Approaches for topological relations between spatial regions with uncertainty | |
| Author | Deng, Min |
| Call Number | AIT Diss. no.RS-04-2 |
| Subject(s) | Geographic information systems Linear topological spaces |
| Note | A dissertation submitted in partial fulfilment of the requirements the Degree of Doctor of Engineering |
| Publisher | Asian Institute of Technology |
| Abstract | Spatial data stored in vector-based Geographic Information Systems (GIS) consist of explicitly stored objects representing real-world entities. There are inevitably uncertainties in the processes of collection, capture, storage, analysis and display of this spatial data. It is hereof argued that spatial objects can be divided into three categories: precise, fuzzy (imprecise), and random (with error). This dissertation mainly involves the uncertainty induced by randomness, where the spatial objects such as points, lines and areas, can be described by location error models. Since the location uncertainty of a spatial object leads to the uncertainty of its boundary and interior in terms of topology, additional uncertainties become apparent for the description and determination of the topological relations between spatial objects, and for spatial analysis, query and reasoning. Hence, it is necessary to develop the models for the topological relations between spatial objects with uncertainty. This is also the goal of this dissertation. In order to fulfil this aspect, the following three aspects are mainly covered. A novel model, which is called the four-intersection-and-difference, is proposed that describes topological relations between spatial objects. Compared to the 4/9-intersection models, the model describes completely their topological relations in certain classification level, and embodies the change of topological properties in the interactions of two involved objects, which has been proven by the topological distance and complexity, as well as the conceptual neighbourhood graph. These characters will be helpful for spatial analysis and spatial reasoning, as the analysis of topological relations under uncertainty. Concerning the model itself, it only involves two operators and four operations, thus it is very simple and convenient for use. In order to identify more details about topological relations of spatial objects, a set of topological invariants (i.cc dimension, the number of separation, types of components, and sequence of components) is presented, upon which hierarchical models of different identification abilities are built. Moreover, each of above models is a complete coverage of the topological relations in certain classification level and their description abilities are improved in turn. With the models mentioned above, a detailed investigation on the effect of location uncertainty of spatial objects on their relations has been made in order to set up a valid link from positional uncertainty propagating to relation uncertainty, at first a new qualitative model for describing topological relations between regions with uncertainty is proposed, which is an extended application of the topological models developed under certainty. Then several basic functions are derived based on statistical modeling of location uncertainty, which are used for analysis of the same point and point-in-polygon under certainty and uncertainty. A determination approach with a combination of qualitative with quantitative representation is further proposed for topological relations under uncertainty, the determination criterion of which is relative possibility. After the resulting description and determination for the topological relations with uncertainty, it needs a treatment for topological inconsistency with consideration of their Semantics, An investigation on basic types of spatial data inconsistency and the procedures for correction has been made. Due to the fact that the topological consistency correction operations often involve changing the position of points of one or more spatial objects, a generalized algorithm and a related error propagation model, which are based on the least square method, have been proposed for point groups snapping within a fuzzy tolerance. Simplified algorithms and models are derived for some special cases with different statistical characteristics of a snapping point group. In addition, computation methods of the length of the generated geographic line and its accuracy are given. A case study is also included. |
| Year | 2004 |
| Type | Dissertation |
| School | School of Engineering and Technology (SET) |
| Department | Department of Information and Communications Technologies (DICT) |
| Academic Program/FoS | Remote Sensing (RS) |
| Chairperson(s) | Chen, Xiaoyong;Michiro, Kusanagi; |
| Examination Committee(s) | Huynh Ngoc Phien;Li, Zhilin; |
| Scholarship Donor(s) | Japanese Government; |
| Degree | Thesis (Ph.D.) - Asian Institute of Technology, 2004 |