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Inverting the statistics of the circle transform

Published online by Cambridge University Press:  14 July 2016

Peter Waksman
Peter Waksman*
Affiliation:
University of Rochester
*
∗Present address: 194 School Street, Acton, MA 01720, USA. Research supported by NSF Grant No. DMS-8602025.
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Abstract

For a plane domain the circle transform assigns to each circle its length of intersection with the domain. The problem is to determine the geometry of the domain given the mean of these intersection lengths as the circles' centers vary and given how that mean varies with circle radius. We also consider the mean square and higher moments of the intersection lengths — as a function of the circle radius. The discussion includes an identification of the geometric content of the mean when centers are inside of a disk and of the second moment when the centers are arbitrary points in the plane. The latter is equivalent to the distribution of distance between pairs of points of the domain.

Keywords

MOMENTSDISTANCE DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 708 - 716
Copyright
Copyright © Applied Probability Trust 1988 

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