相关论文: The Stability of Convergence of Curve Evolutions i…

While successful for various computer vision tasks, deep neural networks have shown to be vulnerable to texture style shifts and small perturbations to which humans are robust. In this work, we show that the robustness of neural networks…

In evolutionary optimization, it is important to understand how fast evolutionary algorithms converge to the optimum per generation, or their convergence rate. This paper proposes a new measure of the convergence rate, called average…

We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…

Where graphs are used for modelling and specifying systems, consistency is an important concern. To be a valid model of a system, the graph structure must satisfy a number of constraints. To date, consistency has primarily been viewed as a…

Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…

The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a…

In this article, we study rectifying curves in arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. We…

We investigate the evolution of open curves with fixed endpoints under the curve shortening flow, which evolves curves in proportion to their curvature. Using a distance comparison of Huisken, we determine the long-term behavior of open…

Long time existence and convergence to a circle is proved for radial graph solutions to a mean curvature type curve flow in warped product surfaces (under a weak assumption on the warp potential of the surface). This curvature flow…

Motion by weighted mean curvature is a geometric evolution law for surfaces and represents steepest descent with respect to anisotropic surface energy. It has been proposed that this motion could be computed numerically by using a…

Over the past 30 years many researchers in the field of evolutionary computation have put a lot of effort to introduce various approaches for solving hard problems. Most of these problems have been inspired by major industries so that…

Video stabilization remains a fundamental problem in computer vision, particularly pixel-level synthesis solutions for video stabilization, which synthesize full-frame outputs, add to the complexity of this task. These methods aim to…

Computing systems are omnipresent; their sustainability has become crucial for our society. A key aspect of this sustainability is the ability of computing systems to cope with the continuous change they face, ranging from dynamic operating…

Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…

For a parabolic surface partial differential equation coupled to surface evolution, convergence of the spatial semidiscretization is studied in this paper. The velocity of the evolving surface is not given explicitly, but depends on the…

The mean curvature flow is an evolution process under which a submanifold deforms in the direction of its mean curvature vector. The hypersurface case has been much studied since the eighties. Recently, several theorems on regularity,…

An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…

Inspired by convolutional neural networks on 1D and 2D data, graph convolutional neural networks (GCNNs) have been developed for various learning tasks on graph data, and have shown superior performance on real-world datasets. Despite their…

In this paper, we study planar polygonal curves from the variational methods. We show an unified interpretation of discrete curvatures and the Steiner-type formula by extracting the notion of the discrete curvature vector from the first…

Here we consider degenerations of stable spin curves for a fixed smoothing of a non-stable curve: we are able to give enumerative results and a description of limits of stable spin curves. We give a geometrically meaningful definition of…