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Estimation of orientation characteristic of fibrous material

Part of: Stochastic processes Survival analysis and censored data Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Salme Kärkkäinnen ,
Antti Penttinen ,
Nikolai G. Ushakov  and
Alexandra P. Ushakova
Salme Kärkkäinnen*
Affiliation:
University of Jyväskylä
Antti Penttinen*
Affiliation:
University of Jyväskylä
Nikolai G. Ushakov*
Affiliation:
Russian Academy of Sciences
Alexandra P. Ushakova*
Affiliation:
Russian Academy of Sciences
*
∗ Postal address: Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35 (MaD), FIN-40351 Jyväskylä, Finland.
∗ Postal address: Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35 (MaD), FIN-40351 Jyväskylä, Finland.
∗∗∗ 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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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.

Keywords

Degradationdigital imageelliptic distributionfibre orientationfibre processline transect samplingsimulationstereology

MSC classification

Primary: 62M30: Spatial processes 60G35: Signal detection and filtering
Secondary: 62N99: None of the above, but in this section
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 33 , Issue 3 , September 2001 , pp. 559 - 575
Copyright
Copyright © Applied Probability Trust 2001 

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