This paper describes a fast corner detection algorithm making use of the Laplacian of Gaussian operator. We propose a general corner model and analyze its behavior in scale space. The study shows that the response of the operator has a stable elliptic extremum which always lies inside the corner. Using a multi-scale representation limited to two scales and the sole laplacian of Gaussian operato...

In this work we propose a generalization of the Heat Kernel Signature (HKS). The HKS is a point signature derived from the heat kernel of the Laplace-Beltrami operator of a surface. In the theory of exterior calculus on a Riemannian manifold, the Laplace-Beltrami operator of a surface is a special case of the Hodge Laplacian which acts on r-forms, i. e. the Hodge Laplacian on 0-forms (functions...

We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.

A new derivation is given of Branson’s factorization formula for the conformally invariant operator on the sphere whose principal part is the k-th power of the scalar Laplacian. The derivation deduces Branson’s formula from knowledge of the corresponding conformally invariant operator on Euclidean space (the k-th power of the Euclidean Laplacian) via conjugation by the stereographic projection ...

In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...

Inspired by the linear Schrödinger operator, we consider a generalized p-Laplacian operator on discrete graphs and present new results that characterize several spectral properties of this with particular attention to nodal domain count its eigenfunctions. Just like one-dimensional continuous p-Laplacian, prove variational spectrum forests is entire spectrum. Moreover, show how transfer Weyl's ...

1 Laplacian Methods: An Overview 2 1.1 De…nition: The Laplacian operator of a Graph . . . . . . . . . . 2 1.2 Properties of the Laplacian and its Spectrum . . . . . . . . . . . 4 1.2.1 Spectrum of L and e L: Graph eigenvalues and eigenvectors: 4 1.2.2 Other interesting / useful properties of the normalized Laplacian (Chung): . . . . . . . . . . . . . . . . . . . . . 6 1.2.3 Laplacians of Weight...