Optimization approaches for generalization and data abstraction

The availability of methods for abstracting and generalizing spatial data is vital for understanding and communicating spatial information. Spatial analysis using maps at different scales is a good example of this. Such methods are needed not only for analogue spatial data sets but even more so for digital data. In order to automate the process of generating different levels of detail of a spatial data set, generalization operations are used. The paper first gives an overview on current approaches for the automation of generalization and data abstraction, and then presents solutions for three generalization problems based on optimization techniques. Least‐Squares Adjustment is used for displacement and shape simplification (here, building groundplans), and Self‐Organizing Maps, a Neural Network technique, is applied for typification, i.e. a density preserving reduction of objects. The methods are validated with several examples and evaluated according to their advantages and disadvantages. Finally, a scenario describes how these methods can be combined to automatically yield a satisfying result for integrating two data sets of different scales.

[1]  J. C. Müller,et al.  Area-patch generalisation: a competitive approach , 1992 .

[2]  W. Baarda,et al.  A testing procedure for use in geodetic networks. , 1968 .

[3]  Bradford George Nickerson,et al.  Automated cartographic generalization for linear map features , 1987 .

[4]  Lars Harrie,et al.  An Optimisation Approach to Cartographic Generalisation , 2001 .

[5]  Lars Harrie,et al.  The Constraint Method for Solving Spatial Conflicts in Cartographic Generalization , 1999 .

[6]  W. Mackaness.  An Algorithm for Conflict Identification and Feature Displacement in Automated Map Generalization , 1994 .

[7]  J. Miiller,et al.  Generalization : state of the art and issues , 1995 .

[8]  T. Kohonen.  Self-Organized Formation of Correct Feature Maps , 1982 .

[9]  Monika Sester,et al.  PARAMETER-FREE CLUSTER DETECTION IN SPATIAL DATABASES AND ITS APPLICATION TO TYPIFICATION , 2000 .

[10]  Sébastien Mustière,et al.  MACHINE LEARNING TECHNIQUES FOR DETERMINING PARAMETERS OF CARTOGRAPHIC GENERALISATION ALGORITHMS , 2000 .

[11]  Helmut Mayer.  MODEL-GENERALIZATION OF BUILDING OUTLINES BASED ON SCALE-SPACES AND SCALE-SPACE EVENTS , 2007 .

[12]  Aaron Sloman,et al.  POP-11: a practical language for artificial intelligence , 1985 .

[13]  Wolfgang Förstner,et al.  Object Location Based on Uncertain Models , 1989, DAGM-Symposium.

[14]  Jonathan Richard Shewchuk,et al.  Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator , 1996, WACG.

[15]  Christopher B. Jones,et al.  Conflict Reduction in Map Generalization Using Iterative Improvement , 1998, GeoInformatica.

[16]  Jan Terje Bjørke.  Framework for Entropy-based Map Evaluation , 1996 .

[17]  Monika Sester.  GENERALIZATION BASED ON LEAST SQUARES ADJUSTMENT , 2000 .

[18]  Karl-Rudolf Koch,et al.  Parameter estimation and hypothesis testing in linear models , 1988 .

[19]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[20]  W. Mackaness,et al.  The application of agents in automated map generalization , 1999 .

[21]  Anne Ruas,et al.  A Method vor Building Displacement in Automated Map Generalisation , 1998, Int. J. Geogr. Inf. Sci..

[22]  P. Højholt.  Solving Space Conflicts in Map Generalization: Using a Finite Element Method , 2000 .

[23]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[24]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[25]  Charles L. Lawson,et al.  Basic Linear Algebra Subprograms for Fortran Usage , 1979, TOMS.