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Abstract

Three-dimensional analysis of the spatial arrangement, spatial orientation and preferential directions of systems of fibers belongs to frequent tasks in many scientific fields, including the plant biology, textile industry, metalography, paper industry and tissue modeling.

The three-dimensional objects are mostly cut on slices of given thickness to make visible their inner structures. With this cutting we can see the object inside but on the other hand we loose the three-dimensional information. To get this information back we can make the reconstruction of the slices and in the case of systems of fibres we can make the approximation of fibres by straight line segments. Thus, we get the line systems depicting the number and orientation of fibres which are defined by the directions of the individual lines and their lengths.

The software esofspy (evaluation of spatial orientation of fiber systems in Python) written in the Python programming language (version 2.6.5) can be used for automatic evaluation of spatial orientation of fiber systems. The esofspy allows for the automatic postprocessing of two-dimesional plots of length densities and roses of directions, as well as the evaluation of preferential directions and the an/isotropy of line systems. To determine the an/isotropy three methods are used: the fractional anisotropy, ellipsoidal anisotropy and chi-square method. The first two methods are based on computing eigenvalues of the length-weighted average tensor of the line segment orientation. The last method involves comparing the observed length densities of lines with the discrete uniform distribution of an isotropic line system using the chi-square-test.

Keywords: line system; length density; rose of directions; cardinal directions; anisotropy; Python

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