Fuzzifying拓扑空间中的强半分离性

在[Fuzzifying]拓扑空间中，运用连续值逻辑[LΝ1]（赋值格为[Lukasiewicz]单位区间）语义的方法，以强半开集、强半邻域、强半闭包和强半内部等概念为工具引入了[SPT0、][SPT1、][SPT2、][SPT3、][SPT4]强半分离公理，并且给出了五种强半分离公理各自的等价刻画，讨论了它们彼此之间的关系。这套分离公理本身是协调的，可以作为对已有分离公理一种很好的补充。     

Set-Theoretical Algebraic Approaches to Connectivity in Continuous or Digital Spaces

Connectivity has been defined in the framework of topological spaces, but also in graphs; the two types of definitions do not always coincide. Serra gave a set of formal axioms for connectivity, which consists in a list of properties of the family of all connected subsets of a space; this definition includes as particular case connected sets in a topological space or in a graph. He gave an equivalent characterization of connectivity in terms of the properties of the operator associating to a subset and a point of that space, the connected component of that subset containing that point. In this paper we give another family of axioms, equivalent to those of Serra, where connectivity is characterized in terms of separating pairs of sets. In the case of graphs, where connected sets are generated by pairs of end-vertices of edges, this new set of axioms is equivalent to the separation axioms given by Haralick.     

Topological landscapes: a terrain metaphor for scientific data

Scientific visualization and illustration tools are designed to help people understand the structure and complexity of scientific data with images that are as informative and intuitive as possible. In this context the use of metaphors plays an important role since they make complex information easily accessible by using commonly known concepts. In this paper we propose a new metaphor, called "Topological Landscapes," which facilitates understanding the topological structure of scalar functions. The basic idea is to construct a terrain with the same topology as a given dataset and to display the terrain as an easily understood representation of the actual input data. In this projection from an $n$-dimensional scalar function to a two-dimensional (2D) model we preserve function values of critical points, the persistence (function span) of topological features, and one possible additional metric property (in our examples volume). By displaying this topologically equivalent landscape together with the original data we harness the natural human proficiency in understanding terrain topography and make complex topological information easily accessible.     

How to Get 3-D for the Price of 2-D—Topology and Consistency of 3-D Urban GIS

This article deals with topological concepts and models which are necessary to represent three-dimensional urban objects in a geographical information system (GIS). Depending on the shape and the representation of features, several classes with increasing topological complexity are identified and described. This complexity has strong impacts on the models and tools which are required to represent, manage and edit the data. One specific model we call 2.8-D map is identified, which covers many 3-D applications in GIS. It is a slight extension of a 2-D or 2.5-D model and preserves the algorithmic and conceptual simplicity of the 2-D case as much as possible. The model is described in a formal way. Integrity axioms are given, which detect errors in corresponding data sets safely and guarantee the consistency of 2.8-D maps in a mathematically sound and provable way. These axioms are effectively and efficiently checkable by automatic procedures. The model extends digital terrain models (2.5-D) by allowing for vertical walls and projections like balconies or ledges. The conceptual simplicity is due to the two-dimensional topology of the model. Thus bridges and tunnels are special cases; it is shown how to detect and handle these cases efficiently. Based on this model, thematic objects and their aggregation structures are defined in a consistent way.     

A two-level topological model for 3D features in CityGML

CityGML, as the standard for the representation and exchange of 3D city models, contains rich information in terms of geometry, semantics, topology and appearance. With respect to topology, CityGML adopts the XLink approach to represent topological relationships between different geometric aggregates or thematic features; however, it is limited to shared objects. This paper proposes a two-level model for representing 3D topological relationships in CityGML: high-level (semantic-level) topology between semantic features and low-level (geometric-level) topology between geometric primitives. Five topological relationships are adopted in this model: touch, in, equal, overlap and disjoint. The semantic-level topology is derived from the geometric-level topology on the basis of the shared geometric primitives. To maintain the 3D topology, topological consistency rules are presented. An Application Domain Extension, called TopoADE, is proposed for the implementation of the topological model. The TopoADE consists of three modules: Topology, Feature and Geometry. Finally, 3D city models with LoD1 to LoD4 are used to test this model. Experimentation on those data sets indicates a validation of the proposed topological model in CityGML.     

Provably correct and complete transaction rules for updating 3D city models

The shapes of our cities change very frequently. These changes have to be reflected in data sets representing urban objects. However, it must be assured that frequent updates do not affect geometric-topological consistency. This important aspect of spatial data quality guarantees essential assumptions on which users and applications of 3D city models rely: viz. that objects do not intersect, overlap or penetrate mutually, or completely cover one another. This raises the question how to guarantee that geometric-topological consistency is preserved when data sets are updated. Hence, there is a certain risk that plans and decisions which are based on these data sets are erroneous and that the tremendous efforts spent for data acquisition and updates become vain. In this paper, we solve this problem by presenting efficient transaction rules for updating 3D city models. These rules guarantee that geometric-topological consistency is preserved (Safety) and allow for the generation of arbitrary consistent 3D city models (Completeness). Safety as well as completeness is proven with mathematical rigor, guaranteeing the reliability of our method. Our method is applicable to 3D city models, which define—besides the terrain surface—complex spatial objects like buildings with rooms and storeys as interior structures, as well as bridges and tunnels. Those objects are represented as aggregations of solids, and their surfaces are complex from a topology point of view. 3D GIS models like CityGML, which are widely used to represent cities, provide the means to define semantics, geometry and topology, but do not address the problem of maintaining consistency. Hence, our approach complements CityGML.     

Consistency constraints and 3D building reconstruction

Virtual architectural (indoor) scenes are often modeled in 3D for various types of simulation systems. For instance, some authors propose methods dedicated to lighting, heat transfer, acoustic or radio-wave propagation simulations. These methods rely in most cases on a volumetric representation of the environment, with adjacency and incidence relationships. Unfortunately, many buildings data are only given by 2D plans and the 3D needs varies from one application to another. To face these problems, we propose a formal representation of consistency constraints dedicated to building interiors and associated with a topological model. We show that such a representation can be used for: (i) reconstructing 3D models from 2D architectural plans (ii) detecting automatically geometrical, topological and semantical inconsistencies (iii) designing automatic and semi-automatic operations to correct and enrich a 2D plan. All our constraints are homogeneously defined in 2D and 3D, implemented with generalized maps and used in modeling operations. We explain how this model can be successfully used for lighting and radio-wave propagation simulations.     

Structuring urban data

Geometric city modeling is an open problem without standard solutions. Within this problem, there appear several sub-problems that must be faced, like the accurate modeling of streets, buildings and other architectonic structures. One important source of geographical information is (measured) cadastral urban data. However, this information is not always well structured, and sometimes it is even simply corrupted GIS data. In this paper we present a robust and generic solution for the generation of block and building layouts based on a repairing process applied when this data is not correct. Our input data is a top projection map of a city which usually has been created by a mixture of photogrammetric restitution and, in a second stage, hand-drawn using any GIS application. Moreover, these maps are under continuous modifications, like in the case of public administrations. This process sometimes results in the introduction of mistakes and anomalies, which are hard to correct without the appropriate tools. Our solution is based on a novel semi-automatic 2D restructuring algorithm, which uniformly corrects errors and ambiguities that are commonly present in corrupted cadastral data. This problem is complex because it is necessary to identify not just simple elements from the input file, but also their connectivity and structure in the real world. The output of our algorithm is the urban data restructured into a hierarchy of blocks and buildings, from which we can get a realistic 3D model by extruding each building using the floor number for each building within the cadastral data.     

