基于单元复形的数字图像多级别层次表达

基于复形理论定义了数字图像空间的拓扑元素及其性质,在此基础上提出一套完备的保持拓扑等价性的层次表达数字图像的数学模型体系框架,并验证了层次表达结构中的Jordan曲线定理.同时,基于单元复形扩展模型,对SPOT影像实施了渐进式离散分割,有效地利用影像蕴含的空间信息,获得了比最大似然分类法更优的分割结果.     

Scattering of waves by a quasi-thin body of arbitrary shape

Summary. The problem of scattering of a wave with a front of arbitrary shape by a curved quasi-thin body bounded by contour L of arbitrary shape is presented. The problem is solved using the Kirchhoff approximation (KA). The reflecting (scattering) properties of the body are given in terms of the reflection (transmission) coefficients. The routine technique of computation in the KA is complemented by significant improvements. The procedure of smooth continuation of the body surface S beyond its boundary contour L is suggested. The invariant presentation of the expressions for the scattered field u _s obtained in the paper is extremely important.
The leading term in the formula for the field u _s is obtained as a product u _s= u _ray W , where u _ray is the reflected wavefield computed, according to the formulae of ray theory, as if the body surface is boundless; W is the so-called weakening function, which takes account of the modification of the ray field caused by diffraction at the edges (the contour L ).
The arguments of the weakening function are dimensionless quantities depending on the relation between the body size and the radii (half-axes) r _f^{( i )} ( i = 1, 2) of the Fresnel zones on the surface S. The values of r _f^{( i )} are obtained in the paper. The method of computation of the function W turns out to depend essentially on the reciprocal position of the Fresnel zone and body contour. When the contour L is of a complex form, the surface S is divided into simple surfaces S_i , each of which is limited by a contour L , which permits the carrying out of a single valued (in the sense of the leading part of the field) smooth continuation of S_i .     

A graph-based algorithm to define urban topology from unstructured geospatial data

Interpretation and analysis of urban topology are particularly challenging tasks given the complex spatial pattern of the urban elements, and hence their automation is especially needed. In terms of the urban scene meaning, the starting point in this study is unstructured geospatial data, i.e. no prior knowledge of the geospatial entities is assumed. Translating these data into more meaningful homogeneous regions can be achieved by detecting geographic features within the initial random collection of geospatial objects, and then by grouping them according to their spatial arrangement. The techniques applied to achieve this are those of graph theory applied to urban topology analysis within GIS environment. This article focuses primarily on the implementation and algorithmic design of a methodology to define and make urban topology explicit. Conceptually, such procedure analyses and interprets geospatial object arrangements in terms of the extension of the standard notion of the topological relation of adjacency to that of containment: the so-called ‘containment-first search’. LiDAR data were used as an example scenario for development and test purposes.     

3-D linearized scattering of surface waves and a formalism for surface wave holography

Summary. Scattering of surface waves by lateral heterogeneities is analysed in the Born approximation. It is assumed that the background medium is either laterally homogeneous, or smoothly varying in the horizontal direction. A dyadic representation of the Green's function simplifies the theory tremendously. Several examples of the theory are presented. The scattering and mode conversion coefficients are shown for scattering of surface waves by the root of an Alpine-like crustal structure. Furthermore a 'great circle theorem'in a plane geometry is derived. A new proof of Snell's law is given for surface wave scattering by a quarter-space. It is shown how a stationary phase approximation can be used to simplify the Fourier synthesis of the scattered wave in the time domain. Finally a procedure is suggested to do 'surface wave holography'.     

