Contribution to the steinhaus' method of assessment of the length of curves in linear stereological analysis

• Autorzy: Bodziony, J.
• Języki publikacji: EN

Abstrakty

EN

The paper contains the development of Steinhaus' method of estimating the length of plane rectifiable curves. Steinhaus considered the most disadvantageous case when the curve is reduced to one segment projected on a finite number of straight lines of uniform orientation on a plane. He carried out detailed calculation of relative errors when the segment is projected on k = 6 straight lines. Generalization of Steinhaus' method consists in the assessment of errors in the determination of the length of a polygonal line composed of m segments projected on n straight lines of coupled directions. It has been found that projecting of m segments on n straight lines is equivalent - with respect to the assessment of errors - to the projection of one segment on k = nm straight lines. Both the extreme relative errors, with overestimation and underestimation, and the standard deviation, are asymptotically inversely proportional to the square of the product k = mn. In the paper it has been demonstrated that the assessment of the errors is independent of the configuration of the segments. They may be linked to form polygonal lines, but may also represent a set of separate segments.

Słowa kluczowe

EN

linear stereological analysis; length of plane curves; Steinhaus estimator

• Czasopismo: Bulletin of the Polish Academy of Sciences. Earth Sciences
• Rocznik: 2000
• Tom: Vol. 48, nr 1
• Strony: 85-98
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Bodziony, J.