Complicated geometrical patterns occur in many areas of science. Their analysis requires creation of mathematical models and development of special mathematical tools. The corresponding area of mathematical research is called Stochastic Geometry. Among more popular applications are Stereology and Tomography. The methods of form analysis are based on analysis of the objects as figures. For these sets, geometrical characteristics are considered that are independent of the position and orientation of the figures (hence they coincide for congruent figures). Classical examples are area and perimeter of a figure. In the last century German mathematician W. Blaschke formulated the problem of investigation of bounded convex domains using probabilistic methods. In particular, the problem of recognition of bounded convex domains by chord length distribution function.

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Orientation-Dependent Section Distributions for Convex Bodies

  • Victor Ohanyan

摘要

Complicated geometrical patterns occur in many areas of science. Their analysis requires creation of mathematical models and development of special mathematical tools. The corresponding area of mathematical research is called Stochastic Geometry. Among more popular applications are Stereology and Tomography. The methods of form analysis are based on analysis of the objects as figures. For these sets, geometrical characteristics are considered that are independent of the position and orientation of the figures (hence they coincide for congruent figures). Classical examples are area and perimeter of a figure. In the last century German mathematician W. Blaschke formulated the problem of investigation of bounded convex domains using probabilistic methods. In particular, the problem of recognition of bounded convex domains by chord length distribution function.