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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)


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.


Corresponding author

Postal address: Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35 (MaD), FIN-40351 Jyväskylä, Finland.
∗∗ Email address:
∗∗∗ 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.


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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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