Modified Virtual Grid Difference for Discretizing the Laplace--Beltrami Operator on Point Clouds
نویسندگان
چکیده
منابع مشابه
Discretizing Laplace–Beltrami Operator from Differential Quantities
The Laplace–Beltrami operator (LBO) is the fundamental geometric object associated with manifold surfaces and has been widely used in various tasks in geometric processing. By understanding that the LBO can be computed by differential quantities, we propose an approach for discretizing the LBO on manifolds by estimating differential quantities. For a point on the manifold, we first fit a quadra...
متن کاملLaplace–Beltrami Operator on Point Clouds Based on Anisotropic Voronoi Diagram
The symmetrizable and converged Laplace–Beltrami operator ( M) is an indispensable tool for spectral geometrical analysis of point clouds. The M, introduced by Liu et al. [LPG12] is guaranteed to be symmetrizable, but its convergence degrades when it is applied to models with sharp features. In this paper, we propose a novel M, which is not only symmetrizable but also can handle the point-sampl...
متن کاملThe Laplace-Beltrami-Operator on Riemannian Manifolds
This report mainly illustrates a way to compute the Laplace-Beltrami-Operator on a Riemannian Manifold and gives information to why and where it is used in the Analysis of 3D Shapes. After a brief introduction, an overview over the necessary properties of manifolds for calculating the Laplacian is given. Furthermore the two operators needed for defining the Laplace-Beltrami-Operator the gradien...
متن کاملConstructing Laplace Operator from Point Clouds
We present an algorithm for approximating the LaplaceBeltrami operator from an arbitrary point cloud obtained from a k-dimensional manifold embedded in the ddimensional space. We show that this PCD Laplace (PointCloud Data Laplace) operator converges to the LaplaceBeltrami operator on the underlying manifold as the point cloud becomes denser. Unlike the previous work, we do not assume that the ...
متن کاملLaplace-Beltrami operator on Digital Curves
Many problems in image analysis, digital processing and shape optimization are expressed as variational problems and involve the discritization of laplacians. Indeed, PDEs containing Laplace-Beltrami operator arise in surface fairing, mesh smoothing, mesh parametrization, remeshing, feature extraction, shape matching, etc. The discretization of the laplace-Beltrami operator has been widely stud...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2018
ISSN: 1064-8275,1095-7197
DOI: 10.1137/16m1065690