Crowd-sourced mapping offers a scalable alternative to creating maps using traditional survey vehicles. Yet, existing methods either rely on prior high-definition (HD) maps or neglect uncertainties in the map fusion. In this work, we present a complete pipeline for HD map generation using production vehicles equipped only with a monocular camera, consumer-grade GNSS, and IMU. Our approach includes on-cloud localization using lightweight standard-definition maps, on-vehicle mapping via an extended object trajectory (EOT) Poisson multi-Bernoulli (PMB) filter with Gibbs sampling, and on-cloud multi-drive optimization and Bayesian map fusion. We represent the lane lines using B-splines, where each B-spline is parameterized by a sequence of Gaussian distributed control points, and propose a novel Bayesian fusion framework for B-spline trajectories with differing density representation, enabling principled handling of uncertainties. We evaluate our proposed approach, B$^2$F-Map, on large-scale real-world datasets collected across diverse driving conditions and demonstrate that our method is able to produce geometrically consistent lane-level maps.
Positional accuracy in cadastral data is fundamental for secure land tenure and efficient land administration. However, many land administration systems, experience difficulties to meet accuracy standards, particularly in areas with digitized historical maps, leading to disruptions in land transactions. This study investigates the use of unsupervised clustering algorithms in order to identify and characterize systematic spatial error patterns in cadastral maps. We compare Fuzzy c-means (FCM), Density-Based Spatial Clustering of Applications with Noise (DBSCAN), and Gaussian Mixture Models (GMM) in clustering error vectors derived from 500 homologous points. These points were obtained by comparing cadastral data with a higher-accuracy land survey within a 7 km² area in Ioannina, Greece, known for its inaccuracies in the Greek National Cadastre. The optimal number of clusters for each algorithm was determined. Results show that DBSCAN and GMM successfully captured a central area of random errors surrounded by a region exhibiting a systematic, counter-clockwise rotational error, whereas FCM did not capture this pattern. DBSCAN, with its ability to isolate noise points in the center of the study area, provided the most interpretable results. This clustering approach can be integrated into automated cadastral map improvement methods, contributing to progressive cadastral renewal efforts.
Aims. Magnetic and abundance maps of chemically peculiar (CP) stars, derived with the help of Zeeman Doppler mapping, have invariably been used as arguments against theories, in particular atomic diffusion theory. We intend to expose the fallacy of these claims. Methods. We have identified in the literature those (5) CP stars for which multiple maps have been published, all based on the same Zeeman Doppler mapping strategy. For each of these stars we have then carried out inter comparisons between the recovered distributions of magnetic field and of abundances. Results. Agreement between maps often turns out to be quite poor in regard to both abundances, field topology and absolute field strengths. Maps based on the same set of observations can differ considerably, even when they are coming from the same authors. Conclusions. It becomes clear that Zeeman Doppler mapping cannot be guaranteed to yield unique results. When a number of physically impossible magnetic geometries all provide good fits to the observed Stokes $IQUV$ profiles, these solutions must necessarily be spurious and cannot be used as constraints to diffusion theory.
Many countries measure poverty based only on income or consumption. However, there is a growing awareness of measuring poverty through multiple dimensions that captures a more reasonable status of poverty. Estimating poverty measure(s) for small geographical areas, commonly referred to as poverty mapping, is challenging due to small or no sample for the small areas. While there is a huge literature available on unidimensional poverty mapping, only a limited effort has been made to address special challenges that arise only in the multidimensional poverty mapping. For example, in multidimensional poverty mapping, a new problem arises involving estimation of relative contributions of different dimensions to overall poverty for small areas. This problem has been grossly ignored in the small area estimation (SAE) literature. We address this issue using a multivariate hierarchical model implemented via a Bayesian method. Moreover, we demonstrate how a multidimensional poverty composite measure can be estimated for small areas. In this paper, we demonstrate our proposed methodology using a survey data specially designed by one of us for multidimensional poverty mapping. This paper adds a new direction to poverty mapping literature.
