相关论文: From Active Contours to Minimal Geodesic Paths: Ne…
Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the…
Computing the epipolar geometry between cameras with very different viewpoints is often problematic as matching points are hard to find. In these cases, it has been proposed to use information from dynamic objects in the scene for…
The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
The motion planning problem involves finding a collision-free path from a robot's starting to its target configuration. Recently, self-supervised learning methods have emerged to tackle motion planning problems without requiring expensive…
Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simple geodesic-based method. A recent subgradient-based study…
This paper investigates a variational model for splines in the image metamorphosis model for the smooth interpolation of key frames in the space of images. The Riemannian manifold of images based on the metamorphosis model defines shortest…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
In this paper, we present a novel method for using Riemannian Motion Policies on volumetric maps, shown in the example of obstacle avoidance for Micro Aerial Vehicles (MAVs). While sampling or optimization-based planners are widely used for…
Motion Planning (MP) is a critical challenge in robotics, especially pertinent with the burgeoning interest in embodied artificial intelligence. Traditional MP methods often struggle with high-dimensional complexities. Recently neural…
We use the r-matrix formulation to show the integrability of geodesic flow on an $N$-dimensional space with coordinates $q_k$, with $k=1,...,N$, equipped with the co-metric $g^{ij}=e^{-|q_i-q_j|}\big(2-e^{-|q_i-q_j|}\big)$. This flow is…
The space of images can be equipped with a Riemannian metric measuring both the cost of transport of image intensities and the variation of image intensities along motion lines. The resulting metamorphosis model was introduced and analyzed…
In this paper, we propose a novel variational active contour model based on Aubert-Aujol (AA) denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model and can be used to segment…
We employ min-max methods to construct uncountably many, geometrically distinct, properly embedded geodesic lines in any asymptotically conical surface of non-negative scalar curvature, a setting where minimization schemes are doomed to…
This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation…
Search-based planning with motion primitives is a powerful motion planning technique that can provide dynamic feasibility, optimality, and real-time computation times on size, weight, and power-constrained platforms in unstructured…
An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…
This paper addresses the morphing of manifold-valued images based on the time discrete geodesic paths model of Berkels, Effland and Rumpf 2015. Although for our manifold-valued setting such an interpretation of the energy functional is not…
Geodesic distance, commonly called shortest path length, has proved useful in a great variety of disciplines. It has been playing a significant role in search engine at present and so attracted considerable attention at the last few…
The classical Euler's problem on optimal configurations of elastic rod in the plane with fixed endpoints and tangents at the endpoints is considered. The global structure of the exponential mapping that parameterises extremal trajectories…
The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build…