Related papers: papaya2: 2D Irreducible Minkowski Tensor computati…
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
Minkowski tensors are comprehensive shape descriptors that robustly capture n-point information in complex random geometries and that have already been extensively applied in the Euclidean plane. Here, we devise a novel framework for…
We apply the Minkowski Tensor statistics to two dimensional slices of the three dimensional density field. The Minkowski Tensors are a set of functions that are sensitive to directionally dependent signals in the data, and furthermore can…
Minkowski tensors, also known as tensor valuations, provide robust $n$-point information for a wide range of random spatial structures. Local estimators for point clouds, e.g., representing voxelized data, however, are unavoidably biased…
Smooth deformations of a Minkowski type metric in a four-dimensional space-time manifold are considered. Deformations of the basic spin-tensorial fields associated with this metric are calculated and their application to calculating the…
Gaussian random fields are among the most important models of amorphous spatial structures and appear across length scales in a variety of physical, biological, and geological applications, from composite materials to geospatial data.…
We apply the Minkowski tensor statistics to three dimensional Gaussian random fields. Minkowski tensors contain information regarding the orientation and shape of excursion sets, that is not present in the scalar Minkowski functionals. They…
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…
Higher-rank Minkowski valuations are efficient means for describing the geometry and connectivity of spatial patterns. We show how to extend the framework of the scalar Minkowski valuations to vector- and tensor-valued measures. The…
The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…
Recently, Minkowski Tensors (MT) have gained popularity for morphological analysis tasks. As opposed to the scalar Minkowski functionals (MF; in 2D given by area, perimeter and Euler characteristic), MT can characterize symmetry and…
PCA can be used for rotation invariant features, describing a shape with its $p_{ab}=E[(x_i-E[x_a])(x_b-E[x_b])]$ covariance matrix approximating shape by ellipsoid, allowing for rotation invariants like its traces of powers. However, real…
For material modeling of microstructured media, an accurate characterization of the underlying microstructure is indispensable. Mathematically speaking, the overall goal of microstructure characterization is to find simple functionals which…
Microwave Imaging is an essential technique for reconstructing the electrical properties of an inaccessible medium. Many approaches have been proposed employing algorithms to solve the Electromagnetic Inverse Scattering Problem associated…
The construction of consistent effective field theories in the infrared demands that models be defined by their underlying gauge symmetries, rather than by an arbitrary tuning of couplings or a cherry-picking of operators which may not be…
We introduce surface Minkowski tensors to characterize rotational symmetries of shapes embedded in curved surfaces. The definition is based on a modified vector transport of the shapes boundary co-normal into a reference point which…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows…
We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which…
We present the PSALTer software for efficiently computing the mass and energy of the particle spectrum for any (e.g. higher-rank) tensor field theory in the Wolfram Language. The user must provide a Lagrangian density which is expanded…