Knowledge diffusion from GIScience to other fields: the example of the usage of weighted surface networks in nanotechnology

This article demonstrates how the generalisation of topographic surfaces has been formalised by means of graph theory and how this formalised approach has been integrated into an ISO standard that is employed within nanotechnology. By applying concepts from higher-dimensional calculus and topology, it is shown that Morse functions are those mappings that are ideally suited for the formal characterisation of topographic surfaces. Based on this result, a data structure termed weighted surface network is defined that may be applied for both the characterisation and the generalisation of the topological structure of a topographic surface. Hereafter, the focus is laid on specific issues of the standard ISO 25178-2; within this standard change trees, a data structure similar to weighted surface networks, are applied to portray the topological information of topographic surfaces. Furthermore, an approach termed Wolf pruning is used to simplify the change tree, with this pruning method being equivalent to the graph-theoretic contractions by which weighted surface networks can be simplified. Finally, some practical applications of the standard ISO 25178-2 within nanotechnology are discussed.     

Geodetic singularities in the gravity field of a non-homogeneous planet

Summary. An inverse geodetic singularity problem is considered for a non-homogeneous spherical planet. The singularity condition is expressed in terms of the density distribution and of the geometrical parameters of the configuration; the condition for the density distribution is deduced which gives rise to singularities of parabolic type in the external gravity field of the planet. The structure of the gravity field in the neighbourhood of the singularities is investigated in detail together with the behaviour of the gradients of the disturbances in the geodetic coordinates.     

地理空间意像模式的Voronoi模型

提出用Voronoi空间模型来表达意像模式，Voronoi模型无岐义空间邻近关系，构建能封装对象间空间关系的拓扑网络，使用该模型将各种空间介词映射为不同的拓扑结构，GIS采用该模型，可按自然语言中空间介词描述的定性空间关系查询检索模糊地理信息。     

Algebraic approach to spatial reasoning

Abstract

A simple, exemplary system is described that performs reasoning about the spatial relationships between members of a set of spatial objects. The main problem of interest is to make sound and complete inferences about the set of all spatial relationships that hold between the objects, given prior information about a subset of the relationships. The spatial inferences are formalized within the framework of relation algebra and procedurally implemented in terms of constraint satisfaction procedures. Although the approach is general, the particular example employs a new ‘complete’ set of topological relationships that have been published elsewhere. In particular, a relation algebra for these topological relations is developed and a computational implementation of this algebra is described. Systems with such reasoning capabilities have many applications in geographical analysis and could be usefully incorporated into geographical information systems and related systems.     

基于遥感监测的城市热岛研究进展

全球正经历快速、高强度的城市化,导致城市热岛加剧,并对城市、区域乃至全球许多的生态环境要素直接或间接地产生多方面的影响,与人类福祉密切相关。遥感具有宽覆盖、信息量大、重复观测周期短等优点,已成为地表城市热岛(Surface Urban Heat Island, SUHI)监测广泛采用的一种方法。针对前人相关研究对热红外数据源、监测指标及SUHI时空变化规律尚缺乏系统总结且内容需要更新等问题,本文首先分类评述了SUHI遥感监测所采用的热红外遥感数据源。其次将现有的SUHI监测指标分为土地覆盖类型驱动型、地表温度格局驱动型及两者复合驱动型3类来述评,详细介绍了它们的计算方法、应用案例及优缺点;并从日间变化、夜间变化及昼夜对比的变化3个方面述评了SUHI的年内时空变化规律;归纳了其年际变化规律。最后,依据现有研究结论中相互冲突或尚需深化的地方,指出几个潜在的关键问题或研究方向。     

A geomagnetic scattering theory for evaluation of earth structure

Summary. Structural features of the Earth's lower crust and upper mantle can be mapped by the analysis of temporal geomagnetic fluctuations using the electromagnetic scattering theory developed in this paper. Decomposing geomagnetic field fluctuations at the Earth's surface into an excitation part and a scattered part forms the basis of a power series development. The vertical field component is interpreted as a scattering of the excitation field. The horizontal gradient and geomagnetic depth sounding methods are special cases of the theory developed. The horizontal gradient sounding method has a tensorial aspect which has not been recognized before; it should be included to obtain correct penetration depth parameter evaluations from field data.     

