The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics

Chen, Jun

Bibliographic data

Monograph

Persistent identifier:: 856566209

Author:: Chen, Jun

Title:: The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics

Sub title:: May 23 - 25, 2001, Bangkok, Thailand

Scope:: VI, 434 Seiten

Year of publication:: 2001

Place of publication:: Pathumthani, Thailand

Publisher of the original:: AIT

Identifier (digital):: 856566209

Illustration:: Illustrationen, Diagramme, Karten

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: MEASURING UNCERTAINTY IN SPATIAL FEATURES IN A THREE-DIMENSIONAL GEOGRAPHICAL INFORMATION SYSTEM. Chui Kwan CHEUNG and Wenzhong SHI

Document type:: Monograph

Structure type:: Chapter

ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 67 II User igation, Liquid -30-28- tal Site sorption i-based nitrate- and lecision »erfund: i Final, sponse, nanual. i, EPA i Risk sources n, P. L. sment: natural hakma. ground relation 5. g fuzzy imental 1990. tanks. otential inadian erence. ee. GIS ESRI dez, Jr. josures d with yls and nent of studies. >n risk ns on Waste lium II, ition of : Lewis atistical sources 8:338- ind Its ton. MEASURING UNCERTAINTY IN SPATIAL FEATURES IN A THREE-DIMENSIONAL GEOGRAPHICAL INFORMATION SYSTEM Chui Kwan CHEUNG and Wenzhong SHI Dept, of LSGJ, the Hong Kong Polytechnic University tracv.cheunq@honqkong.com Keywords: geographical information systems, uncertainty, positional error, numerical integration ABSTRACT In this paper, uncertainty of spatial features including linear features, areal features and volumetric features in a three-dimensional (3D) vector-based geographical information system (GIS) is studied. Existing uncertainty models for 3D spatial features are divided into two directions: (a) a confidence region model derived from a statistical approach and (b) a reliability model based on a simulation technique. The confidence region model for a spatial feature could provide an area inside which the ‘true’ location of the spatial feature is with a predefined probability. In the reliability model, uncertainty was measured by a discrepant area, which is formed by the measured location and the ‘true’ location of a spatial feature and hence was determined in terms of the measured location and the ‘true’ location of the spatial feature in a mathematical expression. Based on an assumption of error of the spatial feature, uncertainty of the spatial feature could be simulated repeatedly and the average discrepant area would be obtained. However, it is known that simulation is quite time-consuming and cannot provide a precise solution. Hence, this study further proposes the development an analytical model on the reliability model on spatial features in a 3D GIS. The expected value of the discrepant area of the spatial feature is expressed as a multiple integral by a statistical approach. The authors proposed to solve the multiple integral based on a numerical integration, resulting in an approximate solution of the expected discrepant area. This uncertainty model is also compared with an earlier simulation model. 1. INTRODUCTION A GIS is defined as a software package, which provides users with a tool to input, store, analyze, retrieve and transform geographical data (Cassettari 1993). It is now widely applied in many different areas including military applications, environmental studies and geological exploration. However, geographical data in GIS is not error-free (Heuvelink 1998). The market of GIS will be affected by evaluating uncertainty in GIS to a certain extent. Uncertainty in GIS may arise from data collection and input in the first step to spatial analyses. Hence, there are many different types of uncertainty in GIS (Burrough and McDonnell 1998). It is virtually impossible to represent the world completely due to the complexity of the geographical world. Some of the man-made utilities such as water pipes and road networks can be represented by points, lines and polygons while most natural phenomena cannot (Burrough 1986). Differences between the database contents and the phenomena they represent are mainly due to the characteristic of phenomena. In addition, measurement errors are introduced during data collection and input and propagated through GIS operations. There are different approaches to describe uncertainty of linear features in two-dimensional GIS (Caspary and Scheuring 1992; Dutton 1992; Stanfel and Stanfel 1993,1994; Shi 1994; Easa 1995; Shi and Liu 2000). However, little research exists in the modeling of uncertainty in higher dimensional spatial features. Shi (1997, 1998) derived a confidence region model for 3D and N-dimensional linear features from strictly statistical approaches. Later on, the reliability of 3D spatial features, including linear features, areal features and volumetric features were studied by a simulation technique (Shi and Cheung 1999). Shi and Cheung (1999) earlier assessed the reliability of a 3D spatial feature by calculating the discrepant area between the measured location and the ‘true’ location of this spatial feature. It was first assumed that nodal error was normally distributed. In such simulation, the measured nodes of the spatial feature were generated and the discrepant area was calculated. After the simulation was repeated many times, the expected value and the variance of the discrepant area for the linear feature (or the discrepancy volume for the area or volumetric feature) were calculated. On the other hand, Stanfel (1996) suggested that a stochastic method could be used to calculate the expected discrepant area in 2D GIS, mainly due to weakness of the simulation technique such as time-consuming and unstable results. An analytical expression for the expected discrepant area (or volume) is derived mathematically in this study. Theoretically, its exact solution will be obtained automatically in GIS given the measured location and the ‘true’ location of the spatial feature. As a result GIS users will aware of the uncertainty of the spatial feature from this indicator. However the analytical expression will be expressed in terms of a multiple integral based on a probability theory. This multiple integral is unable to be solved analytically. This paper thus presents an analytical method with a numerical solution to describe uncertainty of three-dimensional spatial features in GIS. In this paper, we focus on uncertainty model for a 3D spatial feature in a vector-based GIS. Uncertainty of this spatial feature will be determined by discrepancy between the measured location and the ‘true’ location of the spatial feature. In Session 2, we will explain the discrepancy of spatial features including linear features, areal features and volumetric features. Due to the weakness of simulation technique (as stated above), we will withdraw this technique in this paper and express the expected discrepant value analytically and this mathematical expression is also given in Session 2. A numerical integration given in Session 3 will be implemented in order to find the approximate solution for the expected discrepant value. Finally, some experimental studies will be conducted and their numerical results will be compared with the simulation result from the previous simulation model. 2. DISCREPANCY OF 3D SPATIAL FEATURES Uncertainty of spatial features is measured by a discrepancy, which is the difference between the measured location and the ‘true’ location of spatial features. From a statistical point of view, this indicates that a mean of any variable X is close to its actual value. Thus, in this study, the ‘true’ locations of the nodes of spatial features refer to their mean locations. For this study, the following two assumptions are made. First, positional error of a node is within an error ellipsoid whose center corresponds to the ‘true’ location (Stanfel and Stanfel 1994; Easa 1995). Second, the positional error of the nodes is assumed to follow a normal distribution inherent to specific measurement technologies (Stanfel and Stanfel 1993). The authors will therefore model the positional error of spatial features based on positional nodal error of the spatial features.

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