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Abstract. Concepts of fuzzy objects have been put forward by various authors (Burrough and Frank 1996 ) to represent objects with indeterminate boundaries. In most of these proposals the uncertainties in thematic aspects and the geometric aspects are treated separately. Furthermore little attention is paid to methods for object identi cation, whereas it is generally in this stage that the uncertainty aspects of objects become manifest. When objects are to be extracted from image data then the uncertainty of image classes will directly eOE ect the uncertainty of the determination of the spatial extent of objects. Therefore a complete and formalized description of fuzzy objects is needed to integrate these two aspects and analyse their mutual eOE ects. The syntax for fuzzy objects (Molenaar 1998) , was developed as a generalization of the formal syntax model for conventional crisp objects by incorporating uncertainties. This provides the basic framework for the approach presented in this paper. However, the model still needs further development in order to represent objects for diOE erent application contexts. Moreover, the model needs to be tested in practice. This paper proposes three fuzzy object models to represent objects with fuzzy spatial extents for diOE erent situations. The Fuzzy-Fuzzy object (FF-object) model represents objects that have an uncertain thematic description and an uncertain spatial extent, these objects may spatially overlap each other. The Fuzzy-Crisp object (FC-object) model represents objects with an uncertain spatial extent but a determined thematic content and the Crisp-Fuzzy object (CF-object) model represents objects with a crisp boundary but uncertain content. The latter two models are suitable for representing fuzzy objects that are spatially disjoint. The procedure and criteria for identifying the conditional spatial extent and boundaries based upon fuzzy classi cation result are discussed and are formalized based upon the syntactic representation. The identi cation of objects by these models is illustrated by two cases: one from coastal geomorphology of Ameland, The Netherlands and one from land cover classi cation of Hong Kong.

Building patterns are important features that should be preserved in the map generalization process. However, the patterns are not explicitly accessible to automated systems. This paper proposes a framework and several algorithms that automatically recognize building patterns from topographic data, with a focus on collinear and curvilinear alignments. For both patterns two algorithms are developed, which are able to recognize alignment-of-center and alignment-of-side patterns. The presented approach integrates aspects of computational geometry, graph-theoretic concepts and theories of visual perception. Although the individual algorithms for collinear and curvilinear patterns show great potential for each type of the patterns, the recognized patterns are neither complete nor of enough good quality. We therefore advocate the use of a multi-algorithm paradigm, where a mechanism is proposed to combine results from different algorithms to improve the recognition quality. The potential of our method is demonstrated by an application of the framework to several real topographic datasets. The quality of the recognition results are validated in an expert survey.

ONTOLOGY-BASED GEOGRAPHIC DATA SET INTEGRATION PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof. dr. F.A. van Vught, volgens besluit van het College voor Promoties in het openbaar te verdedigen op donderdag 6 september 2001 te 13.

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Evaluation is a key step to examine the quality of generalized maps with respect to map requirements. Map generalization facilitates the recognition of pattern generating processes by preserving and highlighting the patterns at smaller scales. This article focuses specifically on the evaluation of building patterns in topographic maps that are generalized from large to mid scales. Currently, there is a lack of knowledge and functionality on automatically evaluating how these patterns are generalized. The issues of the evaluation range from missing formal map requirements on building alignments to missing automated evaluation techniques. This article firstly analyses the requirements (constraints) related to the generalization of building alignments. Then, it focuses on three more specific constraints, i.e. on existence, orientation of alignments and spatial distribution of composing buildings. Later, a three-step approach is proposed to (1) recognize and (2) match alignments from source and generalized datasets and (3) evaluate building alignments in generalized datasets. Besides, manyto-many and partial matching between initial and target alignments is a side effect of generalization, which reduces the reliability of the evaluation results. This article introduces a confidence indicator to document the reliability and to inform intended users (e.g. cartographers) and/or systems about the reliability of evaluation decisions. The effectiveness of our approach is demonstrated by evaluating the alignments in both interactively (manually) generalized maps and automated generalized maps. Finally, we discuss how our approach can be used to control automated generalization and identify further improvements.