Related papers: John Equation Constraints for the 3D X-ray Transfo…
We investigate in a $2$D setting the scattering of time-harmonic electromagnetic waves by a plasmonic device, represented as a non dissipative bounded and penetrable obstacle with a negative permittivity. Using the $\textrm{T}$-coercivity…
Optical surfaces represented by second-degree polynomials (quadratic or conics) are ubiquitous in optics. We revisit the equations of the conic shapes in the context of grazing incidence optics, gathering together the curves commonly used…
Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an…
The goal of many computer vision systems is to transform image pixels into 3D representations. Recent popular models use neural networks to regress directly from pixels to 3D object parameters. Such an approach works well when supervision…
Geometric consistency, i.e. the preservation of neighbourhoods, is a natural and strong prior in 3D shape matching. Geometrically consistent matchings are crucial for many downstream applications, such as texture transfer or statistical…
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…
Joint ptychography and tomography (JPT) is a recently developed framework that enables high-resolution reconstruction of 3D volumes with significantly relaxed constraints on probe overlap at adjacent scan positions. In ptychographic X-ray…
We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis…
In this paper we characterise cone points of arbitrary subsets of Euclidean space. Given $E \subset \mathbb{R}^n$, $x \in E$ is a cone point of $E$ if and only if \begin{align*} \int_{0}^1 \beta_{E}^{d,2}(B(x,r))^2 \frac{dr}{r} < \infty,…
X-ray images play a vital role in the intraoperative processes due to their high resolution and fast imaging speed and greatly promote the subsequent segmentation, registration and reconstruction. However, over-dosed X-rays superimpose…
3D shape completion is important to enable machines to perceive the complete geometry of objects from partial observations. To address this problem, view-based methods have been presented. These methods represent shapes as multiple depth…
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…
In this paper we consider 3D axis-symmetric (AS) object reconstruction from single cone-beam x-ray projection data. Traditional x-ray CT fails to capture fleeting state of material due to the long time for data acquisition at all angles.…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
X-ray parametric down-conversion is a fundamental nonlinear effect that promises a wide range of possible applications. Nevertheless, it has been scarcely investigated and unequivocal evidence of the effect is still missing for certain…
Accurate angular quadratures are crucial for the numerical solution of three-dimensional (3D) radiative transfer problems, especially when the spectral line polarisation produced by the scattering of anisotropic radiation is included. There…
We report an extension of the source imaging method for analyzing three-dimensional sources from three-dimensional correlations. Our technique consists of expanding the correlation data and the underlying source function in spherical…
Talbot-Lau X-ray phase-contrast imaging is a novel imaging modality, which provides not only an X-ray absorption image, but also additionally a differential phase image and a dark-field image. The dark-field image is related to small angle…
Under conditions that prevent tangential intersection, we prove quadratic convergence of a projection algorithm for the feasibility problem of finding a point in the intersection of a smooth curve and line in $\mathbb{R}^2$. This nonconvex…
Recall that a convex body $K$ is in John's position if the unit Euclidean ball is the maximal volume ellipsoid contained in $K$. Approximating convex body in John's position by polytopes we obtain the following results. 1. Let $n>R_n\ge 1$…