Related papers: Shape Analysis via Functional Map Construction and…
Trace finite element methods have become a popular option for solving surface partial differential equations, especially in problems where surface and bulk effects are coupled. In such methods a surface mesh is formed by approximately…
An inverse problem of identifying inhomogeneity or crack in the workpiece made of nonlinear magnetic material is investigated. To recover the shape from the local measurements, a piecewise constant level set algorithm is proposed. By means…
A classical approach for surface classification is to find a compact algebraic representation for each surface that would be similar for objects within the same class and preserve dissimilarities between classes. We introduce Self…
To analyze nonlinear dynamic systems, we developed a new technique based on the square matrix method. We propose this technique called the \convergence map" for generating particle stability diagrams similar to the frequency maps widely…
While dealing with matching shapes to their parts, we often apply a tool known as functional maps. The idea is to translate the shape matching problem into "convenient" spaces by which matching is performed algebraically by solving a least…
Deep functional maps have recently emerged as a successful paradigm for non-rigid 3D shape correspondence tasks. An essential step in this pipeline consists in learning feature functions that are used as constraints to solve for a…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains. In this paper, the conjugate function method is extended to cover conformal mappings between Riemannian…
Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace operators introduced in a previous work. It is demonstrated…
We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…
Current point cloud processing algorithms do not have the capability to automatically extract semantic information from the observed scenes, except in very specialized cases. Furthermore, existing mesh analysis paradigms cannot be directly…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
We propose a new data analysis approach for the efficient post-processing of bundles of finite element data from numerical simulations. The approach is based on the mathematical principles of symmetry. We consider the case where simulations…
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…
We present an isogeometric analysis technique that builds on manifold-based smooth basis functions for geometric modelling and analysis. Manifold-based surface construction techniques are well known in geometric modelling and a number of…
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
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…