相关论文: Sparse Approximation of 3D Meshes using the Spectr…

Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric…

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 the classical Hamiltonian operator from quantum mechanics to the field…

Spectral methods are widely used in geometry processing of 3D models. They rely on the projection of the mesh geometry on the basis defined by the eigenvectors of the graph Laplacian operator, becoming computationally prohibitive as the…

Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…

Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps…

The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…

Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers…

We introduce the sparse operator compression to compress a self-adjoint higher-order elliptic operator with rough coefficients and various boundary conditions. The operator compression is achieved by using localized basis functions, which…

Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape.…

Eigenanalysis of differential operators, such as the Laplace operator or elastic energy Hessian, is typically restricted to a single shape and its discretization, limiting reduced order modeling (ROM). We introduce the first eigenanalysis…

Representing a signal as a linear combination of a set of basis functions is central in a wide range of applications, such as approximation, de-noising, compression, shape correspondence and comparison. In this context, our paper addresses…

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in…

The eigenfunctions of the Laplace Beltrami operator (Manifold Harmonics) define a function basis that can be used in spectral analysis on manifolds. In [21] the authors recast the problem as an orthogonality constrained optimization problem…

Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of…

When depth sensors provide only 5% of needed measurements, reconstructing complete 3D scenes becomes difficult. Autonomous vehicles and robots cannot tolerate the geometric errors that sparse reconstruction introduces. We propose curvature…

We address the problem of 3D shape registration and we propose a novel technique based on spectral graph theory and probabilistic matching. The task of 3D shape analysis involves tracking, recognition, registration, etc. Analyzing 3D data…

We introduce a novel approach to measure the behavior of a geometric operator before and after coarsening. By comparing eigenvectors of the input operator and its coarsened counterpart, we can quantitatively and visually analyze how well…

The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback…

We ask whether the Hamiltonian, interaction geometry, and symmetries of a quantum many-body system can be inferred from a few low-lying eigenstates without knowing which sites interact with each other. Directly solving the eigenvalue…

In geometry processing, smoothness energies are commonly used to model scattered data interpolation, dense data denoising, and regularization during shape optimization. The squared Laplacian energy is a popular choice of energy and has a…