相关论文: Flat Maps that improve on the Winkel Tripel
The area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite…
The conventional surface reflection method has been widely used to measure the asphalt pavement layer dielectric constant using ground-penetrating radar (GPR). This method may be inaccurate for in-service pavement thickness estimation with…
In this paper, we explore the fixed point theory of $n$-valued maps using configuration spaces and braid groups, focussing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the…
The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where…
This paper presents a real-time 3D mapping framework based on global matching cost minimization and LiDAR-IMU tight coupling. The proposed framework comprises a preprocessing module and three estimation modules: odometry estimation, local…
Thousands of scanned historical topographic maps contain valuable information covering long periods of time, such as how the hydrography of a region has changed over time. Efficiently unlocking the information in these maps requires…
Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and…
We characterize the variety of compatible fundamental matrix triples by computing its multidegree and multihomogeneous vanishing ideal. This answers the first interesting case of a question recently posed by Br{\aa}telund and Rydell. Our…
We formulate scalar field theories coupled non-conformally to gravity in a manifestly frame-independent fashion. Physical quantities such as the $S$ matrix should be invariant under field redefinitions, and hence can be represented by the…
Let (M,g) a compact Riemannian $n$-dimensional manifold with umbilic boundary. It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean…
The auxiliary latitudes are essential tools in cartography. This paper summarizes methods for converting between them with an emphasis on providing full double-precision accuracy. This includes series expansions in the third flattening,…
In this article we introduce a new type of cyclic contraction mapping on a pair of subsets of a metric space with a graph and prove best proximity points results for the same. Also, we demonstrate that the number of such points is same with…
Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichm\"uller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal…
If $X$ is an analytic metric space satisfying a very mild doubling condition, then for any finite Borel measure $\mu$ on $X$ there is a set $N\subseteq X$ such that $\mu(N)>0$, an ultrametric space $Z$ and a Lipschitz bijection $\phi:N\to…
Given a set of astrometric observations of the same object, the problem of orbit determination is to compute the orbit and to assess its uncertainty and reliability. For the next generation surveys, with much larger number density of…
A plane near-triangulation G can be decomposed into a collection of induced subgraphs, described here as the W-components of G, such that G is perfect (respectively, chordal) if and only if each of its W-components is perfect (respectively,…
Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary $\partial M$. Suppose that $(M,g)$ admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric quotient over the…
In recent years, deep learning techniques (e.g., U-Net, DeepLab) have achieved tremendous success in image segmentation. The performance of these models heavily relies on high-quality ground truth segment labels. Unfortunately, in many…
Accurate localization of other traffic participants is a vital task in autonomous driving systems. State-of-the-art systems employ a combination of sensing modalities such as RGB cameras and LiDARs for localizing traffic participants, but…
In this paper the geometry of normal metric contact pair manifolds is studied under the flatness of conformal, concircular and quasi-conformal curvature tensors. It is proved that a conformal flat normal metric contact pair manifold is an…