Handbuch der Oelfabrikation und Oelreinigung: Handbuch der Oelfabrikation und Oelreinigung

Julia de Fontenelle, Jean Sébastien Eugène; Knacker, Justus

Bibliographic data

Monograph

Persistent identifier:: 189734970X

Author:: Ribbentrop, Philipp Christian

Title:: Beschreibung der Straßen, einiger öffentlichen Gebäude und der Kirchen der Stadt Braunschweig

Scope:: 1 ungezähltes Blatt, VIII Seiten, 1 ungezähltes Blatt, 230 Seiten, 1 ungezähltes Blatt

Info on language/writing:: In Fraktur

DOI:: 10.14463/KXP:189734970X

Year of publication:: 1789

Place of publication:: Braunschweig

Identifier (digital):: 189734970X

Illustration:: Frontispitz, Notenbeispiele

Signature of the source:: Haupt 943

Language:: German

Additional Notes:: Verfasser am Ende des Vorworts auf Seite VIII genannt; Der Frontispitz ist ein Kupferstich

Publisher of the original:: gedruckt bey Johann Christoph Meyer

Usage licence:: Public Domain Mark 1.0

Printer:: Meyer, Johann Christoph

Publisher of the digital copy:: Technische Informationsbibliothek (TIB)

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2024

Document type:: Monograph

Collection:: Monographs

Chapter

Title:: Zweiter Abschnitt. Beschreibung der Kirchen.

Document type:: Monograph

Structure type:: Chapter

Section

Title:: K. Michaelis Kirche.

Document type:: Monograph

Structure type:: Section

tri B2. Beijing 2008 1125 UNIVERSAL ERROR PROPAGATION LAW Xiaoyong CHEN a and Shunji MURAI b a Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 12120, Thailand - xychen@ait.ac.th b IIS, University of Tokyo, 4-6-1. Komaba, Meguro-ku, Tokyo 153-8505, Japan - shi939murai@nifty.com Commission II, SS-15 KEY WORDS: Accuracy, Analysis, Modelling, Spatial Information Science, Statistics ABSTRACT: As an ubiquitous statistical theory, Gaussian Distribution (GD) or Gaussian Error Propagation Law (GEPL) has been widely used for modelling random errors in many engineering and application fields since 1809. In recent years, this theory has been extended to handle the uncertainties of spatial data in GIS, such as positional error modelling. But most of the results for spatial error modelling based on GD are contradictory with common senses and natural laws, such as energy law and Tobler’s First Law (TFL) in geography. This paper presents a novel statistical approach for rigorous modelling of positional errors of geometric features in spatial databases. Based on Generalized Gaussian Distribution (GGD) and using errors in local points as the fundamental building blocks, a new spatial statistical theory - Universal Error Propagation Law (UEPL) is presented to handle global error propagations for spatial random sets (or objects). Practical examples and simulations are given to illustrate the error propagations based on UEPL for various spatial objects. Finally, the relationships between UEPL and Newtown’s Universal Gravitation Law (NUGL) and TFL have been successfully established, which shows that UEPL is a new discovered natural law for spatial information field. 1. INTRODUCTION As one of the three most important emerging and evolving fields along with nanotechnology and biotechnology in this century (Gewin, 2004, Nature), Geo-spatial Information System (GIS) plays increasingly important roles in decision-making processes in many disciplines that involve planning, research and management by using spatial data at the different spatial levels. However, more effective use of GIS requires explicit knowledge of the uncertainty inherent in the spatial data. Therefore, the quality of GIS application is strongly dependent on the quality of spatial data which needs a formal theory for handling spatial errors in GISs (Goodchild, 1989). De Morgan (1838) asked, “what do we mean by a law of error?” in Essay on Probabilities and went on to describe "the standard law of facility of error". This law had been used by Gauss (1809) in his first theory of least squares and is called Gaussian Distribution (GD) or Gaussian Error Propagation Law (GEPL) today. As in many other fields of science, GD has played a predominant role in surveying data processing and error modelling (Mikhail and Ackermann, 1976). In the vast majority of these applications, it has been assumed that the point-based observation error under investigation is distributed with GD. This popularity of the Gaussian assumption has been motivated mainly by the theoretical appeal of GD due to the central limit theorem and equally by the desirable analytical properties of Gaussian Probability Density Function (PDF) which generally leads to linear equations. A Gaussian PDF is also the maximum-entropy density (Papoulis, 1991) when only the first two moments of a process are known. In a vector-based GIS, spatial features are defended on the basis of point features, e.g. a line is defined as a sequence of digitized points connected by line segments, and a polygon is defined as the interior of its boundary delimited by a closed line. Then, the positional uncertainty of points should form the basis for uncertainty analysis of all spatial objects. From this point of view, GD and GEPL have been extended for modelling spatial Figure 1. Different uncertainty models. errors in GIS, such as e-band model (Chrisman, 1982), error- band model (Shi, 1994), and generalized e-band model (Leung and Yan, 1998) [Figure 1 (a)-(c)] and etc. In the same way, the spatial features in an image database are defended based on the pixels. Error propagation among the neighbouring pixels plays an important role for analyzing image accuracies. As the example illustrated in Figure 1 (d), the center point r r y e - of a round-target can be estimated by its boundary pixels as v- =tI„' and '■'■■■ Then, its positional accuracies can be estimated by ; . = JWvn and ir- = *- ; A. n based on GEPL, where sr. - and c yi are the standard deviations of a pixel in x andy directions.

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Metadata: Proceedings; XXI International Congress for Photogrammetry and Remote Sensing (Part B2-2)

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