Related papers: Ray Transforms on a Conformal Class of Curves
In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse…
We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robust in the underlying vector field, and is analytic on a…
Let $\mR$ be the restriction of the spherical Radon transform to the set of spheres centered on a hypersurface $\mS$. We study the inversion of $\mR$ by a closed-form formula. We approach the problem by studying an oscillatory integral,…
We give an explicit plane-by-plane filtered back-projection reconstruction algorithm for the transverse ray transform of symmetric second rank tensor fields on Euclidean 3-space, using data from rotation about three orthogonal axes. We show…
Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is done over a family of conical surfaces. We call them \emph{cone transforms} (in 2D they are also called \emph{V-line} or…
The paper is devoted to "uniform" reduction of smooth functions on 2-manifolds to canonical form near critical points by some coordinate changes in some neighbourhoods of these points. For singularity types $E_6,E_8$ and $A_n$, we…
In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…
By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as modular functions, together with the elliptic modular function, we generate the modular function fields of level $N\geq3$.…
We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal…
In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also…
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…
A basic problem in quantizing a field in curved space is the decomposition of the classical modes in positive and negative frequency. The decomposition is equivalent to a choice of a complex structure in the space of classical solutions. In…
The two-dimensional (2D) orientation field transform has been proved to be effective at enhancing 2D contours and curves in images by means of top-down processing. It, however, has no counterpart in three-dimensional (3D) images due to the…
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…
We obtain explicit inversion formulas for the Radon-like transform that assigns to a function on the unit sphere the integrals of that function over hemispheres lying in lower dimensional central cross-sections. The results are applied to…
We present a ray-tracing technique for radiative transfer modeling of complex three-dimensional (3D) structures which include dense regions of high optical depth like in dense molecular clouds, circumstellar disks, envelopes of evolved…
In this paper, we investigate vector fields on polyhedral complexes and their associated trajectories. We study vector fields which are analogue of the gradient vector field of a function in the smooth case. Our goal is to define a nice…
Recovering a function from integrals over conical surfaces recently got significant interest. It is relevant for emission tomography with Compton cameras and other imaging applications. In this paper, we consider the weighted conical Radon…
Realistic modeling of scattering from curved metallic bodies - such as vehicles and roadside structures - is essential for cellular and vehicular channel modeling as well as radar applications. A practical approach is to approximate curved…
Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation…