Refinement and Computation Method for Line/Body Topological Relationships

Effectively selecting discriminative brain regions in multi-modal neuroimages is one of the effective means to reveal the neuropathological mechanism of end-stage renal disease associated with mild cognitive impairment (ESRDaMCI). Existing multi-modal feature selection methods usually depend on the Euclidean distance to measure the similarity between data, which tends to ignore the implied data manifold. A self-expression topological manifold based multi-modal feature selection method (SETMFS) is proposed to address this issue employing self-expression topological manifold. First, a dynamic brain functional network is established using functional magnetic resonance imaging (fMRI), after which the betweenness centrality is extracted. The feature matrix of fMRI is constructed based on this centrality measure. Second, the feature matrix of arterial spin labeling (ASL) is constructed by extracting the cerebral blood flow (CBF). Then, the topological relationship matrices are constructed by calculating the topological relationship between each data point in the two feature matrices to measure the intrinsic similarity between the features, respectively. Subsequently, the graph regularization is utilized to embed the self-expression model into topological manifold learning to identify the linear self-expression of the features. Finally, the selected well-represented feature vectors are fed into a multicore support vector machine (MKSVM) for classification. The experimental results show that the classification performance of SETMFS is significantly superior to several state-of-the-art feature selection methods, especially its classification accuracy reaches 86.10%, which is at least 4.34% higher than other comparable methods. This method fully considers the topological correlation between the multi-modal features and provides a reference for ESRDaMCI auxiliary diagnosis.

Over the last 20 years, the process of measuring and recording a place or position on the surface of the earth has gone through a revolutionary change. There has been a switch from alidades to GPS, from slide rules to pentium computers, from manual to automatic recording and processing of spatial data. The changes include introduction and implementation of two satellite surveying systems (Transit and GPS), transfer of computations to high-speed computers, and processing and graphic presentation of spatial data in real time. Within the GPS domain, techniques have been developed to overcome degradation of the data by the government and to permit positioning to an accuracy of 2–3 mm in some cases.

It is agreed upon that topological relations are of great importance regarding to GIS data sets consistency. A lot of errors that can be found in GIS data sets are coming from a lack of knowledge about topological relations between the geographical objects stored in the database. Consequently, topology can help to find errors in GIS data sets, and can help to correct them. The topic of this paper is to present how topological relation can be used to define, to detect and to correct errors in GIS data sets. Such an approach required three parts: the definition of errors using topological integrity constraints, how to check the database and how to correct errors. This paper focuses on the first and the third part. Errors will be described using topological integrity constraints. This method allows one to define the constraints that fit its own data set, that allows to take the semantics of data into account. Correction will be made by applying transformations to the data. For each error detected, a set of possible corrections will be compute and the end-user will have to choose the appropriate one.

3D spatial data acquired from aerial and remote sensing images by photogrammetric techniques is one of the most accurate and economic data sources for GIS, map production, and spatial data updating. However, there are still many problems concerning storage, structuring and appropriate management of spatial data obtained using these techniques. According to the capabilities of spatial database management systems (SDBMSs); direct integration of photogrammetric and spatial database management systems can save time and cost of producing and updating digital maps. This integration is accomplished by replacing digital maps with a single spatial database. Applying spatial databases overcomes the problem of managing spatial and attributes data in a coupled approach. This management approach is one of the main problems in GISs for using map products of photogrammetric workstations. Also by the means of these integrated systems, providing structured spatial data, based on OGC (Open GIS Consortium) standards and topological relations between different feature classes, is possible at the time of feature digitizing process. In this paper, the integration of photogrammetric systems and SDBMSs is evaluated. Then, different levels of integration are described. Finally design, implementation and test of a software package called Integrated Photogrammetric and Oracle Spatial Systems (IPOSS) is presented.

3D building model reconstruction is of great importance for environmental and urban applications. Airborne light detection and ranging (LiDAR) is a very useful data source for acquiring detailed geometric and topological information of building objects. In this study, we employed a graph-based method based on hierarchical structure analysis of building contours derived from LiDAR data to reconstruct urban building models. The proposed approach first uses a graph theory-based localized contour tree method to represent the topological structure of buildings, then separates the buildings into different parts by analyzing their topological relationships, and finally reconstructs the building model by integrating all the individual models established through the bipartite graph matching process. Our approach provides a more complete topological and geometrical description of building contours than existing approaches. We evaluated the proposed method by applying it to the Lujiazui region in Shanghai, China, a complex and large urban scene with various types of buildings. The results revealed that complex buildings could be reconstructed successfully with a mean modeling error of 0.32 m. Our proposed method offers a promising solution for 3D building model reconstruction from airborne LiDAR point clouds.

Geospatial datasets are currently constructed, managed, and utilized individually according to the spatial scale of the real world, such as the ground/surface/underground or indoor/outdoor, as well the particular purpose of the geospatial data used for location-based services. In addition, LBS applications use an optimal data model and data format according to their particular purpose, and thus, various datasets exist to represent the same spatial features. Such duplicated geospatial datasets and geographical feature-based GIS data cause serious problems in the financial area, compatibility issues among LBS systems, and data integration problems among the various geospatial datasets generated independently for different systems. We propose a geospatial data fusion model called the topological relation-based data fusion model (TRDFM) using topological relations among spatial objects in order to integrate different geospatial datasets and different data formats. The proposed model is a geospatial data fusion model implemented in a spatial information application and is used to directly provide spatial information-based services without data conversion or exchange of geometric data generated by different data models. The proposed method was developed based on an extension of the AnchorNode concept of IndoorGML. The topological relationships among spatial objects are defined and described based upon the basic concept of IndoorGML. This paper describes the concept of the proposed TRDFM and shows an experimental implementation of the proposed data fusion model using commercial 3D GIS software. Finally, the limitations of this study and areas of future research are summarized.

Topological relationship is one of the most basic and the most important relations between two spatial objects in GIS.However,current topological models have deficiencies when they are used to describe detailed topological relations.In this paper,one general descriptive form of topological relation model was proposed based on the node degree and the euler-number aiming at random two objects.In this model,all parts of one spatial object were treated as a whole object,and intersection difference operators were selected from several set operators to distinguish the topological relations,and four types of topological invariants were used for the computational results of contents,dimension,node degree,and euler-number.The topological description form of line-line,line-area,area-area were discussed emphatically.

A three-dimensional stratum model stratum model is a useful auxiliary tool for geotechnical engineering and other exploration work. The existing methods for stratum model construction lack complete topological descriptions of entities, so it is difficult to apply them to 3D geological modeling with complex geometric structures and complex topological relationships between modules. To solve the above problem, in this paper, the boundary representation method is used to represent the arbitrarily-shaped geological entities, and the half winged-edge-face structure topological structure is proposed to describe the topological information of the stratum model for a complex entity. The topological structure can record the topological information of the solid stratum model completely, thereby providing the basis for operations with the model and the applications of various algorithms. Based on this topological structure, the construction process for a 3D solid stratum model is proposed. The reliability and effectiveness of the constructed 3D solid stratum model are verified by an engineering case. The solid stratum model not only solves the geological modeling problem with respect to complex geometric and topological relations, but also provides a new method and idea for 3D geological modeling.

Abstract. The storage of spatial data that consists of spatial and non-spatial properties requires a database management system that possesses spatial functions that can cater to the spatial characteristics of data. These characteristics include the geometrical shape, topological and positional information. Parallel to how geometries describe the shape of an object, topological information is also an important spatial property which describes how the geometries in a space are related to each other. This information describes the connectivity, containment and adjacencies of spatial objects which are the foundation for more complex analysis such as navigation, data reconstruction, spatial queries and others. However, the topological support provided by spatial databases varies. This paper provided an overview on the current implementations of topological support in spatial databases such as ArcGIS, QGIS, PostgreSQL and others. The native topology in most spatial databases was found to be 2D topology maintained by 2D topology rules with limited representation of 3D topological relationships. Consequently, 3D objects represented by 2D topology had to be decomposed into objects of lower dimensions. Approaches to implement additional topological support for spatial databases included the use of topological data models, data structures, operators, and rules. 3D applications such as 3D cadastre required more detailed representations of topological information which required a more comprehensive 3D topological data model. Nonetheless, comprehensive preservation of topological information also mandates voluminous storage and higher computational efficiency. Thus, the appropriate 3D topological support should be provided in spatial databases to accurately represent 3D objects and meet 3D analysis requirements.

The basic properties to be dealt with, when considering initially the research needs related to the integration of remote sensing (RS) information into a geographic information system (GIS), are many-sided. The primary combination of remote sensing and GIS is mainly realized by the transforms of data structure. Because of its own limitations, there is an urgent need to investigate the integration of RS and GIS in higher levels. In this paper, we discuss the different types of combinations of RS with GIS, and propose that GIS data should be directly brought into image processing from the beginning. A tentative idea of how to use the method of granularity to study the common processing unit of RS and GIS is described. The example for the determination of granularity of spatial data processing related to run-length-code line is also given.

Fuzziness is an internal property of spatial objects. How to model fuzziness of a spatial object is a main task of next generation GIS. This paper proposes basic fuzzy spatial object types based on fuzzy topology. These object types are the natural extension of current non-fuzzy spatial object types. A fuzzy cell complex structure is defined for modeling fuzzy regions, lines and points. Furthermore, fuzzy topological relations between these fuzzy spatial objects are formalized based on the 9-intersection approach. This model can be implemented for GIS applications due to its scientific theory basis.KeywordsCell ComplexSpatial ObjectTopological RelationLower Semicontinuous MappingFuzzy ObjectThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Spatial relation between spatial objects is a very important topic for spatial reasoning, query and analysis in global GIS. However, the most popular models in current use, which are based on the 2D Euclidean space (such as raster), exist some fundamental deficiency in theory for spatial relation reasoning in the spherical digital space (SDS). In this paper, a reasoning method of spatial relations in the SDS based on manifold is approached, in which: (1) the topological definitions, properties, and descriptions of spatial objects in SDS are presented; (2) appropriate operators from set operators (i.e. intersection, difference, difference by, symmetric difference, etc.) are utilized to distinguish the spatial relations between neighboring spatial objects; and (3) the value of the Euler number of symmetric difference is used for the detailed computational results of set operations; In this method, the 8 types basic topological relations between spatial objects in SDS can be distinguished accurately and easily from simple to detailed level for different requirements.

A simple, lightweight, and flexible, package in the programming language Julia for managing finite element mesh data structures is presented. The key role in the design of the data structures is granted to the incidence relation. This concept has some interesting implications for the simplicity and efficiency of the implementation. The entire library has less than 500 executable lines. The low memory requirements are also notable. The design of the data structures is not fixed a priori. The user of the library is given the power over the decisions which mesh entities should be represented explicitly in the data structures, and which of the topological relationships should be computed and stored. This enables a small memory footprint, yet affords a sufficiently rich topology description capability.