A General Framework For Error Analysis In Measurement-based Gis
feedback return to old SpringerLink Journal of Geographical SystemsDecember 2004, Volume 6, Issue 4, pp 381–402A general framework for error analysis in measurement-based GIS Part 3: Error analysis in intersections and overlaysAuthorsAuthors and affiliationsYee LeungEmail authorJiang-Hong MaMichael F. GoodchildArticleReceived: 28 June 2004Accepted: 26 August 2004DOI: 10.1007/s10109-004-0143-2Cite this article as: Leung, Y., Ma, J. & Goodchild, M. J Geograph Syst (2004) 6: 381. doi:10.1007/s10109-004-0143-2 8 Citations 135 Views Abstract.This is the third of a four-part series on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we study the characteristics of error structures in intersections and polygon overlays. When locations of the endpoints of two line segments are in error, we analyze errors of the intersection point and obtain its error covariance matrix through the propagation of the error covariance matrices of the endpoints. An approximate law of error propagation for the intersection point is formulated within the MBGIS framework. From simulation experiments, it appears that both the relative positioning of two line segments and the error characteristics of the endpoints can affect the error characteristics of the intersection. Nevertheless, the approximate law of error propagation captures nicely the error characteristics under various situations. Based on the derived results, error analysis in polygon-on-polygon overlay operation is also performed. The relationship between the error covariance matrices of the original polygons and the overlaid polygons is approximately established.Key wordsError analysisline-in-polygon overlaypolygon-on-polygon overlayintersection pointapproximate law of error propagationJEL ClassificationC10C31This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grants Council.Copyright information© Springer-Verlag Berlin Heidelberg 2004Authors and AffiliationsYee Leung1Email authorJiang-Hong Ma2Michael F. Goodchild31.Department of Geography and Resource Management, Center for Environmental Policy and Resource Management, and Joint Laboratory for Geoinformation ScienceThe Chinese University of Hong KongHong Kong2.Department of Mathematics and Information ScienceChang’an University, Xi’anP.R. China3.Department of GeographyUniversity of CaliforniaSanta BarbaraU.S.A About this article Print ISSN 1435-5930 Online ISSN 1435-5949 Publisher Name Springer-Verlag
feedback return to old SpringerLink Journal of Geographical SystemsDecember 2004, Volume 6, Issue 4, pp 355–379A general framework for error analysis in measurement-based GIS Part 2: The algebra-based probability model for point-in-polygon analysisAuthorsAuthors and affiliationsYee LeungEmail authorJiang-Hong MaMichael F. GoodchildArticleReceived: 28 June 2004Accepted: 26 August 2004DOI: 10.1007/s10109-004-0142-3Cite this article as: Leung, Y., Ma, J. & Goodchild, M. J Geograph Syst (2004) 6: 355. doi:10.1007/s10109-004-0142-3 8 Citations 117 Views Abstract.This is the second paper of a four-part http://link.springer.com/article/10.1007/s10109-004-0143-2 series of papers on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we discuss the problem of point-in-polygon analysis under randomness, i.e., with random measurement error (ME). It is well known that overlay is one of the most important operations in GIS, and point-in-polygon analysis http://link.springer.com/article/10.1007/s10109-004-0142-3 is a basic class of overlay and query problems. Though it is a classic problem, it has, however, not been addressed appropriately. With ME in the location of the vertices of a polygon, the resulting random polygons may undergo complex changes, so that the point-in-polygon problem may become theoretically and practically ill-defined. That is, there is a possibility that we cannot answer whether a random point is inside a random polygon if the polygon is not simple and cannot form a region. For the point-in-triangle problem, however, such a case need not be considered since any triangle always forms an interior or region. To formulate the general point-in-polygon problem in a suitable way, a conditional probability mechanism is first introduced in order to accurately characterize the nature of the problem and establish the basis for further analysis. For the point-in-triangle problem, four quadratic forms in the joint coordinate vectors of a point and the vertices of the triangle are constructed. The pr
Request full-text A general framework for error analysis in measurement-based GIS Part 1: The basic measurement-error model and https://www.researchgate.net/publication/220449187_A_general_framework_for_error_analysis_in_measurement-based_GIS_Part_1_The_basic_measurement-error_model_and_related_concepts_Journal_of_Geographical_Systems_6325-354 related conceptsArticle in Journal of Geographical Systems 6(4):325-354 · December 2004 with 9 ReadsDOI: 10.1007/s10109-004-0141-4 · Source: DBLP1st Yee Leung2nd Jiang-Hong Ma3rd Michael F. GoodchildAbstractThis is the first of a four-part series of papers which proposes a general framework for error analysis in measurement-based geographical information systems (MBGIS). The purpose of the series is to investigate the fundamental issues a general involved in measurement error (ME) analysis in MBGIS, and to provide a unified and effective treatment of errors and their propagation in various interrelated GIS and spatial operations. Part 1 deals with the formulation of the basic ME model together with the law of error propagation. Part 2 investigates the classic point-in-polygon a general framework problem under ME. Continuing to Part 3 is the analysis of ME in intersections and polygon overlays. In Part 4, error analyses in length and area measurements are made. In this present part, a simple but general model for ME in MBGIS is introduced. An approximate law of error propagation is then formulated. A simple, unified, and effective treatment of error bands for a line segment is made under the name of “covariance-based error band”. A new concept, called “maximal allowable limit”, which guarantees invariance in topology or geometric-property of a polygon under ME is also advanced. To handle errors in indirect measurements, a geodetic model for MBGIS is proposed and its error propagation problem is studied on the basis of the basic ME model as well as the approximate law of error propagation. Simulation experiments all substantiate the effectiveness of the proposed theoretical construct.Do you want to read the rest of this article?Request full-text CitationsCitations32ReferencesReferences23For