{ This paper presents a model of nite Radon transforms composed of Radon projections. The model generalizes to nite groups projections in the classical Radon transform theory. The Radon projector averages a function on a group over cosets of a subgroup. Reconstruction formulae formally similar to the convolved backprojection ones are derived and an iterative reconstruction technique is found to...

Accurate simulation of X-ray transforms of representative objects plays an important role in the evaluation and improvement of CT reconstruction algorithms. In this paper, we formulate the X-ray transform and 3D Radon transform for ellipsoids and tetrahedra, and verify the resulting formulas by numerical simulation. Here the ellipsoids and tetrahedra may be arbitrarily positioned and rotated. L...

In the literature there are three apparently different definitions of the Radon transform on various spaces of distributions: Gelfand-Graev’s, Helgason’s and Ludwig’s. In this paper a new definition of the Radon transform on the space of the tempered distributions is given and it is proved that, properly understood, the earlier definitions are all equivalent to the new one. A constructive descr...

We propose two algorithms for the reconstruction of a 2D object from its continuous projections. The first algorithm operates on parallel projection data, while the second uses the more practical model of fan-beam projections. Both algorithms are based on the discrete Radon transform, which extends the continuous Radon transform to discrete data. The discrete Radon transform and its inverse can...

In this article, we will develop parallel processing of one-sided Radon transform for the detection of the position and the orientation of a planar motion object. Detection of planar motion based on one-sided Radon transform can be applied to arbitrary shapes and is robust against overlapping of objects but it requires much computation time. Thus, we will construct a parallel computation of one...

We extend the linear Radon transform to a nonlinear space and propose a method by applying the nonlinear Radon transform to Zernike moments to extract shape descriptors. These descriptors are obtained by computing Zernike moment on the radial and angular coordinates of the pattern image's nonlinear Radon matrix. Theoretical and experimental results validate the effectiveness and the robustness ...

In this paper a local Radon representation is proposed and applied to 3-D seismic data analysis. The derivation of the local Radon power spectrum is based on an extension of the relation between the global Radon transform and multi-dimensional Fourier transform to the non-stationary case. This Wigner-Radon power spectrum is closely related to the Cohen’s class of quadratic timefrequency represe...

In this project, we propose a new algorithm that recovers the rigid motion parameters and the underlying density function from a set of noisy measurements of three dimensional (3D) density functions. We measure the Radon transform of each 3D function which are randomly rotated and translated version of a target function that we try to recover. Radon transform is a set of parallel line integrals...

To extract features from digital images, it is useful to be able to find simple shapes (straight lines, circles, ellipses, etc.). In order to achieve this goal, one can be able to detect a group of pixels that are on a straight line or a smooth curve. That is what a Hough transform is supposed to do. Since the Hough transform is a special case of Radon transform then line detection process is a...

The Radon transform is a fundamental tool in many areas. For example, in reconstruction of an image from its projections (CT scanning). Although it is situated in the core of many modern physical computations, the Radon transform lacks a coherent discrete definition for 2D discrete images which is algebraically exact, invertible, and rapidly computable. We define a notion of 2D discrete Radon t...