Stephan Winter and Lemonia Ragia, "Contributions to a Quality Description of Areal Objects in Spatial Data Sets", In Proceedings of ISPRS Commission IV Symposium. Stuttgart, Germany 1998.

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In this paper we present a quality evaluation of two-dimensional building acquisition. We propose methods for identification and quantification of differences between independently acquired regions, and we present a systematic classification of those differences. Differences between acquired sets Rj = rij of regions rij depend on the context of observation, on the technique of observation, and so on. We distinguish topological and em geometrical differences. Topological differences refer to the interior structure of a set of regions as well as to the structure of the boundary of a single region. Geometrical differences refer to the location of the boundary of a single region or of a set of regions, independent of their representation and of the structure of the boundaries. Identification of differences requires a matching of two data sets R1 and R2 which is done here by weighted topological relationships. For the identification of topological differences between two sets R1 and R2 of regions we use the two region adjacency graphs. For an identification of geometrical differences we use the zone skeleton between two matched subsets rp1 and rq2 of the given sets. The zone skeleton is labeled with the local distances of the corresponding boundaries of the subsets; especially we investigate its density function. An example, based on two real data sets of acquired ground plans of buildings, shows the feasibility of the approach.

@inproceedings{Winter1998Contributions,
  author = {Winter, Stephan and Ragia, Lemonia},
  title = {Contributions to a Quality Description of Areal Objects in Spatial Data Sets},
  booktitle = {Proceedings of ISPRS Commission IV Symposium},
  year = {1998}
}

Stephan Winter, "Beobachtungsunsicherheit und topologische Relationen", In Workshop Datenqualität und Metainformation in Geo-Informationssystemen. Rostock, pp. 141-154. 1996.

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In diesem Beitrag wird eine Methode zur Bestimmung der topologischen Relationen zwischen zwei in ihrer Lage unsicheren Regionen vorgestellt. Die Bestimmung basiert auf den Extremwerten einer Abstandsfunktion entlang eines Skeletts durch unsichere Schnittmengen zwischen den Regionen. Mit einer solchen Repräsentation vertiefen wir die Relationskonzepte der 9-Intersektion, indem wir über topologisch invariante Merkmale hinaus auch metrische Information erhalten, um sie zur Unsicherheit in Bezug zu setzen. Die Beobachtung der Abstände wird hier statistisch modelliert. Mit einer Bayes-Klassifikation erhalten wir Abstandsklassen, aus denen wir auf die topologische Relation zurückschließen und deren Wahrscheinlichkeit wir so angeben können.

@inproceedings{Winter1996Beobachtungsunsicherheit,
  author = {Winter, Stephan},
  title = {Beobachtungsunsicherheit und topologische Relationen},
  booktitle = {Workshop Datenqualit\"at und Metainformation in Geo-Informationssystemen},
  year = {1996},
  pages = {141--154}
}

Stephan Winter, "Distances for Uncertain Topological Relations", In ESF-NSF Summer Institute in Geographic Information. Berlin, Germany 1996.

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Considering uncertainty of spatial data in any GIS analysis is a theme of actual research, but far from practicability. One prerequisite is the availability of descriptions concerning uncertainty (meta-data), and another is the attachment of uncertainty to spatial analysis. In our contribution we propose a method to determine the topological relation between two positional uncertain regions. The decision is based on morphological distances along a skeleton through uncertain intersection sets. These measures are equivalent to the known representation by intersection sets, but yield additionally metric information. These distances are applied to a statistical model of the observation process. A Bayesian classification yields distance classes which allow to deduce the topological relationship. We discuss also importance and perspectives of the method.

@inproceedings{Winter1996Distances,
  author = {Winter, Stephan},
  title = {Distances for Uncertain Topological Relations},
  booktitle = {ESF-NSF Summer Institute in Geographic Information},
  year = {1996}
}

Stephan Winter and Adrijana Car, "Report from ESF/NCGIA Summer Institute in GIS, Berlin", In Summer Institute in Geographic Information. 1996.

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[none]

@inproceedings{Winter1996Report,
  author = {Winter, Stephan and Car, Adrijana},
  title = {Report from ESF/NCGIA Summer Institute in GIS, Berlin},
  booktitle = {Summer Institute in Geographic Information},
  year = {1996}
}

Stephan Winter, "Unsichere topologische Beziehungen zwischen ungenauen Flächen". Thesis at: Institute of Photogrammetry, University of Bonn. 1996.

