相关论文: Flat Maps that improve on the Winkel Tripel
We determine all local smooth or formal CR maps from the unit sphere $\mathbb{S}^3\subset \mathbb{C}^2$ into the tube $\mathcal{T}:= \mathcal{C} \times i\mathbb{R}^3 \subset \mathbb{C}^3$ over the future light cone $\mathcal{C}:=…
Geographically Weighted Regression (GWR) is increasingly used in spatial analyses of social and environmental data. It allows spatial heterogeneities in processes and relationships to be investigated through a series of local regression…
In this paper, a method of improving vertical positioning accuracy with the Global Positioning System (GPS) information and barometric pressure values is proposed. Firstly, we clear null values for the raw data collected in various…
Motivated by the Lipschitz rigidity problem in scalar curvature geometry, we prove that if a closed smooth spin manifold admits a distance decreasing continuous map of non-zero degree to a sphere, then either the scalar curvature is…
In this paper we study maps (curved flats) into symmetric spaces which are tangent at each point to a flat of the symmetric space. Important examples of such maps arise from isometric immersions of space forms into space forms via their…
Reconstructing a 3D scene from unordered images is pivotal in computer vision and robotics, with applications spanning crowd-sourced mapping and beyond. While global Structure-from-Motion (SfM) techniques are scalable and fast, they often…
Shape completion networks have been used recently in real-world robotic experiments to complete the missing/hidden information in environments where objects are only observed in one or few instances where self-occlusions are bound to occur.…
Morse functions with exactly two singular points on homotopy spheres and canonical projections of spheres are generalized as special generic maps. A special generic map is, roughly, a smooth map represented as the composition of a smooth…
We provide an updated 5 $^\prime $ $\times $ 5 $^\prime $ global geoid model GGM2022, which is determined based on the shallow layer method (Shen method). First, we choose an inner surface $\Gamma$ below the EGM2008 global geoid by 15 m,…
We analyze the sensitivity of galaxy and weak-lensing surveys to detect preferred directions in the gravitational interaction. We consider general theories of gravity involving additional vector degrees of freedom with non-vanishing spatial…
We give three constructions of a vertex-minimal triangulation of $4$-dimensional real projective space $\mathbb{R}P^4$. The first construction describes a $4$-dimensional sphere on $32$ vertices, which is a double cover of a triangulated…
We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the…
We present a new method to estimate three-point correlations in Cosmic Microwave Background maps. Our Fast Fourier Transform based implementation estimates three-point functions using all possible configurations (triangles) at a controlled…
The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of…
We compare the capabilities of two approaches to approximating graph isomorphism using linear algebraic methods: the \emph{invertible map tests} (introduced by Dawar and Holm) and proof systems with algebraic rules, namely \emph{polynomial…
A result due to Burago and Zalgaller (1960, 1995) states that every orientable polyhedral surface, one that is obtained by gluing Euclidean polygons, has an isometric piecewise linear (PL) embedding into Euclidean space $\mathbb{E}^3$. A…
Detecting the reflection symmetry plane of an object represented by a 3D point cloud is a fundamental problem in 3D computer vision and geometry processing due to its various applications, such as compression, object detection, robotic…
Recent advancements in large language models have demonstrated significant potential in the automated construction of knowledge graphs from unstructured text. This paper builds upon our previous work [16], which evaluated various models…
Recently, parametric mappings have emerged as highly effective surface representations, yielding low reconstruction error. In particular, the latest works represent the target shape as an atlas of multiple mappings, which can closely encode…
Modern unmanned aerial vehicles (UAVs) are irreplaceable in search and rescue (SAR) missions to obtain a situational overview or provide closeups without endangering personnel. However, UAVs heavily rely on global navigation satellite…