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In this work we establish several commutation principles for optimizers of shifts of spectral functions in the context of Euclidean Jordan Algebras (EJAs). For instance, we show that under certain assumptions, if $\bar x$ is a (local)…
A radiograph visualizes the internal anatomy of a patient through the use of X-ray, which projects 3D information onto a 2D plane. Hence, radiograph analysis naturally requires physicians to relate the prior about 3D human anatomy to 2D…
The significance of the broken ray transform (BRT) is due to its occurrence in a number of modalities spanning optical, x-ray, and nuclear imaging. When data are indexed by the scatter location, the BRT is both linear and shift invariant.…
The MARS scanner is designed for the x-ray spectroscopic study of samples with the aid of computer tomography methods. Computer tomography allows the reconstruction of slices of an investigated sample using a set of shadow projections…
In this paper we numerically explore the convergence properties of the pseudo-Newtonian circular restricted problem of three and four primary bodies. The classical Newton-Raphson iterative scheme is used for revealing the basins of…
The reductions of the Heun equation to the hypergeometric equation by polynomial transformations of its independent variable are enumerated and classified. Heun-to-hypergeometric reductions are similar to classical hypergeometric…
Rayleigh's criterion states that it becomes essentially difficult to resolve two incoherent optical point sources separated by a distance below the width of point spread functions (PSF), namely in the subdiffraction limit. Recently,…
The study of the limiting absorption principle for elliptic equations with periodic structures is very challenging when the dimension is greater than 1. The fundamental reason for the dimensional barrier is the mismatch between directional…
Reconstructing the 3D model of a physical object typically requires us to align the depth scans obtained from different camera poses into the same coordinate system. Solutions to this global alignment problem usually proceed in two steps.…
The Zamolodchikov model describes an exact relativistic factorized scattering theory of straight strings in (2+1)-dimensional space-time. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The…
Feed-forward view synthesis models predict a novel view in a single pass with minimal 3D inductive bias. Existing works encode cameras as Pl\"ucker ray maps, which tie predictions to the arbitrary world coordinate gauge and make them…
The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…
X-ray interaction with matter is an energy-dependent process that is contingent on the atomic structure of the constituent material elements. The most advanced models to capture this relationship currently rely on Monte Carlo (MC)…
In this paper, we introduce a novel unsupervised domain adaptation technique for the task of 3D keypoint prediction from a single depth scan or image. Our key idea is to utilize the fact that predictions from different views of the same or…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
The problem of classifying high-dimensional shapes in real-world data grows in complexity as the dimension of the space increases. For the case of identifying convex shapes of different geometries, a new classification framework has…
Slender beam-like structures frequently occur in engineering applications and often interact at discrete locations through joints or connectors. Accurate modeling of such interactions is particularly challenging when different numerical…
We derive new equations using the mixed-frame approach for one- and two-dimensional (axisymmetric) time-dependent radiation transport and the associated couplings with matter. Our formulation is multi-group and multi-angle and includes…
In the settings of Euclidean Jordan algebras, normal decomposition systems (or Eaton triples), and structures induced by complete isometric hyperbolic polynomials, we consider the problem of optimizing a certain combination (such as the…
Camera calibration is a crucial prerequisite in many applications of computer vision. In this paper, a new, geometry-based camera calibration technique is proposed, which resolves two main issues associated with the widely used Zhang's…