Related papers: Tessellation Reconstruction Techniques
The interstellar medium (ISM) exhibits complex, multi-scale structures that are challenging to study due to their projection into two-dimensional (2D) column density maps. We present the Volume Density Mapper, a novel algorithm based on…
We investigate the application of volume statistics to probe the distribution of underdense regions in the large-scale structure of the Universe. This statistic measures the distortion of Eulerian volume elements relative to Lagrangian ones…
We present new techniques to perform adaptive spatial binning of two-dimensional (2D) data to reach a chosen constant signal-to-noise ratio per bin. These methods are required particularly for the proper analysis of Integral Field…
We apply the Delaunay Tessellation Field Estimator (DTFE) to reconstruct and analyze the matter distribution and cosmic velocity flows in the Local Universe on the basis of the PSCz galaxy survey. The prime objective of this study is the…
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the…
Effective transport properties of heterogeneous structures are predicted by geometric microstructural parameters, but these can be difficult to calculate. Here, a boundary element code with a recurrent series method accurately and…
Gaussian Splatting (GS) has emerged as a crucial technique for representing discrete volumetric radiance fields. It leverages unique parametrization to mitigate computational demands in scene optimization. This work introduces…
Joint analyses of the large-scale distribution of galaxies, and their motions under the gravitational influence of this density field, allow powerful tests of the cosmological model, including measurement of the growth rate of cosmic…
We present the implementation of a halo based method for the reconstruction of the cosmic mass density field. The method employs the mass density distribution of dark matter haloes and its environments computed from cosmological N-body…
3D Gaussian Splatting (GS) enables highly photorealistic scene reconstruction from posed image sequences but struggles with viewpoint extrapolation due to its anisotropic nature, leading to overfitting and poor generalization, particularly…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
A new class of random spatial tessellations is introduced -- the so-called column tessellations of three-dimensional space. The construction is based on a stationary planar tessellation. Each cell of the spatial tessellation is a prism…
A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle,…
General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed as extensions of Ord's process, are considered. The interaction may occur on each cell of the tessellation and between neighbour cells. The tessellation may also be…
A method to reconstruct weakly anisotropic inhomogeneous dielectric tensors inside a transparent medium is proposed. The mathematical theory of Integral Geometry is cast into a workable framework which allows the full determination of…
Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of stochastic models for a spatial tessellation are in accordance…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
Unlike other schemes that locally violate the essential stability properties of the analytic parabolic and elliptic problems, Voronoi finite volume methods (FVM) and boundary conforming Delaunay meshes provide good approximation of the…
Deformation gradient tensor fields are reconstructed in three dimensions (mapping all 9 tensor components) using synthetic Dark-Field X-ray Microscopy data. Owing to the unique properties of the microscope, our results imply that the…
We propose finite-time measures to compute the divergence, the curl and the velocity gradient tensor of the point particle velocity for two- and three-dimensional moving particle clouds. For this purpose, a tessellation of the particle…