相关论文: LBONet: Supervised Spectral Descriptors for Shape …

In much of the literature on function approximation by deep networks, the function is assumed to be defined on some known domain, such as a cube or a sphere. In practice, the data might not be dense on these domains, and therefore, the…

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…

Many genus-0 surface mapping tasks such as landmark alignment, feature matching, and image-driven registration, can be reduced (via an initial spherical conformal map) to optimizing a spherical self-homeomorphism with controlled distortion.…

We improve a specific method to obtain the dimension of the eigenspaces of the Laplace-Beltrami operator on lens spaces and establish some applications related to the explicit description of the dimension of the smallest positive eigenvalue…

We introduce a non-backtracking Laplace operator for graphs and we investigate its spectral properties. With the use of both theoretical and computational techniques, we show that the spectrum of this operator captures several structural…

Thermal field reconstruction in post-exposure bake (PEB) is critical for advanced lithography, yet current physics-informed neural networks (PINNs) suffer from inconsistent accuracy due to a misalignment between geometric coordinates,…

Deep learning based landcover classification algorithms have recently been proposed in literature. In hyperspectral images (HSI) they face the challenges of large dimensionality, spatial variability of spectral signatures and scarcity of…

The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…

The main objective of this dissertation is to analyse thoroughly the construction of self-adjoint extensions of the Laplace-Beltrami operator defined on a compact Riemannian manifold with boundary and the role that quadratic forms play to…

In this paper, we propose a fully differentiable pipeline for estimating accurate dense correspondences between 3D point clouds. The proposed pipeline is an extension and a generalization of the functional maps framework. However, instead…

Unsupervised discovery of latent representations, in addition to being useful for density modeling, visualisation and exploratory data analysis, is also increasingly important for learning features relevant to discriminative tasks.…

The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from its eigenvalues and eigenfunctions determines the Riemannian metric. This work proves the…

Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator.…

Unsupervised localization and segmentation are long-standing computer vision challenges that involve decomposing an image into semantically-meaningful segments without any labeled data. These tasks are particularly interesting in an…

Although unsupervised feature learning has demonstrated its advantages to reducing the workload of data labeling and network design in many fields, existing unsupervised 3D learning methods still cannot offer a generic network for various…

Free-boundary diffeomorphism optimization, an important and widely occurring task in geometric modeling, computer graphics, and biological imaging, requires simultaneously determining a planar target domain and a locally bijective map with…

In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below and positive injectivity radius. Denote by L the Laplace-Beltrami operator on M. We assume that the kernel associated to…

The received in-phase and quadrature (I/Q) baseband signals inherently encode physical-layer and channel characteristics of wireless links. Learning robust and transferable representations directly from such raw signals, however, remains…

We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.

In real-world applications with large state and action spaces, reinforcement learning (RL) typically employs function approximations to represent core components like the policies, value functions, and dynamics models. Although powerful…