An inconsistency measure of spatial data sets with respect to topological constraints

An inconsistency measure can be used to compare the quality of different data sets and to quantify the cost of data cleaning. In traditional relational databases, inconsistency is defined in terms of constraints that use comparison operators between attributes. Inconsistency measures for traditional databases cannot be applied to spatial data sets because spatial objects are complex and the constraints are typically defined using spatial relations. This paper proposes an inconsistency measure to evaluate how dirty a spatial data set is with respect to a set of integrity constraints that define the topological relations that should hold between objects in the data set. The paper starts by reviewing different approaches to quantify the degree of inconsistency and showing that they are not suitable for the problem. Then, the inconsistency measure of a data set is defined in terms of the degree in which each spatial object in the data set violates topological constraints, and the possible representations of spatial objects are points, curves, and surfaces. Finally, an experimental evaluation demonstrates the applicability of the proposed inconsistency measure and compares it with previously existing approaches.     

An existence theorem for absolute geodetic singularities

Summary. It is shown that disturbing masses can be found which can give locally rise in the external gravity field of a spherically symmetric earth to singularities both in geodetic and in gravity space coordinates; in this connection the concept of absolute geodetic singularities is introduced. It is also shown that the previous results hold independently of the mass of the disturbing body and for densities of the disturbing mass which can be lower than the mean Earth density. The connection between the geodetic singularity problem and the study and design of gravity gradient compensators for orbital experiments is put into light.     

A linear tessellation model to identify spatial pattern in urban street networks

Street patterns reflect the distribution characteristics of a street network and affect the urban structure and human behavior. The recognition of street patterns has been a topic of interest for decades. In this study, a linear tessellation model is proposed to identify the spatial patterns in street networks. The street segments are broken into consecutive linear units with equal length. We define five focal operations using neighborhood analysis to extract the geometric and topological characteristics of each linear unit for the purpose of grid-pattern recognition. These are then classified by Support Vector Machine, and the result is optimized based on Gestalt principles. The experimental results demonstrate that our method is effective for mining grid patterns in a street network.     

Space and sustainability: an exploratory essay on the production of social spaces through city-work

The purpose of this essay is to locate the making of social spaces as a particularly salient approach for understanding sustainability. Castells' spaces of places and spaces of flows are interpreted generically and a new social theory, Jacobs' moral syndromes, is introduced to underpin the production of these two spatial forms: commercial agents through their network practices make spaces of flows; guardian agents through their territorial practices make spaces of places. Both spaces are considered to be the outcome of city-work. A new division of labour is devised: four primary types of city-work are identified: hinter-work, net-work, territorial-work and hierarch-work. These ideas are considered as tools for thinking about developing spatial policies for sustainability. In conclusion, Jacobs' theory is used to discuss what the general strategy has to be for tackling sustainability.     

Analysis of surface changes using primitive events

This paper develops a method for analysing changes in a surface, a scalar function defined over a two-dimensional region. The method is based on the topological method for static surfaces that uses critical points (peaks, bottoms, and cols) and their connecting lines. To extend the topological method to spatiotemporal domain, four types of primitive events are proposed: (1) generation, (2) disappearance, (3) movement, and (4) switch. The change of a surface is described by a combination of these primitives. From surfaces of two times a set of primitive events that cause the change is deduced. They are stored in GIS as spatial objects with attributes, and their spatio-temporal pattern is visually analysed. To test the validity of the method, the change of a retail cluster in Shinjuku and Shibuya area in Tokyo is analysed. The empirical study yielded some interesting findings that help us understand changes in the spatial structure of retailing.     