Using the norm operator method, which extends and corrects the conventional boson expansion theories, we investigate two boson mappings of the boson expansion theory, the so-called mapping after truncation and the mapping before truncation. The difference between them stems from the treatment of the phonon excitation modes; those not adopted as boson excitation modes in the former mapping are first all adopted as boson excitation modes and then truncated later in the latter mapping. If and only if the commutation relations among the phonon operators are closed among the excitation modes adopted as the boson excitation modes in the mapping after truncation, the mapping after and the mapping before truncation coincide, not depending on the types, Hermitian and non-Hermitian. We also investigate the Park operator, which judges whether a boson state vector is physical, and reveal that the conventional claim, which claims that it is applicable only when the mapping is that of the whole fermion space, is incorrect.
Online dense mapping of urban scenes forms a fundamental cornerstone for scene understanding and navigation of autonomous vehicles. Recent advancements in mapping methods are mainly based on NeRF, whose rendering speed is too slow to meet online requirements. 3D Gaussian Splatting (3DGS), with its rendering speed hundreds of times faster than NeRF, holds greater potential in online dense mapping. However, integrating 3DGS into a street-view dense mapping framework still faces two challenges, including incomplete reconstruction due to the absence of geometric information beyond the LiDAR coverage area and extensive computation for reconstruction in large urban scenes. To this end, we propose HGS-Mapping, an online dense mapping framework in unbounded large-scale scenes. To attain complete construction, our framework introduces Hybrid Gaussian Representation, which models different parts of the entire scene using Gaussians with distinct properties. Furthermore, we employ a hybrid Gaussian initialization mechanism and an adaptive update method to achieve high-fidelity and rapid reconstruction. To the best of our knowledge, we are the first to integrate Gaussian representation into online dense mapping of urban scenes. Our approach achieves SOTA reconstruction accuracy while only employing 66% number of Gaussians, leading to 20% faster reconstruction speed.
This paper uses the renowned Kechris-Pestov-Todorčević machinery to show that (big) mapping class groups are not extremely amenable unless the underlying surface is a sphere or a once-punctured sphere, or equivalently when the mapping class group is trivial. The same techniques also show that the pure mapping class groups, as well as compactly supported mapping class groups, of a surface with genus at least one can never be extremely amenable.
Accurate mapping of large-scale environments is an essential building block of most outdoor autonomous systems. Challenges of traditional mapping methods include the balance between memory consumption and mapping accuracy. This paper addresses the problem of achieving large-scale 3D reconstruction using implicit representations built from 3D LiDAR measurements. We learn and store implicit features through an octree-based, hierarchical structure, which is sparse and extensible. The implicit features can be turned into signed distance values through a shallow neural network. We leverage binary cross entropy loss to optimize the local features with the 3D measurements as supervision. Based on our implicit representation, we design an incremental mapping system with regularization to tackle the issue of forgetting in continual learning. Our experiments show that our 3D reconstructions are more accurate, complete, and memory-efficient than current state-of-the-art 3D mapping methods.
We investigate the relation between the topological entropy of pseudo-Anosov maps on surfaces with punctures and the rank of the first homology of their mapping tori. On the surface $S$ of genus $g$ with $n$ punctures, we show that the entropy of a pseudo-Anosov map is bounded from above by $\dfrac{(k+1)\log(k+3)}{|χ(S)|}$ up to a constant multiple when the rank of the first homology of the mapping torus is $k+1$ and $k, g, n$ satisfy a certain assumption. This is a partial generalization of precedent works of Tsai and Agol-Leininger-Margalit.
In this paper, we revisit our paper "Matrix Riccati Equations, Kaluza-Klein, Finsler Spaces, and Mapping Among Manifolds"[1]. We will build mapping among generalized quadratic Hamiltonians and we construct Calabi's Riemmannian Line Elements for non-quadratic and generalized Hamiltonians. As an application, we use conformally flat forms of two general pseudo-Riemannian line elements embedded in two flat manifolds and obtain an analytical and exact solution of the mapping between these two manifolds as well as an infinite set of exact solutions of the associated matrix Riccati equation.