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Summary
Uncertainty is an inherent property of observations. Abstracting the real world to conceptional objects is a step of generalization, and the measurement, taking place on abstracted objects, propagates this uncertainty, due to additional systematic, gross or random errors. Each spatial analysis is infected by these sources of uncertainty. It is necessary to introduce propagation of uncertainty in spatial reasoning to allow an assessment of the results. The scope of the thesis is to combine the process of observation with a mathematical model of qualitative spatial relations, modelling the randomness of the observations. A methodology is presented for probability-based decisions about spatial relations. When determining spatial relations from positional uncertain objects, one has to distinguish between quantitative relations, which become imprecise, and qualitative relations, which become uncertain. Topological relations, being of qualitative nature, mayor may not be true in presence of positional uncertainty. Assuming the overlay of two independent objects indicates a very small overlap, the question arises whether the two objects could be neighboured in reality. Comparing the degree of overlap to the size of uncertainty will allow to make a decision, and to assess this decision. Because of the essential importance of considering uncertainty in spatial analysis, a theoretically well-based model of uncertainty is preferred against limitations in validity or meaning. Therefore, in this thesis, positional uncertainty will be described stochastically, and the inference from this description to the uncertainty of derived spatial relations is treated with a statistical classification approach. Probabilities of single relations are determined, and the relation with maximum probability, given the evidence from observation, is chosen. At the beginning the separation of abstraction and measurement within the observation process is discussed. The complexity of regions is limited by the smoothness of the boundary when related to its uncertainty. In the following chapter the space of possible relations is reduced to two sub-graphs of the conceptual-neighbourhood-graph of binary relations between regions. Depending on the sub-graph that the relation between two regions belongs to, different sets of intersection sets between the two objects become uncertain. To describe the uncertainty a morphological distance function is defined, based on the skeleton. It is shown that it is sufficient to use the minimum and maximum distance, and to classify the relation, depending on the signs of these two values. For the first time the imprecision of measurement and the uncertainty of abstraction are described using probability densities. They are used to determine a vector of probabilities the sign of the distance values have, which is the basis for a Bayesian classification. From these distance classes the decision about the topological relation of the two objects is derived. In the last chapter examples show the versatility of the proposed methodology. Other approaches for handling uncertainty are discrete, using error bands, or fuzzy, with the problem of weaker results. With the strong connection to an observation process we hope to give a more valuable decision method, with probabilities as interpretable results, which should be useful for the assessment and propagation in spatial reasoning processes.
Zusammenfassung
Beobachtungen sind prinzipiell unsicher. Die Abstraktion der realen Welt auf konzeptionelle Objekte stellt eine Generalisierung dar, und eine daran anschließende Aufnahme dieser abstrahierten Objekte ist ein Meßprozeß, der die Generalisierung festhält und zusätzlich mit systematischen, groben und zufälligen Fehlern behaftet ist. Jede räumliche Analyse wird durch die Beobachtungsunsicherheit räumlicher Daten beeinflußt. Daher ist es notwendig, die Fortpflanzung der Unsicherheit in der räumlichen Analyse einzuführen, um die Ergebnisse bewerten zu können. In dieser Arbeit wird der Beobachtungsprozeß mit einem mathematischen Modell qualitativer räumlicher Relationen verknüpft. Mit einer stochastischen Beschreibung der Unsicherheit wird eine wahrscheinlichkeitsbasierte Entscheidung über die räumliche Relation möglich. Die Lageunsicherheit räumlicher Objekte führt bei der Ableitung kontinuierlicher Werte zu ungenauen Ergebnissen und bei der Bestimmung diskreter oder qualitativer Aussagen zu unsicheren Ergebnissen. Topologische Relationen sind qualitativer Natur. Unter sicheren Objekten können sie daher richtig oder falsch bestimmt werden. Nehmen wir an, zwei flächenhafte Objekte aus unabhängigen Beobachtungen würden sich in kleinen Restflächen überlappen, dann stellt sich die Frage, ob sie in der realen Welt auch benachbart sein könnten. Eine Beurteilung der Situation wird die Größe der Lageunsicherheit mit dem Maß der überlappung beider Objekte in Verbindung setzen. Wegen der grundsätzlichen Bedeutung, die Lageunsicherheit in jeder räumlichen Analyse zu berücksichtigen, wird auf das theoretische Fundament eines Ansatzes besonderer Wert gelegt. Aus diesem Grund wird in dieser Arbeit Lageunsicherheit stochastisch beschrieben. Für die Schlußfolgerung aus der Beschreibung der Lageunsicherheit auf die Unsicherheit der abgeleiteten räumlichen Beziehungen wird ein statistischer Klassifikationsansatz gewählt. Nach der Berechnung von Wahrscheinlichkeiten einzelner Klassen wird eine Entscheidung für diejenige Relation gefällt, die bei gegebener Evidenz aus der Beobachtung die größte Wahrscheinlichkeit besitzt. Am Anfang wird die Aufteilung des Beobachtungsprozesses in Abstraktion und Messung näher diskutiert. Außerdem werden Grundvoraussetzungen über die Kompaktheit und die Glattheit des Randes von Objekten in Bezug auf ihre Lageunsicherheit getroffen. Im nächsten Kapitel wird der Raum möglicher topologischer Relationen in zwei disjunkte Teilgraphen des conceptulal-neighborhood-Graphen binärer topologischer Beziehungen. zerlegt. Je nachdem zu welchem Teilgraphen die Beziehung zweier Objekte zählt, werden unterschiedliche Mengen von Schnittmengen unsicher. Um diese Unsicherheit zu beschreiben, wird eine morphologische Abstandsfunktion, basierend auf einem Skelett, definiert. Es wird gezeigt, dass es hinreichend ist, sich auf Minimum und Maximum unter den Abständen zu beschränken, und dass sich darüberhinaus allein aus dem Vorzeichen dieser Abstände die topologische Beziehung bestimmen läßt. Danach wird erstmalig die Meßungenauigkeit und die Abstraktionsunsicherheit durch Wahrscheinlichkeitsdichten modelliert. Damit läßt sich ein Wahrscheinlichkeitsvektor für die Vorzeichenklasse des Abstandsminimums und des Abstandsmaximums berechnen, der Grundlage einer Bayes-Klassifikation ist. Aus diesen Abstandsklassen wird auf die topologische Beziehung geschlossen. Zum Schluß wird der Nutzen des Verfahrens an Beispielen gezeigt. Andere Ansätze zur Handhabung von Lageunsicherheit arbeiten mit diskreten Mengen, z. B. Fehlerbändern, oder mit unscharfen Mengen, mit dem Nachteil schwächerer Ergebnisse. Durch die starke Kopplung an den Beobachtungsprozeß stellen wir ein aussagekräftiges Entscheidungsverfahren vor, das in Form von Wahrscheinlichkeiten interpretierbare Ergebnisse liefert, die zur Beurteilung sowie zur Fortpflanzung in der räumlichen Analyse benutzt werden können.