Preserving Topology by a Digitization Process

The main task of digital image processing is to recognize properties of real objects based on their digital images. These images are obtained by some sampling device, like a CCD camera, and represented as finite sets of points that are assigned some value in a gray-level or color scale. Based on technical properties of sampling devices, these points are usually assumed to form a square grid and are modeled as finite subsets of Z². Therefore, a fundamental question in digital image processing is which features in the digital image correspond, under certain conditions, to properties of the underlying objects. In practical applications this question is mostly answered by visually judging the obtained digital images. In this paper we present a comprehensive answer to this question with respect to topological properties. In particular, we derive conditions relating properties of real objects to the grid size of the sampling device which guarantee that a real object and its digital image are topologically equivalent. These conditions also imply that two digital images of a given object are topologically equivalent. This means, for example, that shifting or rotating an object or the camera cannot lead to topologically different images, i.e., topological properties of obtained digital images are invariant under shifting and rotation.     

GIS中复杂地图的事务约束规则

GIS中事务约束规则对于保证数据库更新时数据的完整性和一致性具有重要的意义。论文在一组基本拓扑约束规则的基础上,对复杂地图即包含岛或洞可分离地图中的事务约束规则进行了详细的研究,并提出了一组完整的事务约束规则。这组约束规则包括分裂面,合并面以及改变几何形状而保证拓扑关系不变。     

Tracking topological entity changes in 3D collaborative modeling systems

One of the key problems in collaborative geometric modeling systems is topological entity correspondence when topological structure of geometry models on collaborative sites changes.In this article,we propose a solution for tracking topological entity alterations in 3D collaborative modeling environment.We firstly make a thorough analysis and detailed categorization on the alteration properties and causations for each type of topological entity,namely topological face and topological edge.Based on collaborative topological entity naming mechanism,a data structure called TEST (Topological Entity Structure Tree) is introduced to track the changing history and current state of each topological entity,to embody the relationship among topological entities.Rules and algorithms are presented for identification of topological entities referenced by operations for correct execution and model consistency.The algorithm has been verified within the prototype we have implemented with ACIS.     

Tracking People on a Torus

We present a framework for monocular 3D kinematic pose tracking and viewpoint estimation of periodic and quasi-periodic human motions from an uncalibrated camera. The approach we introduce here is based on learning both the visual observation manifold and the kinematic manifold of the motion using a joint representation. We show that the visual manifold of the observed shape of a human performing a periodic motion, observed from different viewpoints, is topologically equivalent to a torus manifold. The approach we introduce here is based on the supervised learning of both the visual and kinematic manifolds. Instead of learning an embedding of the manifold, we learn the geometric deformation between an ideal manifold (conceptual equivalent topological structure) and a twisted version of the manifold (the data). Experimental results show accurate estimation of the 3D body posture and the viewpoint from a single uncalibrated camera.     

Achieving Integrity in Geographic Information Systems—Maps and Nested Maps

This article provides a formal data model which allows to establish geometrical-topological integrity of areal objects in a geographical information system (GIS). The data model leads to an automatic tool able to check consistency of a given set of data and to avoid inconsistencies caused by updates of the database. To this end we start from the mathematical notion of a map which provides an irregular tessellation, i.e., a partition of the plane which is non-overlapping and covering. From another perspective, a map is a plane graph with an explicit representation of faces as its atomic areal components. The concept of nested maps extends this standard notion by the specification of a hierarchical structure which aggregates the set of faces. Such aggregations are common in political and administrative structures. Whereas the mathematical notion of a map is familiar in GIS and the base for many tools supporting topological editing, there was a lack of effectively checkable integrity constraints which are correct and complete, i.e., equivalent, for maps. This article provides an axiomatic, effectively checkable characterization of maps which is equivalent to the standard mathematical one, extends it to nested maps and discusses how to use them in order to achieve and maintain integrity in a GIS.     

