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The L1 norm has been tremendously popular in signal and image processing in the past two decades due to its sparsity-promoting properties. More recently, its generalization to non-Euclidean domains has been found useful in shape analysis applications. For example, in conjunction with the minimization of the Dirichlet energy, it was shown to produce a… (More)

- Yoni Choukroun
- 2017

We introduce a Schrödinger operator for spectral approximation of meshes representing surfaces in 3D. The operator is obtained by modifying the Laplacian with a potential function which defines the rate of oscillation of the harmonics on different regions of the surface. We design the potential using a vertex ordering scheme which modulates the Fourier… (More)

- Yoni Choukroun, Elie Semmel, Yonathan Aflalo
- 2014

- Yoni Choukroun, Alon Shtern, Ron Kimmel
- ArXiv
- 2016

Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator. In this paper, we propose to adapt a classical operator from quantum mechanics to the field of shape analysis where we suggest to integrate a scalar function through a unified elliptical Hamiltonian operator. We study the… (More)

- Yoni Choukroun, Gautam Pai, Ron Kimmel
- ArXiv
- 2017

The discrete Laplace operator is ubiquitous in spectral shape analysis, since its eigenfunctions are provably optimal in representing smooth functions defined on the surface of the shape. Indeed, subspaces defined by its eigenfunctions have been utilized for shape compression, treating the coordinates as smooth functions defined on the given surface.… (More)

Many shape analysis methods treat the geometry of an object as a metric space captured by the Laplace-Beltrami operator. In this thesis we present an adaptation of a classical operator from quantum mechanics to shape analysis where we suggest to integrate a scalar function through a unified elliptical Hamiltonian operator. We study the addition of a… (More)

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