Related papers: Coupled quasi-harmonic bases
Given a set of $p$ symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these $p$ matrices is as close as possible to a diagonal…
The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigenfunctions. A rigorous analysis is performed to show the…
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian…
Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match…
Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is…
Copying an element from a photo and pasting it into a painting is a challenging task. Applying photo compositing techniques in this context yields subpar results that look like a collage --- and existing painterly stylization algorithms,…
Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple small-degree vertices, in order to allow for more efficient…
Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighbourhood of each atom in the system. Symmetry considerations support the use of…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
Spectral analysis of open surfaces is gaining momentum for studying surface morphology in engineering, computer graphics, and medical domains. This analysis is enabled using proper parameterization approaches on the target analysis domain.…
A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes in flat domains while preserving…
Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…
Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the…
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…
How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to…