منابع مشابه
Antinorms and Radon curves
In this paper we consider two notions that have been discovered and rediscovered by geometers and analysts since 1917 up to the present day. The first is that of a Radon curve, introduced by Radon in 1917 [50]. It is a special kind of centrally symmetric closed convex curve in the plane. Any centrally symmetric closed convex curve in the plane defines a norm turning the plane into a two-dimensi...
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The Radon transformations of generalized functions concentrated on lines and curves are deduced using a geometric approach and a limiting process. It is shown that any curve may be replaced by its tangents for the purposes of transformation and that each tangent will produce a maximum value in transform space which may be located using a one dimensional convolution filter. The locations of such...
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In his seminal work of 1981, A M Cormack has established that Radon transforms defined on two remarkable families of curves in the plane are invertible and admit explicit inversion formulas via circular harmonic decomposition. A sufficient condition for finding larger classes of curves enjoying the same property is given in this paper. We show that these generalized Cormack’s curves are given b...
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Residential and occupational exposure to radon is the second leading cause of lung cancer after cigarette smoking. As many as eight million homes in the US have elevated radon levels according to Environmental Protection Agency estimates. High exposure levels in homes are largely a result of radon-contaminated gas rising from the soil. This makes it an unusual indoor air pollutant in that it ha...
متن کاملUsing the generalized Radon transform for detection of curves in noisy images
In this paper the discrete generalized Radon transform will be investigated as a tool for detection of curves in noisy digital images. The discrete generalized Radon transform maps an image into a parameter domain, where curves following a specific parameterized curve form will correspond to a peak in the parameter domain. A major advantage of the generalized Radon transform is that the curves ...
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ژورنال
عنوان ژورنال: Aequationes mathematicae
سال: 2006
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-006-2825-y