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Regularity of Radon Transform on a Convex Shape
Adv. Sci. Technol. Eng. Syst. J. 7(4), 121–126 (2022);
DOI: 10.25046/aj070416
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.
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