Cartographic generalisation of lines based on a B‐spline snake model

References

• Arge , E. and DÆhlen , M. 1999 . Data Reduction of Piecewise Linear Curves Technical Report STF33 A94042, SINTEF Informatics, Oslo, Norway
   Google Scholar
• Bader , M. 2001 . “ Energy minimization methods for feature displacement in map generalization. ” . PhD thesis, Department of Geography, University of Zurich, Switzerland
   Google Scholar
• Beard , K. 1991a . “ Constraints on rule formation. ” . In Map Generalization , Edited by: Buttenfield , B and McMaster , R. B . 121 – 135 . London : Longman .
   Google Scholar
• Beard , K. 1991b . Theory of the cartographic line revisited. . Cartographica , 28 (4) : 32 – 58 .
   Google Scholar
• Brigger , P. , Hoeg , J. and Unser , M. 2000 . B‐Spline snakes: a flexible tool for parametric contour detection. . IEEE Transactions on Image Processing , 9 (9) : 1484 – 1496 .
   PubMedGoogle Scholar
• Burghardt , D. 2005 . Controlled line smoothing by snakes. . GeoInformatica , 9 (3) : 237 – 252 .
   Google Scholar
• Burghardt , D. and Meier , S. 1997 . “ Cartographic displacement using the snakes concept. ” . In Semantic Modeling for the Acquisition of Topographic Information From Images and Maps , Edited by: Forstner , W and Plumer , L . 59 – 71 . Basel : Birkhauser Verlag .
   Google Scholar
• Buttenfield , B. 1991 . “ A rule for describing line feature geometry. ” . In Map Generalization: Making Rules for Knowledge Representation , Edited by: Buttenfield , B and McMaster , R. B . 150 – 171 . London : Longman Scientific & Technical .
   Google Scholar
• Cromley , R. G. and Campbell , G. M. 1992 . Integrating quantitative and qualitative aspects of digital line simplification. . The Cartographic Journal , 29 (1) : 25 – 30 .
   Google Scholar
• Douglas , D. H. and Peucker , T. K. 1973 . Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. . The Canadian Cartographer , 10 (2) : 112 – 122 .
   Google Scholar
• Eck , M. and Hadenfeld , J. 1995 . Knot removal for B‐spline curves. . Computer Aided Geometric Design , 12 : 259 – 282 .
   Google Scholar
• Farin , G. 2001 . Curves and Surfaces for CAGD , San Francisco, CA : Morgan‐Kaufmann . 5th edition
   Google Scholar
• Freeman , H. 1978 . Shape description via the use of critical points. . Pattern Recognition , 10 : 159 – 166 .
   Web of Science ®Google Scholar
• Fritsch , E. 1997 . “ Repre‐sentation de la géométrie et des contraintes cartographiques pour la généralisation du linéaire routier. ” . PhD thesis, Université de Marne‐la‐Vallée
   Google Scholar
• Gaffuri , J. 2006 . “ How to merge optimization and agent‐based techniques in a single generalization model? ” . In Proceedings of the ICA Workshop on map generalization and multiple representation Vancouver
   Google Scholar
• Guilbert , E. and Lin , H. 2006 . “ B‐spline curve smoothing under position constraints for line generalisation. ” . In Proceedings of the ACM GIS'06 , Edited by: Nittel , S and De By , R . 3 – 10 . New York : Acm Press .
   Google Scholar
• Guilbert , E. and Lin , H. 2007 . Isobathymetric line simplification with conflict removal based on a B‐spline snake model. . Marine Geodesy , 30 (1–2) : 169 – 195 .
   Google Scholar
• Guilbert , E. , Saux , E. and Daniel , M. 2003 . “ A hierarchical structure for locating intersections in large sets of B‐spline curves. ” . In Curves and Surfaces Design , Edited by: Lyche , T , Mazure , M. L and Schumaker , L. L . 205 – 214 . Brentwood, , USA : Nashboro Press .
   Google Scholar
• Guilbert , E. , Saux , E. and Daniel , M. 2006 . Conflict removal between B‐spline curves for isobathymetric line generalization using a snake model. . Cartography and Geographic Information Science , 33 (1) : 37 – 52 .
