Results 81 to 90 of about 752 (172)

RHG-DETR: Riemannian Hyper-Graph Transformer with Dynamic Receptive Fields for Detecting Special Targets in Degraded UAV Imagery

Remote Sensing
Special target detection in UAV remote sensing imagery is challenged by composite multi-type degradation, which collectively erodes target structure across every stage of a detection pipeline.
Kaipeng Wang, Guanglin He, Wenhao Kong, Yuzhe Fu, Zongze Li   +4 more
doaj   +1 more source

Curvature exponent and geodesic dimension on Sard-regular Carnot groups

Analysis and Geometry in Metric Spaces
In this study, we characterize the geodesic dimension NGEO{N}_{{\rm{GEO}}} and give a new lower bound to the curvature exponent NCE{N}_{{\rm{CE}}} on Sard-regular Carnot groups.
Golo Sebastiano Nicolussi, Zhang Ye
doaj   +1 more source

Singularities in sub-Riemannian geometry

, 2018
We investigate the relationship between features of of sub-Riemannian geometry and an array of singularities that typically arise in this context.With sub-Riemannian Whitney theorems, we ensure the existence of global extensions of horizontal curves defined on closed set by requiring a non-singularity hypothesis on the endpoint-map of the nilpotent ...
openaire   +2 more sources

Metric lines in the jet space

Analysis and Geometry in Metric Spaces
In the realm of sub-Riemannian manifolds, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of kk-jets of a real function of one real variable xx, denoted by Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}),
Bravo-Doddoli Alejandro
doaj   +1 more source

Good continuation in 3D: the neurogeometry of stereo vision

Frontiers in Computer Science
Classical good continuation for image curves is based on 2D position and orientation. It is supported by the columnar organization of cortex, by psychophysical experiments, and by rich models of (differential) geometry.
Maria Virginia Bolelli, Maria Virginia Bolelli, Giovanna Citti, Alessandro Sarti, Steven W. Zucker   +4 more
doaj   +1 more source

The Sub-Riemannian Foundations of Contact Geometry

This paper explores the profound and intrinsic connections between sub-Riemannian geometry and contact geometry. It demonstrates how the non-integrable distributions inherent in contact manifolds naturally give rise to sub-Riemannian structures. We delve into the fundamental definitions and theorems governing both fields, elucidating how contact forms ...
Revista, Zen, MATH, 10
openaire   +1 more source

Analytic torsion of nilmanifolds with (2, 3, 5) distributions

Analysis and Geometry in Metric Spaces
We consider generic rank two distributions on five-dimensional nilmanifolds and show that the analytic torsion of their Rumin complex coincides with the Ray-Singer torsion.
Haller Stefan
doaj   +1 more source

Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates

Advanced Nonlinear Studies
On general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using the Rumin complex has been considered in (M. Rumin, “Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie ...
Baldi Annalisa, Tripaldi Francesca
doaj   +1 more source

Connections and Curvature in sub-Riemannian geometry

, 2009
For a subRiemannian manifold and a given Riemannian extension of the metric, we define a canonical global connection. This connection coincides with both the Levi-Civita connection on Riemannian manifolds and the Tanaka-Webster connection on strictly pseudoconvex CR manifolds.
openaire   +2 more sources

The Contact Geometry of Sub-Riemannian Structures

Sub-Riemannian geometry, a field that has gained significant traction since the late 20th century, investigates differentiable manifolds endowed with a sub-bundle of the tangent space and a Riemannian metric defined solely on this sub-bundle. This structure, arising naturally in control theory, robotics, and mathematical physics, leads to fascinating ...
Revista, Zen, MATH, 10
openaire   +2 more sources