Robust Spherical Parameterization of Triangular Meshes

Parameterization of 3D mesh data is important for many graphics and mesh processing applications, in particular for texture mapping, remeshing and morphing. Closed, manifold, genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a 3D triangle mesh onto the 3D sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity do not overlap. This is called a spherical triangulation. In this paper we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical triangulation. We formulate and solve an optimization procedure to produce spherical triangulations which reflect the geometric properties of a given 3D mesh in various ways.     

3D Interactive Topological Modeling using Visible Human Dataset

Availability of Visible Human Dataset (VHD)has provided numerous possibilities for its exploitation in both medical applications and 3D animation. In this paper, we present our interactive tools which enable extraction of surfaces for different organs, including bones, muscles, fascia, and skin, from the VHD. The reconstructed surfaces then are used for defining the inter-relationship of organs, a process we refer to as topological modeling. A data base is constructed, which encapsulates structural, topological, mechanical and other relevant information about organs. A 3D interactive tool enables the building and editing of this data base. Such a data base can later be used for different applications in fields such as medicine, sports, education, and entertainment.     

基于机载视频量测的3维城市建模

3维城市模型的快速获取及更新是近十年来计算机视觉及数字摄影测量领域研究的热点。从实用、经济的角度出发，提出了集成城市数字地图、LIDAR data以及机载视频序列影像多数据源，基于数字摄影测量理论的半自动获取3维城市模型的解决办法，并在3维导航的数据生产实践中进行了验证，取得较好的生产效率及效果。     

Complete classification of raw LIDAR data and 3D reconstruction of buildings

LIDAR (LIght Detection And Ranging) data are a primary data source for digital terrain model (DTM) generation and 3D city models. This paper presents a three-stage framework for a robust automatic classification of raw LIDAR data as buildings, ground and vegetation, followed by a reconstruction of 3D models of the buildings. In the first stage the raw data are filtered and interpolated over a grid. In the second stage, first a double raw data segmentation is performed and then geometric and topological relationships among regions resulting from segmentation are computed and stored in a knowledge base. In the third stage, a rule-based scheme is applied for the classification of the regions. Finally, polyhedral building models are reconstructed by analysing the topology of building outlines, building roof slopes and eaves lines. Results obtained on data sets with different ground point density, gathered over the town of Pavia (Italy) with Toposys and Optech airborne laser scanning systems, are shown to illustrate the effectiveness of the proposed approach.     

结合体元数据结构的机载LIDAR建筑物检测

目的 目前,点云、栅格格网及不规则三角网等建筑物检测中常用的离散机载激光雷达（LIDAR）点云数据表达方式存在模型表达复杂、算法开发困难、结果表达不准确及难以表达多返回数据等缺点。为此,针对LIDAR点云体元结构模型构建及在此基础上的建筑物检测展开研究,提出一种基于体元的建筑物检测算法。方法 首先将点云数据规则化为二值（即1、0值,分别表示体元中是否包含有激光点）3D体元结构。然后利用3D滤波算法将上述体元结构中表征数据点的体元分类为地面和非地面体元。最后,依据建筑物边缘的接近直线、跳变特性从非地面体元中搜寻建筑物边缘作为种子体元进而标记与其3D连通的非地面体元集合为建筑物体元。结果 实验基于ISPRS（international society for photogrammetry and remote sensing）提供的包含了不同的建筑物类型的城区LIDAR点云数据测试了"邻域尺度"参数的敏感性及提出算法的精度。定量评价的结果表明：56邻域为最佳邻域尺度;建筑物的检测质量可达到95%以上——平均完整度可达到95.61%、平均正确率可达95.97%。定性评价的结果表明：对大型、密集、不规则形状、高低混合及其他屋顶类型比较特殊的复杂建筑物均可成功检测。结论 本文提出的建筑物检测算法采用基于体元空间邻域关系的搜索标记方式,可有效实现对各类建筑目标特别是城市建筑目标的检测,检测结果易于建模3D建筑物模型。