Three-dimensional induction in a non-uniform thin sheet at the surface of a uniformly conducting earth

Summary. A new method for solving problems in three-dimensional electromagnetic induction in which the Earth is represented by a uniformly conducting half-space overlain by a surface layer of variable conductance is presented. Unlike previous treatments of this type of problem the method does not require the fields to be separated into their normal and anomalous parts, nor is it necessary to assume that the anomalous region is surrounded by a uniform structure; the model may approach either an E- or a B -polarization configuration at infinity. The solution is expressed as a vector integral equation in the horizontal electric field at the surface. The kernel of the integral is a Green's tensor which is expressed in terms of elementary functions that are independent of the conductance. The method is applied to an illustrative model representing an island near a bent coastline which extends to infinity in perpendicular directions.     

The use of the Born approximation in seismic scattering problems

Summary. In view of recent work on seismic scattering by small-scale heterogeneities in the Earth, which has been based on single-scattering perturbation theory (that is, the Born approximation), we attempt to define the region within which this approximation may be regarded as reasonably accurate. Comparison with the exact solution for scattering by an embedded sphere shows that the inequalities obtained, governing the ranges of the parameters of the problem, are appropriate.
However, application of these constraints on the parameters imply that, in almost all cases, application of the Born approximation to upper and lower mantle scattering is probably invalid.     

Meltwater production in Antarctic blue-ice areas: sensitivity to changes in atmospheric forcing

In the near coastal regions of Dronning Maud Land, Antarctica, below-surface ice-melt in blue-ice areas has been observed. The low scattering coefficients of the large-grained blue-ice allow penetration of solar radiation, thus providing an energy source below the ice surface. The sub-surface meltwater is significant enough to show up on remote-sensing imagery in the form of ice-covered lakes. Adjacent snow-accumulation areas have much higher scattering coefficients and consequently limit solar radiation penetration in these regions. These snow and ice surfaces are generally below freezing, and little surface melting occurs. To assess the response of these melt features to changes in atmospheric forcings such as cloudiness, air temperature, and snow accumulation, a physically-based model of the coupled atmosphere, radiation, snow, and blue-ice system has been developed. The model consists of a heat transfer equation with a spectrally-dependent solar-radiation source term. The penetration of radiation into the snow and blue-ice depends on the surface albedo, and the snow and blue-ice grain size and density. Model simulations show that ice melt occurring in this area is sensitive to potential variations in atmospheric forcing. Under certain conditions more traditional surface melting occurs and, under other conditions, the existing melt processes can be shut down completely. In light of the sensitivity of this system to variations in atmospheric forcing, and the ability to view melt-related features using remote sensing, a tool exists to efficiently monitor variations in Antarctic coastal climate.     

Generalized Born scattering of elastic waves in 3-D media

It is well known that when a seismic wave propagates through an elastic medium with gradients in the parameters which describe it (e.g. slowness and density), energy is scattered from the incident wave generating low-frequency partial reflections. Many approximate solutions to the wave equation, e.g. geometrical ray theory (GRT), Maslov theory and Gaussian beams, do not model these signals. The problem of describing partial reflections in 1-D media has been extensively studied in the seismic literature and considerable progress has been made using iterative techniques based on WKBJ, Airy or Langer type ansätze. In this paper we derive a first-order scattering formalism to describe partial reflections in 3-D media. The correction term describing the scattered energy is developed as a volume integral over terms dependent upon the first spatial derivatives (gradients) of the parameters describing the medium and the solution. The relationship we derive could, in principle, be used as the basis for an iterative scheme but the computational expense, particularly for elastic media, will usually prohibit this approach. The result we obtain is closely related to the usual Born approximation, but differs in that the scattering term is not derived from a perturbation to a background model, but rather from the error in an approximate Green's function. We examine analytically the relationship between the results produced by the new formalism and the usual Born approximation for a medium which has no long-wavelength heterogeneities. We show that in such a case the two methods agree approximately as expected, but that in a media with heterogeneities of all wavelengths the new gradient scattering formalism is superior. We establish analytically the connection between the formalism developed here and the iterative approach based on the WKBJ solution which has been used previously in 1-D media. Numerical examples are shown to illustrate the examples discussed.