Related papers: The Radon transform and the Hough transform: a uni…
The modern imaging techniques of Positron Emission Tomography and of Single Photon Emission Computed Tomography are not only two of the most important tools for studying the functional characteristics of the brain, but they now also play a…
Aerial image registration or matching is a geometric process of aligning two aerial images captured in different environments. Estimating the precise transformation parameters is hindered by various environments such as time, weather, and…
We study the Radon transform in the plane in parallel geometry possibly undersampled in the angular variables. We study resolution, aliasing artifacts, and edge recovery.
We propose iterative inversion algorithms for weighted Radon transforms $R_W$ along hyperplanes in $R^3$. More precisely, expandingthe weight $W = W (x, \theta), x \in R^3 , \theta \in S^2$ , into the series of spherical harmonics in…
We establish range characterizations, or data consistency conditions, for an integral transform that maps a function to its weighted integrals over conical surfaces in $\mathbb{R}^n$. We consider two different geometries for the cone…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
Global point cloud registration is an essential module for localization, of which the main difficulty exists in estimating the rotation globally without initial value. With the aid of gravity alignment, the degree of freedom in point cloud…
Image registration (IR) is a process that deforms images to align them with respect to a reference space, making it easier for medical practitioners to examine various medical images in a standardized reference frame, such as having the…
We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner…
Computed Tomography (CT) imaging is one of the most influential diagnostic methods. In clinical reconstruction, an effective energy is used instead of total X-ray spectrum. This approximation causes an accuracy decline. To increase the…
Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on…
This paper proposes a spatial-Radon domain CT image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of joint image and Radon domain inpainting model of \cite{Dong2013X} and…
Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as…
X-ray fluorescence holography (XFH) is a method for obtaining diffraction-limited images of the local atomic structure around a given type of emitter. The reconstructed wave-field represents a distorted image of the scatterer electron…
The article describes the application of the Hough transform to a honeycomb block image. The problem of cutting a mold from a honeycomb block is described. A number of image transformations are considered to increase the efficiency of the…
Compton scatter tomography is an emerging technique with attractive applications in several fields in imaging such as non-destructive testing and medical scanning. In this paper, we introduce a novel modality in three dimensions with a…
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…
We consider different norms for the Radon transform $Rf$ of a function $f$ and investigate under which conditions they can be estimated from above or below by some standard norms for $f$. We define Fourier-based norms for $Rf$ which can be…
This work focuses on the Fast Hough Transform (FHT) algorithm proposed by M.L. Brady. We propose how to modify the standard FHT to calculate sums along lines within any given range of their inclination angles. We also describe a new way to…
We present a unified approach to the study of Radon transforms related to symmetric groups and to general linear groups GL(n,q) regarded as q-analogues of the former. In both cases, we define a sequence of generalized Radon transforms which…