@phdthesis{Winter1996Unsichere,
  author = {Winter, Stephan},
  title = {Unsichere topologische Beziehungen zwischen ungenauen Fl\"achen},
  school = {Institute of Photogrammetry, University of Bonn},
  year = {1996}
}

Stephan Winter, "Topological Relations between Discrete Regions", In Advances in Spatial Databases Proceedings of the Fourth International Symposium on Large Spatial Databases (SSD '95). Egenhofer, Max J. and Herring, John R. (Eds.) Portland, Maine, pp. 310-327. 1995.

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Topological reasoning is important for speeding up spatial queries, e.g. in GIS or in AI (robotics). While topological relations between spatial objects in the vector model (R2) are investigated thoroughly, we run into inconsistencies in the raster model (Z2). But instead of reducing our requirements in case of reasoning in raster images we change from simple raster to a cellular decomposition of R2 - what we call a hyper-raster - which is also discrete, but preserves the topology of R2. The finite representation limits the computational effort against the vector model. We will introduce a data structure for the hyper-raster, which represents regions, curves and points. Then we will present algorithms for digitization and elementary image processing in hyper-raster. With that the intersection sets, as needed for the determination of a topological relation between two objects, are calculated simply by logical joins of binary images. Without extending our model we can also compute further refinements of the relationship. We will show that applying the 9-intersection, originally developed for the vector model, to the hyper-raster leads exactly to the set of known eight relations between regions without holes in R2.

@inproceedings{Winter1995Topological,
  author = {Winter, Stephan},
  editor = {Egenhofer, Max J. and Herring, John R.},
  title = {Topological Relations between Discrete Regions},
  booktitle = {Advances in Spatial Databases Proceedings of the Fourth International Symposium on Large Spatial Databases (SSD '95)},
  year = {1995},
  pages = {310--327},
  doi = {10.1007/3-540-60159-7_19}
}

Stephan Winter, "DT - Modul zur Distanztransformation" 1995.

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[none]

@techreport{Winter1995DT,
  author = {Winter, Stephan},
  title = {DT - Modul zur Distanztransformation},
  year = {1995}
}

Stephan Winter, "Fourth Symposium on Large Spatial Databases (SSD 95)" 1995.

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[none]

@techreport{Winter1995Fourth,
  author = {Winter, Stephan},
  title = {Fourth Symposium on Large Spatial Databases (SSD 95)},
  year = {1995}
}

Stephan Winter, "Uncertainty in Topological Relationships in GIS", In Proceedings of ISPRS Comm. III Symposium on Spatial Information from Digital Photogrammetry and Computer Vision. München 1994.

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We present a concept for representing uncertain topological relations and their derivation from uncertain sets, useful for spatial and temporal reasoning in GIS. The concept is based on the notion of a stochastic boundary of a geometric set and on tests performed to decide the validity of relations between the sets. It uses the power-function to derive the probabilities of the found relations. The concept is applicable to all questions where uncertain geometric queries or analysis have to be performed.

@inproceedings{Winter1994Uncertainty,
  author = {Winter, Stephan},
  title = {Uncertainty in Topological Relationships in GIS},
  booktitle = {Proceedings of ISPRS Comm. III Symposium on Spatial Information from Digital Photogrammetry and Computer Vision},
  year = {1994}
}

Stephan Winter, "Bericht über die AGDM 94" 1994.

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[none]

@techreport{Winter1994Bericht,
  author = {Winter, Stephan},
  title = {Bericht \"uber die AGDM 94},
  year = {1994}
}