Related papers: Wavelet-based Heat Kernel Derivatives: Towards Inf…
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression…
A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of…
Heat diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate…
Kernel extreme learning machine (KELM) is a novel feedforward neural network, which is widely used in classification problems. To some extent, it solves the existing problems of the invalid nodes and the large computational complexity in…
A new method is presented for the construction of a natural continuous wavelet transform on the sphere. It incorporates the analysis and synthesis with the same wavelet and the definition of translations and dilations on the sphere through…
In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…
We study the low-energy approximation for calculation of the heat kernel which is determined by the strong slowly varying background fields in strongly curved quasi-homogeneous manifolds. A new covariant algebraic approach, based on taking…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and…
We introduce and study new invariants associated with Laplace type elliptic partial differential operators on manifolds. These invariants are constructed by using the off-diagonal heat kernel; they are not pure spectral invariants, that is,…
Spectral shape descriptors have been used extensively in a broad spectrum of geometry processing applications ranging from shape retrieval and segmentation to classification. In this pa- per, we propose a spectral graph wavelet approach for…
We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat kernel…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
Network theory provides a principled abstraction of the human brain: reducing a complex system into a simpler representation from which to investigate brain organisation. Recent advancement in the neuroimaging field are towards representing…
Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling…
The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…
A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…
The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space. Towards this end, we introduce a \textit{multiwavelet-based neural operator learning scheme}…