Related papers: Objects as volumes: A stochastic geometry view of …
We introduce a new way to implicitly represent swept volumes in 3D. We first implicitize the base volume and then apply the time-dependent rigid transformation to build an implicit representation of the swept volume. This way, we build a…
Neural volume rendering became increasingly popular recently due to its success in synthesizing novel views of a scene from a sparse set of input images. So far, the geometry learned by neural volume rendering techniques was modeled using a…
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to…
We review and develop a new class of "dark energy" models, in which the relativistic theory of solids is used to construct material models of dark energy. These are models which include the effects of a continuous medium with well defined…
Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary…
A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time.…
The development of high-resolution imaging methods such as electron and scanning probe microscopy and atomic probe tomography have provided a wealth of information on structure and functionalities of solids. The availability of this data in…
A probabilistic representation formula for general systems of linear parabolic equations, coupled only through the zero-order term, is given. On this basis, an implicit probabilistic representation for the vorticity in a 3D viscous fluid…
We integrate in closed implicit form the Navier-Stokes equations for an incompressible fluid and the kinematical dynamo equation, in smooth manifolds and Euclidean space. This integration is carried out by applying Stochastic Differential…
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…
The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that conic intrinsic volumes are valuable for understanding the behavior of random…
In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…
We introduce a new technique to create a mesh of convex polyhedra representing the interior volume of a triangulated input surface. Our approach is particularly tolerant to defects in the input, which is allowed to self-intersect, to be…
We aim to reconstruct the shape of an exogenous, heavy solid contained in a tank from measurements of the liquid level in the tank as it drains (driven by gravity) through a small orifice in its side. (Because the solid displaces liquid,…
We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics…
The optical theorem is an important tool for scattering analysis in acoustics, electromagnetism, and quantum mechanics. We derive an extended version of the optical theorem for the scattering of elastic waves by a spherical inclusion…
We introduce a "Hamiltonian"-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the…
We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $\mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the…