We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green’s function of an isotropic diffusion equation on a manifold is analytically represented using the eigenfunctions of the Laplace-Beltraimi operator. The Green’s function is then used in explicitly constructing heat kernel smoothing as a series expansion of the eigenfunctions. Unlike many previous ...

This paper gives a generalization of the Pseudo-Laplace transform. In the special cases of semirings, the pseudo-exchange formula is proved. Also, for these semirings the forms of the Pseudo-Laplace transform and inverse operator are given. The results can be applied in dynamical programming for finding the maximum and minimum of the utility functions. AMS Mathematics Subject Classification (19...

In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds (M, g) for the following general heat equation ut = ∆V u+ au log u+ bu where a is a constant and b is a differentiable function defined onM×[0,∞). We suppose that the Bakry-Émery curvature and the N -dimensional Bakry-Émery curvature are bounded from below, respectively. Then we obtain the gradient estimat...

We study a semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. Key results are semiboundedness theorem of the Schrödinger operator, Laplace-type asymptotic formula and IMS localization formula. We also make a remark on semiclassical problem of a Schrödinger operator on a path space over a Riemannian manifold. MSC: Primary 81Q20, Secondary 60H07, 35J10.

This paper presents a lifting wavelet based edge detection algorithm for NaXi Pictographs, effectively reducing noises while improving the precision, which makes up the drawbacks of traditional edge detection. It is proved by emulation that compared with Laplace operator, Sobel operator, Canny operator, and multi-scale wavelet edge detection algorithm, this algorithm has better detection effect.

1. Integration on manifolds. 1 2. The extension of the Levi-Civita connection. 4 3. Covariant derivatives. 7 4. The Laplace operator. 9 5. Self-adjoint extension of the Laplace operator. 11 6. The Poincaré Lemma. 13 7. de Rham Theorem. 14 8. Formal Hodge Theorem. 16 9. The Hodge theorem. 17 10. Proof of the Hodge Theorem. 17 11. More about elliptic regularity. 22 12. Semigroups and their genera...

The P1 discretization of the Laplace operator on a triangulated polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the P1 discretization of the Laplace operator. Among all triangles, an equilateral triangle has the maximal first positive eigenvalue. Among all cyclic quadrilateral, a square has the maximal first positive ...

Mesh segmentation offers a desirable divide-and-conquer strategy for many graphics applications. In this paper, we present a novel, efficient, and intrinsic method to segment meshes following the minima rule. The eigenfunctions of the Laplace-Beltrami operator define locality and volume-shape preserving functions over a surface. Inspired on Manifold learning theory, we use these functions as th...

This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new...

The ubiquity of the Laplace-Beltrami operator in shape analysis can be seen by observing the wide variety of applications where it has been found to be useful. Here we demonstrate a small subset of such uses with their latest developments including a scale invariant transform for general triangulated meshes, an effective and efficient method for denoising meshes using Beltrami flows via high di...