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Unformatted text preview: MODEL-GENERALIZATION OF BUILDING OUTLINES BASED ON SCALE-SPACES AND SCALE-SPACE EVENTS Helmut Mayer Chair for Photogrammetry and Remote Sensing Technische Universit¨at M¨unchen, D-80290 Munich, Germany E-mail: [email protected] URL: http://www.photo.verm.tu-muenchen.de Commission III, Working Group IV/III.1 KEY WORDS: Model-generalization, scale-space, scale-space events, building outlines ABSTRACT Generalization is not only mandatory to make maps more readable, or to make the visualization of larger areas computa- tionally feasible. It is also needed in the form of model-generalization, to transform data into the right level of abstraction for a particular analysis task. In this paper the formally well-defined theory of scale-spaces is introduced as a basis for model-generalization. More specifically, an approach is proposed which simplifies building outlines employing vector-based morphology and discrete curvature space. So-called scale-space events, for which the link to the semantics of objects has been shown, play a major role for the simplification. The proposed approach renders it possible to preserve and even enforce right angles, and makes the link to iterative cartographic displacement easy. Results show the validity of the approach. 1 INTRODUCTION Generalization is not only mandatory to make maps more readable, or to make the visualization of larger areas com- putationally feasible, but it is also needed in the form of model-generalization, to transform data into the right level of abstraction for a particular analysis task, e.g., in a geo- graphic information system (GIS). This paper deals with the model-generalization of building outlines based on the for- mally well-defined theory of scale-spaces, and particularly on so-called “scale-space events”, for which the link to the semantics of objects has been shown in (Mayer, 1996). Mathematical morphology and the so-called “discrete cur- vature space” are the main scale-spaces used in this paper. They are employed on vector data of the building outline. Vector data does not only render it possible to preserve right angles, but it also gives means to enforce them. In this paper the scale-spaces are incrementally applied, i.e., the vector outline of the building is shifted in small steps. An important reason for an incremental processing is the occurrence of scale-space events. They occur, when parts of the building like a porch are eliminated, when a building is split into parts, when an inner courtyard arises, or when two buildings merge. The events are classified into internal and external events. To handle the events, simple geomet- rical rules can be defined. Sections 2 and 3 give an overview over the state of the art of model-generalization and scale-space theory, respec- tively. Section 4 introduces the link of scale-space events in an image or a geometry based representation to the ab- straction in a symbolical representation. Section 5 presents the main body of the paper, namely the definition of the in-...
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This note was uploaded on 03/27/2010 for the course CS 123 taught by Professor Darghooz during the Spring '10 term at Albion College.
- Spring '10
- The Land