   Google Scholar
• Guilbert , E. , Saux , E. and Daniel , M. 2004 . Combining geometrical and mechanical displacements for suppressing intersections in cartographic generalization. . WSCG Short Communications , : 87 – 94 .
   Google Scholar
• Harrie , L. 2005 . “ Integrating graphic generalisation methods in a system for real‐time maps. ” . In Proceedings of ScanGIS 2005 , 63 – 74 . Stockholm : Department of Planning and Environment, KTH .
   Google Scholar
• Harrie , L. 1999 . The constraint method for solving spatial conflicts in cartographic generalization. . Cartography and Geographic Information Science , 26 (1) : 55 – 69 .
   Google Scholar
• Harrie , L. and Weibel , R. 2007 . “ Modelling the overall process of generalisation. ” . In Generalisation of Geographic Information: Cartographic Modelling and Applications , Edited by: Mackaness , W , Ruas , A and Sarjakoski , L. T . 67 – 87 . Amsterdam : Elsevier Science .
   Google Scholar
• Imai , H. and Iri , M. 1986 . Computational‐geometric methods for polygonal approximations of a curve. . Computer Vision, Graphics, and Image Processing , 36 : 31 – 41 .
   Google Scholar
• Jenks , G. F. 1989 . Geographic logic in line generalization. . Cartographica , 26 : 27 – 42 .
   Google Scholar
• Kass , M. , Witkin , A. and Terzopoulos , D. 1987 . “ Snakes: active contour models. ” . In Proceedings of International Conference on Computer Vision , 259 – 268 . Washington, DC : IEEE Computer Press .
   Google Scholar
• Kulik , L. , Duckham , M. and Egenhofer , M. J. 2005 . Ontology‐driven map generalization. . Journal of Visual Languages and Computing , 16 (3) : 245 – 267 .
   Google Scholar
• Lafranche , Y. and Le Méhauté , A. 1989 . “ A knot removal strategy for scattered data in R2. ” . In Mathematical Methods in Computer Aided Geometric Design , Edited by: Lyche , T and Schumaker , L. L . 419 – 426 . Boston : Academic Press .
   Google Scholar
• Lawford , G. J. 2006 . Fourier series and the cartographic line. . International Journal of Geographical Information Science , 20 (1) : 31 – 52 . 2006
   Google Scholar
• Li , Z. , Khoshelham , K. and Ding , X. 2004 . “ Empirical mode decomposition (EMD) transform for spatial analysis. ” . In Advances in Spatial Analysis and Decision Making , Edited by: Li , Z , Zhou , Q and Kainz , W . 19 – 29 . Lisse, , Netherlands : Balkema .
   Google Scholar
• Li , Z. and Openshaw , S. 1993 . A natural principle for the objective generalization of digital maps. . Cartography and Geographic Information Systems , 20 (1) : 19 – 29 .
   Google Scholar
• Lyche , T. and Morken , K. 1987 . Knot removal for parametric B‐spline curves and surfaces. . Computer Aided Geometric Design , 4 : 217 – 230 .
   Google Scholar
• McMaster , R. B. 1989 . The integration of simplification and smoothing algorithms in line generalization. . Cartographica , 26 (1) : 101 – 121 .
   Google Scholar
• Nickerson , B. 1988 . Automated cartographic generalization for linear features. . Cartographica , 25 (3) : 15 – 66 .
   Google Scholar
• Opheim , H. 1982 . Fast data reduction of a digitized curve. . Geo‐Processing , 2 : 33 – 40 .
   Google Scholar
• Pottmann , H. , Leopoldseder , S. and Hofer , M. 2002 . “ Approximation with Active B‐Spline Curves and Surfaces. ” . In Proceedings of Pacific Graphics 02 , 8 – 25 . Washington, , DC : IEEE Computer Society .
   Google Scholar
• Ramer , U. 1972 . An iterative procedure for the polygonal approximation of plane curves. . Computer Graphics and Image Processing , 1 : 244 – 256 .
