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Estimation of orientation characteristic of fibrous material

  • Salme Kärkkäinnen (a1), Antti Penttinen (a1), Nikolai G. Ushakov (a2) and Alexandra P. Ushakova (a2)

Abstract

A new statistical method for estimating the orientation distribution of fibres in a fibre process is suggested where the process is observed in the form of a degraded digital greyscale image. The method is based on line transect sampling of the image in a few fixed directions. A well-known method based on stereology is available if the intersections between the transects and fibres can be counted. We extend this to the case where, instead of the intersection points, only scaled variograms of grey levels along the transects are observed. The nonlinear estimation equations for a parametric orientation distribution as well as a numerical algorithm are given. The method is illustrated by a real-world example and simulated examples where the elliptic orientation distribution is applied. In its simplicity, the new approach is intended for industrial on-line estimation of fibre orientation in disordered fibrous materials.

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Corresponding author

Postal address: Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35 (MaD), FIN-40351 Jyväskylä, Finland.
∗∗ Email address: penttine@maths.jyu.fi
∗∗∗ Current address: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway.
∗∗∗∗ Postal address: Institute of Microelectronics Technology, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russia.

References

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[1] Cowan, W. F. and Cowdrey, E. J. K. (1974). Evaluation of paper strength components by short-span tensile analysis. Tappi 57, 9093.
[2] Cressie, N. A. C. (1993). Statistics for Spatial Data, Revised edn. John Wiley, New York.
[3] Danielsen, R. and Steenberg, B. (1947). Quantitative determination of fibre orientation in paper. Svensk Papperstidn. 50, 301305.
[4] Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and their Applications. Cambridge University Press.
[5] Erkkilä, A.-L., Pakarinen, P. and Odell, M. (1998). Sheet forming studies using layered orientation analysis. Pulp Paper Canad. 99, T39T43.
[6] Forgacs, O. L. and Strelis, J. (1963). The measurement of the quantity and orientation of chemical pulp fibres in the surfaces of newsprint. Pulp Paper Mag. Canad. 64, T3T13.
[7] Glasbey, C. A. and Horgan, G. W. (1995). Image Analysis for the Biological Sciences. John Wiley, Chichester.
[8] Hanisch, K.-H. (1981). On classes of random sets and point process models. Serdica 7, 160166.
[9] Hilliard, J. E. (1962). Specification and measurement of microstructural anisotropy. Trans. Metall. Soc. Am. Inst. Metall. Eng. 224, 12011211.
[10] Hutten, I. M. (1994). Paper machine evaluation by fiber orientation profile analysis. Tappi J. 77, 187192.
[11] Jensen, E. B. V. (1998). Local Stereology. World Scientific, Singapore.
[12] Jeulin, D. (1989). Morphological modeling of images by sequential random functions. Signal Proc. 16, 403431.
[13] Jeulin, D. (2000). Variograms of the dead leaves model. Res. Rept, Centre de Morphologie Mathématique, École des Mines de Paris.
[14] Krkkinen, S. and Jensen, E. B. V. (2001). On the orientational analysis of Boolean fibres from digital images. Res. Rept 15, Laboratory for Computational Stochastics, Department of Mathematical Sciences, University of Aarhus.
[15] Matheron, G. (1972). Ensembles fermés aléatoires, ensembles semi-Markoviens et polyèdres poissoniens. Adv. Appl. Prob. 4, 508541.
[16] Matheron, G. (1975). Random Sets and Integral Geometry. John Wiley, New York.
[17] Mecke, J. (1981). Formulas for stationary planar fibre processes III—intersections with fibre systems. Math. Operationsforsch. Statist., Ser. Statist. 12, 201210.
[18] Mecke, J. and Stoyan, D. (1980). Formulas for stationary planar fibre processes I—general theory. Math. Operationsforsch. Statist., Ser. Statist. 11, 267279.
[19] Molchanov, I. S. (1997). Statistics of the Boolean Model for Practitioners and Mathematicians. John Wiley, Chichester.
[20] Molchanov, I. S. and Stoyan, D. (1994). Directional analysis of fibre processes related to Boolean models. Metrika 41, 183199.
[21] Paakkari, T., Serimaa, R., Hattula, T. and Ahtee, M. (1984). Determination of fibre orientation in a paper sample using X-ray diffraction. Paperi ja puu 66, 569575.
[22] Penttinen, A. and Stoyan, D. (1989). Statistical analysis for a class of line segment processes. Scand. J. Statist. 16, 153168.
[23] Sadowski, J. W. (1979). Measurement of fibre orientation in paper by optical Fourier transform. Paperi ja puu 61, 588595.
[24] Serra, J. (1982). Image Analysis and Mathematical Morphology. Academic Press, London.
[25] Stoyan, D., Kendall, W. S. and Mecke, J. (1995). Stochastic Geometry and its Applications, 2nd edn. John Wiley, Chichester.
[26] Venables, W. N. and Ripley, B. D. (1999). Modern Applied Statistics with S-PLUS, 3rd edn. Springer, New York.
[27] Wells, W. M. (1986). Efficient synthesis of Gaussian filters by cascaded uniform filters. IEEE Trans. Pattern Anal. Mach. Intell. 8, 234239.

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Estimation of orientation characteristic of fibrous material

  • Salme Kärkkäinnen (a1), Antti Penttinen (a1), Nikolai G. Ushakov (a2) and Alexandra P. Ushakova (a2)

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