Inverting the statistics of the circle transform
Keyword(s):
The Mean
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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.
2018 ◽
Vol 98
(3)
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pp. 383-388
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Keyword(s):
1978 ◽
Vol 48
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pp. 227-228
2003 ◽
Vol 14
(3)
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pp. 265-268
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1974 ◽
Vol 39
(1)
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pp. 119-122
1974 ◽
Vol 29
(6)
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pp. 901-904
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Keyword(s):
2021 ◽
Vol 17
(1)
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pp. 155014772199170
Keyword(s):