Related papers: Estimation of surface area
In the real world, we often come across soft objects having spatially varying stiffness, such as human palm or a wart on the skin. In this paper, we propose a novel approach to render thin, deformable objects having spatially varying…
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…
In the calculation of thermodynamic properties and three dimensional structures of macromolecules, such as proteins, it is important to have a good algorithm for computing solvent accessible surface area of macromolecules. Here we propose a…
We explore various notions of stability for surfaces embedded and immersed in spacetimes and initial data sets. The interest in such surfaces lies in their potential to go beyond the variational techniques which often underlie the study of…
Approximation problems involving a single convex body in $d$-dimensional space have received a great deal of attention in the computational geometry community. In contrast, works involving multiple convex bodies are generally limited to…
In this paper, we will give an upper bound and a lower bound of the arithmetic Hilbert-Samuel function of projective hypersurfaces, which are uniform and explicit. These two bounds have the optimal dominant terms. As an application, we use…
We give an explicitly computable lower bound for the arithmetic self-intersection number of the dualizing sheaf on a large class of arithmetic surfaces. If some technical conditions are satisfied, then this lower bound is positive. In…
We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin in this context. As applications, we study various…
Given a totally nonholonomic distribution of rank two on a three-dimensional manifold we investigate the size of the set of points that can be reached by singular horizontal paths starting from a same point. In this setting, the Sard…
The asymptotic properties of multivariate Sz\'{a}sz-Mirakyan estimators for cumulative distribution functions (cdf) supported on the nonnegative orthant are investigated. Explicit bias and variance expansions are derived on compact subsets…
We prove convergence of Hausdorff measure of level sets of smooth Gaussian fields when the levels converge. Given two coupled stationary fields $f_1, f_2$ , we estimate the difference of Hausdorff measure of level sets in expectation, in…
We study the problem of {\em list-decodable mean estimation} for bounded covariance distributions. Specifically, we are given a set $T$ of points in $\mathbb{R}^d$ with the promise that an unknown $\alpha$-fraction of points in $T$, where…
This work aims to estimate 6Dof (6D) object pose in background clutter. Considering the strong occlusion and background noise, we propose to utilize the spatial structure for better tackling this challenging task. Observing that the 3D mesh…
This paper presents novel methods to predict the surface and volume of the ham through a camera. This implies that the conventional weight measurement to obtain in the object's volume can be neglected and hence it is economically effective.…
We tackle the problem of the estimation of the level sets L_f({\lambda}) of the density f of a random vector X supported on a smooth manifold M\subsetR^d , from an iid sample of X. To do that we introduce a kernel-based estimator f^n,h ,…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
Let $\mathbb{S}^{d-1}$ denote the unit sphere in Euclidean space $\mathbb{R}^d$, $d\geq 2$, equipped with surface measure $\sigma_{d-1}$. An instance of our main result concerns the regularity of solutions of the convolution equation \[…
To probe cosmological fields beyond the Gaussian level, three-point statistics can be used, all of which are related to the bispectrum. Hence, measurements of CMB anisotropies, galaxy clustering, and weak gravitational lensing alike have to…
We study numerically the fractal structure of the intrinsic geometry of random surfaces coupled to matter fields with $c=1$. Using baby universe surgery it was possible to simulate randomly triangulated surfaces made of 260.000 triangles.…
My main results are simple formulas for the surface area of d-dimensional lattice polytopes using Ehrhart theory.