Related papers: Smooth Interpolation of Key Frames in a Riemannian…
We carry out a Carlotto-Schoen-type gluing with interpolating scalar curvature on cone-like sets, or deformations thereof, in the category of smooth Riemannian asymptotically Euclidean metrics.
We present a method to compute a fitting curve B to a set of data points d0,...,dm lying on a manifold M. That curve is obtained by blending together Euclidean B\'ezier curves obtained on different tangent spaces. The method guarantees…
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial…
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…
Multilevel strategies are an integral part of many image registration algorithms. These strategies are very well-known for avoiding undesirable local minima, providing an outstanding initial guess, and reducing overall computation time.…
Interactive segmentation allows efficient label generation by leveraging user-provided clicks to progressively refine predictions, which is critical when fully supervised labels are costly or generalization to unseen classes is needed.…
We develop a local polynomial spline interpolation scheme for arbitrary spline order on bounded intervals. Our method's local formulation, effective boundary considerations and optimal interpolation error rate make it particularly useful…
Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…
This paper presents some applications using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain decomposition…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and…
Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions…
This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis…
Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…
In this work, we propose and develop efficient and accurate numerical methods for solving the Kirchhoff-Love plate model in domains with complex geometries. The algorithms proposed here employ curvilinear finite-difference methods for…
We revisit the classical problem of 3D shape interpolation and propose a novel, physically plausible approach based on Hamiltonian dynamics. While most prior work focuses on synthetic input shapes, our formulation is designed to be…