Regularity of Radon Transform on a Convex Shape
Volume 7, Issue 4, Page No 121-126, 2022
Author’s Name: Pat Vatiwutiponga)
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Department of Mathematics and Computer Science, Kamnoetvidya Science Academy, Rayong, 21210, Thailand
a)whom correspondence should be addressed. E-mail: pat.v@kvis.ac.th
Adv. Sci. Technol. Eng. Syst. J. 7(4), 121-126 (2022); 
DOI: 10.25046/aj070416
Keywords: Radon transform, Regularity property, Convex shape
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Radon transform is a mathematical tool widely applied in various domains, including biophysics and computer tomography. Previously, it was discovered that applying the Radon transform to a binary image comprising circle forms resulted in discontinuity. As a result, the line detection approach based on it became discontinued. The d-Radon transform is a modified version of the Radon transform that is presented as a solution to this problem. The properties of the circle cause the Radon transform to be discontinuous. This work extends this finding by looking into the Radon transform’s regularity property and a proposed modification to a convex shape. We discovered that regularity in the Radon space is determined by the regularity of the shape’s point. This leads to the continuity condition for the line detection method.
Received: 18 June 2022, Accepted: 16 August 2022, Published Online: 24 August 2022
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