The article analyzes the conceptual and terminological support in the field of economics of nature management and environmental protection. The need for an in-depth etymological study of the terminological apparatus related to the concept of "land resource potential", namely the concepts of "resource", "potential", "land" in terms of increasing competition among businesses for resources and markets for manufactured products. In this regard, a significant amount of bibliographic and electronic Internet sources, both foreign and domestic authors and researchers. The role of resource potential in the agro-industrial complex of Ukraine is substantiated and determined. The author's interpretation of the concept of "land resource potential" as a set of land, labor, material and economic resources, endowed with the potential for the development of productive forces and characterized by indispensability in the production of dependent and territorially spheres of production. The generalization of concepts is carried out and the mathematical interpretation of the concept "land resource potential" is offered. The establishment of classification features is substantiated and the species classification of resources is carried out. In the course of the research the functional properties of land resource potential were identified and generalized. The role of land resources as one of the main ones in the structure of the nature management system is determined.Key words: land resource potential, land use, nature management, economics of nature management, land.
All geospatial data are updated periodically. Cadastral parcel mapping, however, has special update requirements that set it apart from other geospatial data. Mapped boundaries change continuously to fit with new survey plans. Additionally, new parcels have to be fitted and aligned with adjoining parcels to merge them into existing cadastral mapping. This is preferably performed by a spatial adjustment approach to systematically improve its accuracy over time. This paper adapts methods for analysis and adjustment of survey networks to improve the accuracy of cadastral mapping with better coordinate positioning and survey plan dimensions. Case studies for both hypothetical and real cadastral mapping are used to illustrate the issues and spatially resolve errors. Adjustment results achieve an accuracy consistent with other GIS layers and boundary features visible in high-resolution orthoimagery. Graphical charts based on stress–strain relationships provide a simplified means to interpret post-adjustment results to identify and fix potential errors.
Doris Pivac, Miodrag Roić, Josip Križanović
et al.
A systematic approach to the establishment of the Franciscan Cadastre, which has been performed in most Central European countries, has resulted in the following documents: cadastral maps, cadastral municipality boundary demarcation records, lists of land parcels, lists of building parcels and lists of possessors. The documentation, which is stored in various archives, is digitized and made available to users through catalogs. The availability of documentation was examined in this study using three services in the catalogs—discovery, view and download—of which the largest percentage of documents is available through the discovery service. Documents that are available through the discovery service are described by the metadata standards. In this study, we examined the applicability of geographic information metadata standards and metadata standards to archival documentation in catalogs in which cadastral documentation was found. We determined a lack of application of geoinformation metadata standards, as it was a cadastral dataset, which represented one of the fundamental spatial datasets. The semantic mapping of elements between the applied standards in the catalogs and the geoinformation metadata standard (ISO 19115) showed that it was possible to apply the ISO 19115 standard to documents resulting from the establishment of the cadastre.
Felipe de Souza Pimenta, Frederico Vasconcelos Ribeiro, Dionísio Costa Cruz Júnior
This research proposed the construction and performance evaluation of multiple linear regression models (conventional and spatial) for the city of Itororó (BA) and thus enable the elaboration of a Generic Values Plant (PVG) and estimation of the Urban Property Tax (IPTU). To this end, the elaboration process of these models included aerophotogrammetric mapping, and real state register, spatial analyzes, multicollinearity, normality and homoscedasticity of the residues, as well as spatial dependence tests according to NBR 14.653-2/2011. The results indicated that incorporating the effects of spatial autocorrelation through the reduced spatial lag model provided better performance than the conventional one. However the construction of the geographically weighted regression model also reduced, able to model spatial heterogeneity, it was even more adequate, providing almost all the explanation of the predicted values variation, as well as a sharp reduction of the prediction errors and the dispersion coefficient. The extrapolation of this model provided the elaboration of PVG with total values and simulation of IPTU. Thus, the increase in the 1% tax rate would provide a considerable share of internal revenues for municipal revenue.
