Extended model of topological relations between spatial objects in geographic information systems

This paper presents an extended model for describing topological relations between two sets (objects) in geographic information systems (GIS). First, based on the definition of the topological relations between two objects, we uncover a sequence of topological relations between two convex sets.Second, an extended model for topological relations between two sets is proposed based on the new definition. The topological relations between two convex sets are expressed as a sequence of 4 × 4 matrices, which are the topological properties of A^o ∩ B^o, A^o\B, B^o\A, ∂A ∩ ∂B. The model is also extended for handling the properties of the topological relations between two non-convex sets, where the factor of first fundamental group is added to A ∪ B to handle these complex relations.The results show that the number of topological relations between the two sets is not as simple as finite but infinite and can be approximated by a sequence of matrices.     

移动目标空间拓扑关系的度量描述

针对传统9交模型对移动目标空间拓扑关系表达及量化描述的不足,基于格网化思想,提出了度量参数量化描述的方法。首先对移动目标和参考目标进行格网化,划分为固定大小的格网阵列;然后利用9交模型确定空间目标间拓扑关系的形式化描述;最后引入内部分量、边界分量、外部分量3种度量参数对移动目标空间拓扑关系进行度量化描述。试验证明,该方法计算简单、直观,能更加有效地度量移动目标间的拓扑关系。     

多尺度表达中空间拓扑关系等价性评价模型

本文主要讨论不同尺度下地理目标之间拓扑关系的等价性问题。根据人类认知习惯,得出从大比例尺地理空间中拓扑关系抽象为小比例尺空间中拓扑关系应当遵循的基本规则,并利用模糊函数将这些规则定量化;在此基础上,得到评价地理空间场景中多个空间目标之间拓扑关系在不同尺度下是否等价的综合评价模型。该模型可以用于检验和维护空间数据质量、为地图自动综合提供空间关系处理和评价方法的参考。     

在空间抽象中线状目标间拓扑关系的等价转换

拓扑关系在抽象过程中的等价转换是维护多尺度空间关系一致性的基础。本文以空间拓扑关系组合推理所描述的线状目标之间的拓扑关系为例,采用成分抽象的等价转换方法,研究了线之间拓扑关系等价转换的原则,并绘出了相应的等价转换图。     

Quantitative relations between spatial similarity degree and map scale change of individual linear objects in multi-scale map spaces

Quantitative relations between spatial similarity degree and map scale change in multi-scale map spaces play important roles in map generalization and construction of spatial data infrastructure. Nevertheless, no achievements have been made regarding this issue. To fill the gap, this paper firstly proposes a model for calculating spatial similarity degrees between an individual linear object at one scale and its generalized counterpart at the other scale. Then psychological experiments are designed to validate the new model, taking four different individual linear objects at five different scales as test samples. The experiments have shown that spatial similarity degrees calculated by the new model can be accepted by a majority of the subjects. After this, it constructs a formula that can calculate spatial similarity degree using map scale change (and vice versa) for individual linear objects in multi-scale map spaces by the curve fitting method using the point data from the psychological experiments. Both the formula and the model can calculate quantitative relations between spatial similarity degree and map scale change of individual linear objects in multi-scale map spaces, which facilitates automation of map generalization algorithms for linear features.     

居民地与道路之间拓扑关系一致性的模糊评价

在地图制图综合中必须保持不同尺度同一区域地图要素之间拓扑关系的一致性,但目前有关的一致性评价方面的研究较少,本文讨论了不同比例尺地图中居民地与道路之间拓扑关系一致性的模糊评价问题.从制图规则和视觉限制的角度,分析了多尺度地图表达中居民地与道路之间的应该保持拓扑关系的一致性的几项规则;基于模糊数学理论提出了制图综合中拓扑关系的一致性评价模型,并通过一个简单实例证明了该方法的可行性.     

Creating a Population of 12‐Digit Headwater Basins within the Albemarle‐Pamlico Estuary System

Ecological research within the US Environmental Protection Agency's Office of Research and Development has recently changed its focus to quantifying and mapping ecosystem services provided to humans. Our local research group has been charged to develop a regional assessment of several ecosystem services in the Albemarle‐Pamlico Estuary System (APES). Time, data, and funding constraints precluded explicit modeling of the entire APES, so in Phase 1 of our research plan we chose to model ecosystem services in a random sample of headwater catchments. After observing numerous inconsistencies between the National Hydrography Dataset‐Plus (NHDPlus) stream network and the Virginia/North Carolina Watershed Boundary Dataset 12‐digit HUC coverage, we began by creating modified 12‐digit hydrologic units (HUCs) by aggregating smaller catchments delineated within the NHDPlus. In defining our population of interest (headwater 12‐digit HUCs with perennial, natural, wadeable pour points), we generally excluded HUCs that had multiple pour points, no pour points, or whose pour points were intermittent streams, artificial segments, ditches/canals, or lentic systems (lakes and reservoirs). After taking these actions, 318 HUCs remained and a stratified random sample (Omnerik ecoregions as strata) of 50 HUCs was chosen from this population.     

Establishing robustness of a spatial dataset in a tolerance‐based vector model

Spatial data are usually described through a vector model in which geometries are represented by a set of coordinates embedded into an Euclidean space. The use of a finite representation, instead of the real numbers theoretically required, causes many robustness problems which are well known in the literature. Such problems are made even worse in a distributed context, where data is exchanged between different systems and several perturbations can be introduced in the data representation. In order to discuss the robustness of a spatial dataset, two implementation models have to be distinguished: the identity and the tolerance model. The robustness of a dataset in the identity model has been widely discussed in the literature and some algorithms of the Snap Rounding (SR) family can be successfully applied in such contexts. Conversely, this problem has been less explored in the tolerance model. The aim of this article is to propose an algorithm inspired by those of the SR family for establishing or restoring the robustness of a vector dataset in the tolerance model. The main ideas are to introduce an additional operation which spreads instead of snapping geometries, in order to preserve the original relation between them, and to use a tolerance region for such an operation instead of a single snapping location. Finally, some experiments on real‐world datasets are presented, confirming how the proposed algorithm can establish the robustness of a dataset.     

Exploring the effectiveness of location‐based social media in modeling user activity space: A case study of Weibo

Location‐based social media (LBSM) has been widely utilized to supplement traditional survey methods in modeling human activity patterns. However, there has not been sufficient study to assess the reliability of these data in deriving human movement. This research aims to evaluate how data collection duration and sample sizes affect the reliability of LBSM data in activity modeling based on two indicators: radius of gyration (ROG) and entropy. We use a linear regression model with logarithmic transformation to approximate how the magnitude of each indicator changes with different data collection durations—from 1 to 12 months. The results indicate that both ROG and entropy increase when the amount of data increases. However, the rate of increase slows down and approaches zero eventually. We also approximated the limit values and verified that with 12‐month data, we are at approximately >95% magnitude of the limit values for both indicators in all three cities. The clustering analysis also demonstrated that there are outlier users who exhibit distinct patterns. This case study focuses on three Chinese cities (Beijing, Shanghai, and Guangzhou) and provides a useful reference to explore the balance point between data effectiveness and an appropriate sample size from LBSM data.