相关论文: Active Contour with A Tangential Component

We present the list of unavoidable local phenomena (transitions) occurring on the configuration of the parabolic and flecnodal curves of evolving smooth surfaces in R^3 (or RP^3). We also present the list of transitions occurring on the…

Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based…

In representation learning on the graph-structured data, under heterophily (or low homophily), many popular GNNs may fail to capture long-range dependencies, which leads to their performance degradation. To solve the above-mentioned issue,…

Accurate geometric reconstruction of deformable tissues in monocular endoscopic video remains a fundamental challenge in robot-assisted minimally invasive surgery. Although recent volumetric and point primitive methods based on neural…

Pursuit-evasion games (PEGs) model interactions between a team of pursuers and an evader in graph-based environments such as urban street networks. Recent advancements have demonstrated the effectiveness of the pre-training and fine-tuning…

Below the roughening temperature, the equilibrium crystal shape (ECS) is composed of both facets and a smoothly curved surface. As for the ``normal'' profile (perpendicular to the facet contour), the ECS has the exponent 3/2 which is…

We discuss a semi-implicit numerical scheme that allows for minimizing the bending energy of curves within certain isotopy classes. To this end we consider a weighted sum of the bending energy and the tangent-point functional. Based on…

In this article we investigate a system of geometric evolution equations describing a curvature driven motion of a family of 3D curves in the normal and binormal directions. Evolving curves may be subject of mutual interactions having both…

We introduce a simple algorithm, True Asymptotic Natural Gradient Optimization (TANGO), that converges to a true natural gradient descent in the limit of small learning rates, without explicit Fisher matrix estimation. For quadratic models…

The problem of optimization of a cycle of tangential deformations of the surface of a spherical object (microsquirmer) self-propelling in a viscous fluid at low Reynolds numbers is represented in a noncanonical Hamiltonian form. The…

Saddle points provide a hierarchical view of the energy landscape, revealing transition pathways and interconnected basins of attraction, and offering insight into the global structure, metastability, and possible collective mechanisms of…

Regime shifts are quite common in complex systems like cell regulations, disease transmissions, ecosystems, marine ice instability, etc. Several statistical indicators known as early warning signals (EWS) have been theorized to anticipate…

Transformers have achieved remarkable performance in a myriad of fields including natural language processing and computer vision. However, when it comes to the graph mining area, where graph neural network (GNN) has been the dominant…

In this paper, we study the motion by mean curvature of curves in the plane perturbed by scale-dependent noise. We first introduce a so-called scale-dependent noise from the physics background to the curve shortening flow. To be more…

A variant of consensus based distributed gradient descent (\textbf{DGD}) is studied for finite sums of smooth but possibly non-convex functions. In particular, the local gradient term in the fixed step-size iteration of each agent is…

In bistable actuators and other engineered devices, a homogeneous stimulus (e.g. mechanical, chemical, thermal, or magnetic) is often applied to an entire shell to initiate a snap-through instability. In this work, we demonstrate that…

In this study, we tackle the challenging fine-grained edge detection task, which refers to predicting specific edges caused by reflectance, illumination, normal, and depth changes, respectively. Prior methods exploit multi-scale…

Optimal curve methods provide a fundamental framework for tubular centerline tracking. Point-wise approaches, such as minimal paths, are theoretically elegant but often suffer from shortcut and short-branch combination problems in complex…

In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…

Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…