Qualitative Spatial Reasoning: Extracting and Reasoning with Spatial Aggregates BaileyKellogg

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Qualitative Spatial Reasoning Extracting and
Reasoning with Spatial Aggregates
Bailey-KelloggZhao, 2004

• Ceyhun B. Akgül, MS in EE
• Bogaziçi University, Istanbul
• May 2004

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Introduction

• Qualitative Spatial Reasoning (QSR)
• Reasoning about spatially distributed data and
  their relationships qualitatively
• Applications
• Geographic Information Systems (GIS)
• Meteorological and Fluid Flow Analysis
• Computer-Aided Design
• Protein Structure Databases
• Etc.

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Introduction

• Complementary Problems in QSR
• Data-Poor Problems
• Designing representations that can answer
  qualitative queries without much numerical
  information
• Data-Rich Problems
• Derive and manipulate Q-spatial representations
  for abstracting spatial aspects of underlying data

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QSR for Data-Poor Problems

• Recall Qualitative Simulation with QDEs
• Temporal Primitives
• Predicates concerning reasonable functions
• Similarly in QSR
• Topological descriptions of spatial objects and
  their relationships

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QSR for Data-Poor Problems

• A representative approach
  Region-Connection Calculus Cui et al., 1992
• Arbitrary topological regions
• A set of predicates (RCC-8)
• Boolean functions to compose complex spatial
  objetcs

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QSR for Data-Poor Problems

• Other qualitative aspects can also be
  incorporated
• Size and shape (of objetcs)
• Distance and orientation (between objects)
• Often metric information should be brought in
  order to allow significant inference
• Poverty Conjecture Forbus et al., 1991
• There is no problem-independent, purely
  qualitative representation of space or shape.
• ? Qualitativeness vs. Generality

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QSR for Data-Poor Problems

• Compromising Theories
• Metric Diagram / Place Vocabulary
• Forbus et al., 1991
• Spatial Semantic Hierarchy
• KuipersLevitt, 1988 Kuipers, 2000

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QSR for Data-Rich Problems

• Spatially distributed numerical data are abundant
  in scientific/engineering applications

Fluid flow
Meteorogical Map
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QSR for Data-Rich Problems

• A central problem for data-rich applications
• Automatic construction of qualitive spatial
  representations from a given data set
• Numerical methods for spatial data analysis exist
• Segmentation, Data Reduction, Clustering,
  Scale-Space, Feature Extraction etc.
• These are all abstraction in some sense

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QSR for Data-Rich Problems

• QSR supports more abstract representations
• Abstraction ? Multiple levels of resolution
• Example Meterorologists abstract patterns into
• Isobars, pressure troughs, pressure cells etc.
• Physical properties such as continuity and
  locality give rise to regions of uniformity in
  spatially distributed data
• QSR
• ? Scientific Visualization, Spatial Data
  Mining

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Spatial AggregationYipZhao, 1996

• Spatial Aggregation (SA) is a particular form of
  QSR for data-rich domains.
• SA performs successive steps of abstraction in a
  multi-layered fashion

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Spatial Aggregation

• SA has its own data types and operators
• These make explicit use of domain specific
  knowledge

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Spatial Aggregation
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Case StudyReasoning with Weather Data

• Troughs and ridges are important features in
  weather analysis
• They are only qualitatively understood even
  sometimes experts give different answers

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Case StudyReasoning with Weather Data

• SA approach to trough finding
• Input ? A gridded pressure data set
• Output ? A contoured pressure chart with troughs
  labeled
• Preprocessing
• Iso-bar points interpolated from gridded data,
  yielding a set of iso-points with pressure at
  specified contour level.
• 1st Level of Aggregation
• Points ? Iso-bars
• 2nd Level of Aggregation
• Iso-bar segments ? Troughs and ridges

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Case StudyReasoning with Weather Data
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Case StudyReasoning with Weather Data
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Future Research Directions

• QSR is an important aspect of common-sense
  reasoning.
• Additional primitives and inference operators
• Incorporation of probabilistic information
• Synthesizing the data-poor and data-rich
  approaches
• Data-rich approaches to build models for
  data-poor problems
• General QSR Theory?