Related papers: Sampling the X-ray transform on simple surfaces
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) is a modern imaging technique used in material research to study nanoscale materials. Reconstruction of the parameters of an imaged object imposes an ill-posed inverse problem that is…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
In this article, we study the properties of the geodesic X-ray transform for asymptotically Euclidean or conic Riemannian metrics and show injectivity under non-trapping and no conjugate point assumptions. We also define a notion of lens…
Geodesic slice sampling, introduced in Durmus et al., 2024, is a slice sampling based Markov chain Monte Carlo method for approximate sampling from distributions on Riemannian manifolds. We prove that it is uniformly ergodic for…
This paper presents a new method to model X-ray scattering on random rough surfaces. It combines the approaches we presented in two previous papers -- \zs\cite{zhao03} \& \pz\cite{zhao15}. An actual rough surface is (incompletely) described…
We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on general orientable surfaces with a boundary and we study the geodesics from a uniformly chosen random point. These metric spaces…
It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard.…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…
We lay the foundations for a new fast method to reconstruct the electron density in x-ray scanning applications using measurements in the dark field. This approach is applied to a type of machine configuration with fixed energy sensitive…
In this study, we explore the challenge of efficiently representing scenes with a constrained number of Gaussians. Our analysis shifts from traditional graphics and 2D computer vision to the perspective of point clouds, highlighting the…
We present two range characterizations for the attenuated geodesic X-ray transform defined on pairs of functions and one-forms on simple surfaces. Such characterizations are based on first isolating the range over sums of functions and…
Probability measures on the sphere form an important class of statistical models and are used, for example, in modeling directional data or shapes. Due to their widespread use, but also as an algorithmic building block, efficient sampling…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
This paper deals with finding surfaces in $\mathbb{R}^3$ which are as close as possible to being flat and span a given contour such that the contour is a geodesic on the sought surface. We look for a surface which minimizes the total…