Applying Soft Computing in Defining Spatial Relations

Geometric properties and relations play central roles in the description and processing of spatial data. The properties and relations studied by mathematicians usually have precise definitions, but verbal descriptions often involve imprecisely defined concepts such as elongatedness or proximity. The methods used in soft computing provide a framework for formulating and manipulating such concepts. This volume contains eight papers on the soft definition and manipulation of spatial relations and gives a comprehensive summary on the subject.

Fuzzifying Spatial Relations.- 1 Motivation.- 2 Imprecision in Spatial Relations.- 2.1 Conceptual Neighborhoods.- 2.2 Fuzzification of Allen Relations.- 3 Applying Allen’s Algorithm to Fuzzy Relations.- 4 Other Fuzzy Relations.- 5 Fuzzy Constraint Satisfaction.- 6 Conclusion.- Acknowledgement.- References.- Path Composition of Positional Relations Integrating Qualitative and Fuzzy Knowledge.- 1 Introduction.- 2 Composition of Positional Relations.- 2.1 Qualitative Distance Relations.- 2.2 Composition of Positional Relations.- 3 Path Composition.- 4 Integrating Qualitative and Fuzzy Knowledge.- 5 Fuzzy Knowledge Coming from Particular Distance Systems.- 6 Conclusions.- Acknowledgments.- References.- Spatial Relations Based on Dominance of Fuzzy Sets.- 1 Spatial Relations.- 1.1 Introduction.- 1.2 Modeling of Spatial Relations.- 1.3 Comparison of Definitions of Spatial Relations.- 1.4 Summary.- 2 Spatial Relations Among Fuzzy Subsets.- 2.1 Introduction.- 2.2 The Idea of Projections.- 2.3 Definitions of Spatial Relations for Fuzzy Objects.- 2.4 Properties of Spatial Relations for Fuzzy Objects.- 2.5 Separation Measure.- 2.6 The Model for Spatial Relationships.- 2.7 Results of Sample Systems.- 2.8 Conclusions.- References.- Mathematical Morphology and Spatial Relationships: Quantitative, Semi-Quantitative and Symbolic Settings.- 1 Introduction.- 2 Basic Morphological Operations, Fuzzy and Logical Extensions.- 2.1 Classical Morphology on Sets and Functions.- 2.2 Fuzzy Mathematical Morphology.- 2.3 Morpho-Logics.- 3 Computing Spatial Relationships from Mathematical Morphology: Quantitative and Semi-Quantitative Setting.- 3.1 Set Relationships.- 3.2 Adjacency.- 3.3 Distances.- 3.4 Directional Relative Position from Conditional Fuzzy Dilation.- 3.5 Example.- 4 Spatial Representations of Spatial Relationships.- 4.1 Spatial Fuzzy Sets as a Representation Framework.- 4.2 Set Relationships.- 4.3 Adjacency.- 4.4 Distances.- 4.5 Relative Directional Position.- 4.6 Example on Brain Structures.- 5 Symbolic Representations of Spatial Relationships.- 5.1 Topological Relationships.- 5.2 Distances.- 5.3 Directional Relative Position.- 6 Conclusion.- References.- Understanding the Spatial Organization of Image Regions by Means of Force Histograms: A Guided Tour.- 1 Introduction.- 2 The Notion of the Histogram of Forces.- 2.1 Description.- 2.2 Properties.- 2.3 Inverse Problem.- 3 Comparing Force Histograms.- 3.1 Principle.- 3.2 Application to Fuzzy Scene Matching.- 4 Defining Fuzzy Spatial Relations.- 4.1 Directional Relations.- 4.2 Other Spatial Relations.- 5 Generating Linguistic Spatial Descriptions.- 5.1 Principle.- 5.2 Application to Image Scene Description.- 5.3 Application to Human-Robot Communication.- 6 Conclusion.- Acknowledgments.- References.- Fuzzy Spatial Relationships and Mobile Agent Technology in Geospatial Information Systems.- 1 Introduction.- 2 Background.- 3 Fuzzy Directional Relationships and Querying.- 4 Extensions to the Model.- 4.1 Extensions to the Standard MBR Representation.- 4.2 Geometric Modeling Capabilities.- 4.3 An Extension for Expert System Implementation.- 4.4 A CLIPS Implementation.- 4.5 Fuzzy Querying of Binary Spatial Relationships.- 4.6 Modifications for Anomalous Cases.- 4.7 Oracle Implementation.- 5 Intelligent Agent Technology.- 5.1 Overview.- 5.2 Rule-Based Reasoning.- 5.3 Knowledge-Based Reasoning.- 5.4 Implementation.- 6 Summary and Future Work.- Acknowledgments.- References.- Using Fuzzy Spatial Relations to Control Movement Behavior of Mobile Objects in Spatially Explicit Ecological Models.- 1 Introduction.- 1.1 Information-Based Approaches to Ecological Modeling.- 1.2 Framework for Spatially Explicit Ecological Modeling.- 2 Modeling Habitat Landscape.- 2.1 Fuzzy Spatial Relations in Habitat Evaluation.- 2.2 An Example of Fuzzy Habitat Evaluation.- 2.3 Land Cover Classification and Habitat Modeling.- 3 Fuzzy Control of Spatial Movement.- 3.1 Perceptual Range as Fuzzy Spatial Relation.- 3.2 Controlling Foraging Movement.- 3.3 Controlling Exploratory Movement.- 3.4 Spatially Explicit Conspecific Interactions.- 4 Discussion.- 4.1 Fuzzy Rule-Base Models.- 4.2 Movement Direction and Memory.- 4.3 Fuzzy Logic and Robotics.- 4.4 Defining Fuzzy Spatial Relations.- 4.5 GIS Database Issues.- 4.6 Concluding Comment.- References.- A Fuzzy Set Model of Approximate Linguistic Terms in Descriptions of Binary Topological Relations Between Simple Regions.- 1 Introduction.- 2 Related Literature.- 2.1 The 9-Intersection Model of Topological Relations.- 2.2 Cognitive Aspects of Spatial Relations.- 2.3 Models of Spatial Relations Between Fuzzy Regions.- 2.4 Approximate Linguistic Terms in Descriptions of Spatial Relations.- 3 Fuzziness of Approximate Linguistic Terms — Preliminary Cognitive Evidences.- 3.1 Experimental Design.- 3.2 Results from Experiment One.- 3.3 Results from Experiment Two.- 4 A Fuzzy Set Model of Approximate Linguistic Terms.- 5 Discussion.- 6 Concluding Remarks.- Acknowledgements.- References.- About the Editors.