For a definable continuous mapping $f$ from a definable connected open subset $Ω$ of $\mathbb R^n$ into $\mathbb R^n,$ we show that the following statements are equivalent: (i) The mapping $f$ is open. (ii) The fibers of $f$ are finite and the Jacobian of $f$ does not change sign on the set of points at which $f$ is differentiable. (iii) The fibers of ${f}$ are finite and the set of points at which $f$ is not a local homeomorphism has dimension at most $n - 2.$ As an application, we prove that Whyburn's conjecture is true for definable mappings: A definable open continuous mapping of one closed ball into another which maps boundary homeomorphically onto boundary is necessarily a homeomorphism.
Mislav Blažević, Stefan Canzar, Khaled Elbassioni
et al.
The well-studied Tai mapping between two rooted labeled trees $T_1(V_1, E_1)$ and $T_2(V_2, E_2)$ defines a one-to-one mapping between nodes in $T_1$ and $T_2$ that preserves ancestor relationship. For unordered trees the problem of finding a maximum-weight Tai mapping is known to be NP-complete. In this work, we define an anti Tai mapping $M\subseteq V_1\times V_2$ as a binary relation between two unordered labeled trees such that any two $(x,y), (x', y')\in M$ violate ancestor relationship and thus cannot be part of the same Tai mapping, i.e. $(x\le x' \iff y\not \le y') \vee (x'\le x \iff y'\not \le y)$, given an ancestor order $x<x'$ meaning that $x$ is an ancestor of $x'$. Finding a maximum-weight anti Tai mapping arises in the cutting plane method for solving the maximum-weight Tai mapping problem via integer programming. We give an efficient polynomial-time algorithm for finding a maximum-weight anti Tai mapping for the case when one of the two trees is a path and further show how to extend this result in order to provide a polynomially computable lower bound on the optimal anti Tai mapping for two unordered labeled trees. The latter result stems from the special class of anti Tai mapping defined by the more restricted condition $x\sim x' \iff y\not\sim y'$, where $\sim$ denotes that two nodes belong to the same root-to-leaf path. For this class, we give an efficient algorithm that solves the problem directly on two unordered trees in $O(|V_1|^2|V_2|^2)$.
It is proved that the mapping class group of any closed surface with finitely many marked points is quasiisometric to a CAT(0) cube complex. We provide two distinct proofs, one tailored to mapping class groups, and one applying to a larger class of groups.
For $g\geq 2$, let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g$. In this paper, we obtain necessary and sufficient conditions under which a given pseudo-periodic mapping class can be a root of another up to conjugacy. Using this characterization, the canonical decomposition of (non-periodic) mapping classes, and some known algorithms, we give an algorithm for determining the conjugacy classes of roots of arbitrary mapping classes. Furthermore, we derive realizable bounds on the degrees of roots of pseudo-periodic mapping classes in $\mathrm{Mod}(S_g)$, the Torelli group, the level-$m$ subgroup of $\mathrm{Mod}(S_g)$, and the commutator subgroup of $\mathrm{Mod}(S_2)$. In particular, we show that the highest possible (realizable) degree of a root of a pseudo-periodic mapping class $F$ is $3q(F)(g+1)(g+2)$, where $q(F)$ is a unique positive integer associated with the conjugacy class of $F$. Moreover, this bound is realized by a root of a power of a Dehn twist about a separating curve of genus $[g/2]$ in $S_g$, where $g\equiv 0,9 \pmod{12}$. Finally, for $g\geq 3$, we show that any pseudo-periodic mapping class having a nontrivial periodic component that is not the hyperelliptic involution, normally generates $\mathrm{Mod}(S_g)$. Consequently, we establish that $\mathrm{Mod}(S_g)$ is normally generated by a root of bounding pair map or a root of a nontrivial power of a Dehn twist.
The article describes the creation of a geo-information basis for cadastral registration of land plots using the cartometric method for development of the technology of the cartometric method by Microsoft Office and AutoCad tools.