相关论文: Expected Distances on Manifolds of Partially Orien…

Using geometric landmarks like lines and planes can increase navigation accuracy and decrease map storage requirements compared to commonly-used LiDAR point cloud maps. However, landmark-based registration for applications like loop closure…

In this paper, we consider the flag manifold of $p$ orthogonal subspaces of equal dimension which carries an action of the cyclic group of order $p$. We provide a complete calculation of the associated Fadell-Husseini index. This may be…

Real flag manifolds are the isotropy orbits of noncompact symmetric spaces $G/K$. Any such manifold $M$ enjoys two very peculiar geometric properties: It carries a transitive action of the (noncompact) Lie group $G$, and it is embedded in…

We consider manifolds of oriented flags SO(n)/SO(2)xSO(n-3) (n>=4) as 4- and 6-symmetric spaces and indicate characteristic conditions for invariant Riemannian metrics under which the canonical f-structures on these homogeneous…

In this paper we study flag codes on $\mathbb{F}_q^n$, being $\mathbb{F}_q$ the finite field with $q$ elements. Special attention is given to the connection between the parameters and properties of a flag code and the ones of a family of…

The main result of this paper is a new parameterization of the orbits of a symmetric subgroup on a partial flag variety. The parameterization is in terms of certain Spaltenstein varieties, on one hand, and certain nilpotent orbits, on the…

Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several…

When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…

We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…

Image analysis frequently deals with shape estimation and image reconstruction. The ob jects of interest in these problems may be thought of as random sets, and one is interested in finding a representative, or expected, set. We consider a…

A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…

Let $X$ be a $d$-dimensional random vector and $X_\theta$ its projection onto the span of a set of orthonormal vectors $\{\theta_1,...,\theta_k\}$. Conditions on the distribution of $X$ are given such that if $\theta$ is chosen according to…

The need for efficiently comparing and representing datasets with unknown alignment spans various fields, from model analysis and comparison in machine learning to trend discovery in collections of medical datasets. We use manifold learning…

In this paper we obtain estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situation where the systems are defined in different phase spaces and we…

We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depending on the problem at hand, may often not be the best…

Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…

We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…

In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…

Many interesting geometric structures can be described as regular infinitesimal flag structures, which occur as the underlying structures of parabolic geometries. Among these structures we have for instance conformal structures, contact…