Recognition of Convex Bodies by Covariograms
The present paper contains a review of the main results of Yerevan research group in tomography of planar bounded convex domains. The applications of these problems are known in both geometric and computer tomography. Complicated geometrical patterns occur in many areas of science. Their analysis re...
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| Format: | Article |
| Language: | Russian |
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Academic Publishing House Researcher
2013-01-01
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| Series: | Evropejskij Issledovatelʹ |
| Subjects: | |
| Online Access: | http://www.erjournal.ru/pdf.html?n=1368983154.pdf |
| Summary: | The present paper contains a review of the main results of Yerevan research group in tomography of planar bounded convex domains. The applications of these problems are known in both geometric and computer tomography. 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, i.e. as subsets of the plane. 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 in the plane using probabilistic methods. In particular, the problem of recognition of bounded convex domains by chord length distribution |
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| ISSN: | 2219-8229 2224-0136 |