The beneficial properties of the Radon transform make it an useful intermediate representation for the extraction of invariant features from pattern images for the purpose of indexing/matching. This paper revisits the problem of Radon image utilization with a generic view on a popular Radon transform-based transform and pattern descriptor, the R-transform and R-signature, bringing in a class of...

Extraction of primitives, such as lines, edges and curves, is often a key step in an image analysis procedure. The most popular technique for curve detection is based on the Hough transform. The original formulation of the Hough transform is inherently discrete. It is therefore difficult to assess which properties are inherent to the transform-based technique and which are due to its discrete n...

Focusing in the radon domain can be affected by data and operator aliasing. Antialiasing conditions can be imposed on the parabolic radon transform (PRT) operator by dip limiting the summation path. These dip limits in time translate into frequency limits in the Fourier domain. Consequently, antialiasing the PRT enables better focusing in the radon domain. If the radon domain is computed via in...

where S + x denotes the setf-s + x i s e S ) . Thus, the Radon transform can be thought of as a way of replacing/by a "smeared out" version of /. This form of the transform represents a simplified model of the kind of averaging which occurs in certain applied settings, such as various types of tomography and recent statistical averaging techniques. A fundamental question which arises in connect...

The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore-Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.

These notes provide an introduction to the mathematics used in medical imaging. In Section 6 we review the basics of calculus and multivariable calculus. In Section 2 we introduce Fourier Series, which is a premonition for the introduction of the Fourier Transform in Section 3. Finally, we will treat the mathematics of CT-Scans with the introduction of the Radon Transform in Section 4. Section ...

| The 3D Radon transform of an object is an important intermediate result in many analytically exact cone-beam reconstruction algorithms. In this paper, we present a new, highly eecient method for 3D Radon inversion, i.e. reconstruction of the image from the 3D Radon transform, called Direct Fourier Inversion (DFI). The method is based directly on the 3D Fourier Slice Theorem. From the 3D Radon...

The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore–Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.