Related papers: Sampling the X-ray transform on simple surfaces
Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions…
Superresolution theory and techniques seek to recover signals from samples in the presence of blur and noise. Discrete image registration can be an approach to fuse information from different sets of samples of the same signal. Quantization…
We study the X-ray transform over a generic family of smooth curves in $\mathbb{R}^2$ with a Riemannian metric $g$. We show that the singularities cannot be recovered from local data in the presence of conjugate points, and therefore…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…
The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex…
Geometric reconstruction of opaque surfaces from images is a longstanding challenge in computer vision, with renewed interest from volumetric view synthesis algorithms using radiance fields. We leverage the geometry field proposed in recent…
Gaussian Splatting has become the method of choice for 3D reconstruction and real-time rendering of captured real scenes. However, fine appearance details need to be represented as a large number of small Gaussian primitives, which can be…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
We give a universal upper bound for the total curvature of minimizing geodesic on a convex surface in the Euclidean space.
We study rotational surfaces in Euclidean 3-space whose Gauss curvature is given as a prescribed function of its Gauss map. By means of a phase plane analysis and under mild assumptions on the prescribed function, we generalize the…
In this paper, we introduce a new discretization of the Gaussian curvature on surfaces, which is defined as the quotient of the angle defect and the area of some dual cell of a weighted triangulation at the conic singularity. A discrete…
We study the microlocal properties of the geodesic X-ray transform $\mathcal{X}$ on a manifold with boundary allowing the presence of conjugate points. Assuming that there are no self-intersecting geodesics and all conjugate pairs are…
Realistic scene appearance modeling has advanced rapidly with Gaussian Splatting, which enables real-time, high-quality rendering. Recent advances introduced per-primitive textures that incorporate spatial color variations within each…
We investigate the problem of estimating geodesic tortuosity and constrictivity as two structural characteristics of stationary random closed sets. They are of central importance for the analysis of effective transport properties in porous…
In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…
We consider the problem of reconstructing a compactly supported function from samples of its Fourier transform taken along a spiral. We determine the Nyquist sampling rate in terms of the density of the spiral and show that below this rate…
The Riemannian manifold of curves with a Sobolev metric is an important and frequently studied model in the theory of shape spaces. Various numerical approaches have been proposed to compute geodesics, but so far elude a rigorous…
We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to…
We consider geodesics on the surfaces obtained by weak deformations of the standard 2D-sphere. The dynamics of a particle on the surface can be asymptotically described by the averaged evolution of the particle's angular momentum. It is…
This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…