Related papers: The Geometric Refinement Transform: A Novel Uncoun…
In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…
We prove that the moduli space of holonomy G_2-metrics on a closed 7-manifold is in general disconnected by presenting a number of explicit examples. We detect different connected components of the G_2-moduli space by defining an…
A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
We use Lie sphere geometry to describe two large categories of generalized Voronoi diagrams that can be encoded in terms of the Lie quadric, the Lie inner product, and polyhedra. The first class consists of diagrams defined in terms of…
Differentiable rendering is a technique to connect 3D scenes with corresponding 2D images. Since it is differentiable, processes during image formation can be learned. Previous approaches to differentiable rendering focus on mesh-based…
Image enhancement is a technique that frequently utilized in digital image processing. In recent years, the popularity of learning-based techniques for enhancing the aesthetic performance of photographs has increased. However, the majority…
We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…
We study algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry,…
This paper introduces a new approach toward characterizing local structural features of two-dimensional particle systems. The approach can accurately identify and characterize defects in high-temperature crystals, distinguish a wide range…
Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…
This paper establishes $L^p$-improving estimates for a variety of Radon-like transforms which integrate functions over submanifolds of intermediate dimension. In each case, the results rely on a unique notion of curvature which relates to,…
We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its…
We consider a one-dimensional Radon transform on the group SO(3) which is motivated by texture goniometry. In particular we will derive several inversion formulae and compare them with the inversion of the one-dimensional spherical Radon…
In recent years, Radon type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that…
Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly…
We investigate a geometric dynamical mechanism arising in the class $\mathcal{O}_C$ of domains containing a fixed convex set $C$ and satisfying two geometric normals properties introduced by Barkatou \cite{Barkatou2002}. The first property…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
We interpret the setting for a Radon transform as a submanifold of the space of generalized functions, and compute its extrinsic curvature: it is the Hessian composed with the Radon transform.