This book is devoted to a discrete Radon transform named the Mojette transform. The Radon transform specificity is to mix Cartesian and radial views of the plane. However, it is straightforward to obtain a discrete lattice from a Cartesian grid while it is impossible from a standard equiangular radial grid. The only mathematical tool is to use discrete geometry that replaces the equiangular rad...

A method for producing a radar-reflectivity map of the polar regions of the Moon or a planet from polar orbit with only the frequency shift of the reflected signals is described and simulated. A Radon transform of the reflectivity is obtained during multiple passes over the pole. Inversion of this Radon transform enables a map of radar reflectivity to be synthesized.

This paper describes the discrete Radon transform (DRT) and the exact inversion algorithm for it. Similar to the discrete Fourier transform (DFT), the DRT is defined for periodic vector-sequences and studied as a transform in its own right. Casting the forward transform as a matrix-vector multiplication, the key observation is that the matrix-although very large-has a block-circulant structure....

The Radon transform constitutes a fundamental concept for x-rays in medical imaging, and more generally, in image reconstruction problems from diverse fields. The Radon transform in Euclidean spaces assigns to functions their integrals over affine hyperplanes. This can be extended so that the integration is performed on affine k-dimensional subspaces, the corresponding transform is called k-pla...

Introduction: Diabetic retinopathy (DR) is the single largest cause of sight loss and blindness in the working age population of Western countries; it is the most common cause of blindness in adults between 20 and 60 years of age. Early diagnosis of DR is critical for preventing vision loss so early detection of microaneurysms (MAs) as the first signs of DR is important. This paper addresses th...

Gaussian measure is constructed for any given hyperplane in an infinite dimensional Hilbert space, and this is used to define a generalization of the Radon transform to the infinite dimensional setting, using Gauss measure instead of Lebesgue measure. An inversion formula is obtained and a support theorem proved.

In this paper, we proposed a rotation invariant image descriptor based on Radon transform (RT) and energy operator. Radon transform captures the directional features of the pattern image by projecting the pattern onto different orientation slices, and its most attractive ability is to transform rotational components to circular shift components. Meanwhile, the energy operator can remove the cir...

In this paper, we propose an effective watermarking scheme using self-patch correlation based on Radon transform for image. The robustness against Rotation, Scaling, and Translation (RST) attacks is achieved using the translation property of the Radon transform and self-patch correlation. The Radon transform emphasizes and detects the linear characteristic to calculate the angle of image rotati...