Ceylan, R., Dirgenali, F., Kara, S., and Ozbay, Y., Classification of carotid artery Doppler signals in the early phase of atherosclerosis using complex-valued artificial neural network. Comput. Biol. Med. 37:28–36, 2007.

    Article  Google Scholar 

  18. Özbay, Y., and Ceylan, M., Effects of window types on classification of carotid artery Doppler signals in the early phase of atherosclerosis using complex-valued artificial neural network. Comput. Biol. Med. 37:287–295, 2007.

    Article  Google Scholar 

  19. Hirose, A., (Editor), Complex-valued neural networks: Theories and applications. World Scientific, 2003.

  20. Pande, A., and Goel, V., Complex-valued neural network in image recognition: a study on the effectiveness of radial basis function. Proceedings of World Academy of Science, engineering and Technology 20:220–225, 2007.

    Google Scholar 

  21. Beylkin, G., Coifman R., and Rokhlin, V., Fast wavelet transforms and numerical algorithms. Commun. Pure Appl. Math. 141–183,1991.

  22. Bernard, C. P., Discrete wavelet analysis for fast optic flow computation, Techical Report, Ecole Polytechnique, 1999.

  23. Unser, M., Texture classification and segmentation using wavelet frames. IEEE Trans. Image Process. 4:1549–1560, 1995.

    Article  Google Scholar 

  24. Neumann, J., and Steidl, G., Dual-Tree complex wavelet transform in the frequency domain and an application to signal classification, Technical Report, University of Mannheim, 2003.

  25. Donoho, D. L., De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41:613–627, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  26. Shukla, P. D., Complex wavelet transforms and their applications, PhD Thesis, The University of Strathclyde, 2003.

  27. Fernandes, F., Directional, shift-insensitive, complex wavelet transforms with controllable redundancy, PhD Thesis, Rice University, 2002.

  28. Strang, G., and Hguyen, T., Wavelets and filter banks. Wellesley-Cambridge Press, 1996.

  29. Oppenheim, A. V., and Lim, J. S., The importance of phase in signals. Proc. IEEE 69:529–541, 1981.

    Article  Google Scholar 

  30. Lorenzetto, G. P., and Kovesi, P., A phase based image comparison technique, DICTA99, University of Western Australia, 1999.

  31. Driesen, J., and Belmasn, R., Time-frequency analysis in power measurement using complex wavelets. IEEE Int. Sympo. On Circuits and Systems, ISCAS2002, 681–684, 2002.

  32. Lina, J. M., Image processing with complex daubechies wavelets Journal of Math. Imaging Vis. 7:211–223, 1997.

    Article  MathSciNet  Google Scholar 

  33. Bulow, T., and Sommer, G., Hypercomplex signals- a novel extension of the analytic signal to the multidimensional case. IEEE Trans. Signal Process. 49:2844–2852, 2001.

    Article  MathSciNet  Google Scholar 

  34. Selesnick, I. W., Baraniuk, R. G., and Kingsbury, N. G., The dual-tree complex wavelet transform. IEEE Signal Process. Mag. 22:123–151, 2005.

    Article  Google Scholar 

  35. Georgin, N., and Koutsougeras, C., Complex domain backpropagation. IEEE Trans. CAS 39:330–334, 1992.

    Google Scholar 

  36. Nitta, T., An extension of the back-propagation algorithm to complex numbers. Elsevier Science Direct Neural Network 10:1391–1415, 1997.

    Google Scholar 

  37. Nitta, T., An analysis of the fundamental structure of complex-valued neurons. Neural Process. Lett. 12:239–246, 2000.

    Article  MATH  Google Scholar 

  38. Haykin, S., Adaptive filter theory. Prentice Hall, 2002.

  39. Morgenthaler, D. G., Three-dimensional simple points: serial erosion, parallel thinning and skeletonization. Tech. Rep. TR-1005, 1981.

  40. Borgefors, G., Nystrom, I., and di Baja, G. S., Computing skeletons in three dimensions. Pattern Recogn. 32(7):1225–1236, 1999.

    Article  Google Scholar 

  41. Aufort, G., Jennane,R., Harba, R., Gasser, A., Soulat, D., and Benhamou, C. L., Mechanical assessment of porous media using hybrid skeleton graph analysis and finite elements. Application to trabecular bone. In Proc. EUSIPCO-2007, Poznan, Poland.

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Authors and Affiliations

  1. Instiut PRISME/LESI, University of Orleans, 12, rue de Blois, 45067, Orléans Cedex 2, France

    Rachid Jennane & Gabriel Aufort

  2. Equipe INSERM U658, Hospital of Orleans, 1, rue Porte Madeleine, 45000, Orléans, France

    Claude Laurent Benhamou

  3. Engineering and Architecture Faculty, Department of Electrical and Electronics Engineering, Selçuk University, 42075, Konya, Turkey

    Murat Ceylan & Yüksel Özbay

  4. Department of Electrical and Electronics Engineering, Istanbul University, 34850, Avcilar, Istanbul, Turkey

    Osman Nuri Ucan

Authors
  1. Rachid Jennane
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  2. Gabriel Aufort
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  3. Claude Laurent Benhamou
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  4. Murat Ceylan
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  5. Yüksel Özbay
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  6. Osman Nuri Ucan
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Correspondence to Murat Ceylan.

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Jennane, R., Aufort, G., Benhamou, C.L. et al. A New Method for 3D Thinning of Hybrid Shaped Porous Media Using Artificial Intelligence. Application to Trabecular Bone. J Med Syst 36, 497–510 (2012). https://doi.org/10.1007/s10916-010-9495-y

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  • DOI: https://doi.org/10.1007/s10916-010-9495-y

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