Related papers: John Equation Constraints for the 3D X-ray Transfo…
Differentiable 3D-Gaussian splatting (GS) is emerging as a prominent technique in computer vision and graphics for reconstructing 3D scenes. GS represents a scene as a set of 3D Gaussians with varying opacities and employs a computationally…
The gauging of equations method, introduced in the preceding paper, is applied to the four-dimensional integral equations describing the strong interactions of three identical relativistic particles. In this way we obtain gauge invariant…
This paper presents the exact error analysis of point positioning equation used for airborne three-dimensional(3D) imaging sensor. With differential calculus and principles of precision analysis a mathematics formula on the point position…
A motivation for studying the following problems comes from applications to Biology; see \cite{cifuentes20233d}. In the $3$-dimensional Euclidean space ${\bf{E}}^3$, fix six pairwise distinct points \begin{equation*} \label{eqA}…
In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…
Uncalibrated photometric stereo aims at estimating the 3D-shape of a surface, given a set of images captured from the same viewing angle, but under unknown, varying illumination. While the theoretical foundations of this inverse problem…
The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…
Displacement estimation is a critical step of virtually all Ultrasound Elastography (USE) techniques. Two main features make this task unique compared to the general optical flow problem: the high-frequency nature of ultrasound…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
We present some recent progress achieved in the application of symmetry adaptation techniques to n-photon absorption spectroscopy of rare earth ions in finite symmetry. More specifically, this work is concerned with the determination of the…
The cone-beam transform consists of integrating a function defined on the three-dimensional space along every ray that starts on a certain scanning set. Based on Grangeat's formula, Louis [2016, Inverse Problems 32 115005] states…
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…
Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \cite{friesecke_twisted_2016}. Building on an…
Determining crystal symmetry from powder X-ray diffraction is a central problem in materials characterization, yet multiple space groups can produce indistinguishable patterns, making automated classification difficult. We show that…
In this paper, an improved scatter correction with moving beam stop array (BSA) for x-ray cone beam (CB) CT is proposed. Firstly, correlation between neighboring CB views is deduced based on John's Equation. Then, correlation-based…
We study the spherical slice transform which assigns to a function on the $n$-dimensional unit sphere the integrals of that function over cross-sections of the sphere by $k$-dimensional affine planes passing through the north pole. These…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
We present a theoretical formulation for the multiphoton diffraction phenomenology in the nonrelativistic limit, suitable for interpreting high-energy x-ray diffraction measurements using synchrotron radiation sources. A hierarchy of…