T he Hough transform is a useful technique in the detection of straight lines and curves in an image. Due to the mathematical similarity of the Hough transform and the forward Radon transform, the Hough transform can be computed using the Radon transform which, in turn, can be evaluated using the central slice theorem. This involves a two-dimensional Fourier transform, an x-y to rmapping and a ...

A method for derivation of inversion formulas for the Radon transform of f (x) is given. This method allows one to construct functions ψ(x) which are easy to compute and which have the same wave fronts as f (x). This, in turn, allows one to calculate the singular support S of f (x) by computing ψ(x) given tomographic data. A simple geometrical relation between the singular supports of f andˆf ,...

We consider a weighted Radon transform in the plane, Rm(ξ, η) = R R f(x, ξx + η)m(x, ξ, η)dx, where m(x, ξ, η) is a smooth, positive function. Using an extension of an argument of Strichartz we prove a local injectivity theorem for Rm for essentially the same class of m(x, ξ, η) that was considered by Gindikin in his article in this issue.

A new proof of the Second Main Theorem with truncation level 1 for Zariski-dense holomorphic curves into Abelian varieties, which has just been proved by Yamanoi [Y2], is presented. Our proof is based on the idea of the “Radon transform” introduced in [K2] combined with consideration on certain singular perturbation of the probability measures on the parameter space which appears in the “Radon ...

We consider the inverse prolem of the recovery of a gauge field in R 2 modulo gauge transformations from the non-abelian Radon transform. A global uniqueness theorem is proven for the case when the gauge field has a compact support. Extensions to the attenuated non-abelian Radon transform in R 2 and applications to the inverse scattering problem for the Schrödinger equation in R 2 with non-comp...

This paper is the tomographic images reconstruction simulation for defects detection in specimen. The specimen is the thin cylindrical steel contained with low density materials. The defects in material are simulated in three shapes.The specimen image function will be transformed to projection data. Radon transform and its inverse provide the mathematical for reconstructing tomographic images f...

We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S nor to S. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms fr...

Background: Several epidemiological studies conducted on underground miner’s show that exposure to elevated levels of radioactive radon gas is expected to increase the risk of lung cancer. Relative risk of lung cancer is almost linear with radon exposure. Elevated concentrations of radon are not only reported within mines but also for closed indoor environment of general public houses....

In this paper, skew estimation and correction method for document image has been presented. Image of text document can be acquired via camera or other type of machines which cause sometime a skew angle (alignment) on its horizontal direction. To find skew angle of document image, the Radon transform method is used here. The skew angle used in database within the range of ±90o w.r.t x-axis. Kew ...