   Google Scholar
• Reumann , K. and Witkam , A. P. M. 1974 . “ Optimizing curve segmentation in computer graphics. ” . In International Computer Symposium , Edited by: Gunther , A , Levrat , B and Lipps , H . 467 – 472 . New York : Amer. Elsevier .
   Google Scholar
• Robergé , J. 1985 . A data reduction algorithm for planar curves. . Computer Vision, Graphics, and Image Processing , 29 : 168 – 195 .
   Google Scholar
• Ruas , A. 1999 . “ Modèle de généralisation de données géographiques à base de contraintes et d'autonomie. ” . Université de Marne‐la‐Vallée
   Google Scholar
• Sarjakoski , T. and Kilpeläinen , T. 1999 . “ Holistic cartographic generalization by least squares adjustement for large data sets. ” . In Proceedings of the 19th ICA/ACI Conference , 1091 – 1098 . Ottawa : Canadian Institute of Geomatics .
   Google Scholar
• Saux , E. 2003 . B‐spline functions and wavelets for cartographic line generalization. . Cartography and Geographic Information Science , 30 (1) : 33 – 50 .
   Google Scholar
• Saux , E. 1998 . “ B‐spline curve fitting: application to cartographic generalization of maritime lines. ” . In Proceedings of the 8th International Conference on Computer Graphics and Visualization (GraphiCon’98) 196 – 203 . Keldysh Institute of Applied Mathematics
   Google Scholar
• Saux , E. and Daniel , M. 1999 . Data reduction of polygonal curves using B‐splines. . Computer‐Aided Design , 31 (8) : 507 – 515 .
   Google Scholar
• Sester , M. 2000 . Masstabsabhängige Darstellungen in digitalen räumlichen Datenbeständen, Habilitationsschrift, Institut fur Photogrammetrie, Universität Stuttgart
   Google Scholar
• Shea , K. S. and McMaster , R. B. 1989 . “ Cartographic generalization in a digital environment: when and how to generalize. ” . In The 9th International Symposium on Computer‐Assisted Cartography , 56 – 67 . Baltimore : ASPRS‐ASCM .
   Google Scholar
• Shi , W. and Cheung , C. 2006 . Performance evaluation of line simplification algorithms for vector generalization. . The Cartographic Journal , 43 (1) : 27 – 44 .
   Google Scholar
• Sklansky , J. and Gonzalez , V. 1980 . Fast polygonal approximation of digitized curves. . Pattern Recognition , 12 : 327 – 331 .
   Web of Science ®Google Scholar
• Steiniger , S. and Meier , S. 2004 . “ Snakes: a technique for line smoothing and displacement in map generalisation. ” . In Proceedings of the 7th ICA Workshop on Generalisation and Multiple Representation 41 pages. Available online at http://aci.ign.fr/leicester/paper/steiniger‐v2‐ICAworkshop.pdf
   Google Scholar
• Thapa , K. 1989 . “ Data compression and critical points detection using normalized symmetric scattered matrix. ” . In Proceedings of Auto Carto 9 , 78 – 89 . Baltimore : ASPRS‐ASCM .
   Google Scholar
• Toussaint , G. T. 1985 . “ On the complexity of approximating polygonal curves in the plane. ” . In Proceedings of the IASTED, International Symposium on Robotics and Automation 59 – 62 . (Lugano)
   Google Scholar
• Visvalingam , M. and Whyatt , J. 1990 . The Douglas‐Peucker algorithm for line simplification: reevaluation through visualization. . Computer Graphic Forum , 9 (3) : 213 – 228 .
   Google Scholar
• Wang , Z. and Müller , J. C. 1998 . Line generalization based on analysis of shape characteristics. . Cartography and Geographic Information Systems , 25 (1) : 3 – 15 .
   Google Scholar
• Weibel , R. and Dutton , G. 1999 . “ Generalising spatial data and dealing with multiple representations. ” . In Geographical Information Systems , Edited by: Longley , P. A , Goodchild , M. F , Maguire , D. J and Rhind , D. W . 125 – 155 . New York : Wiley .
   Google Scholar
• Williams , C. M. 1978 . An efficient algorithm for the piecewise linear approximation of planar curves. . Computer Graphics and Image Processing , 8 : 286 – 293 .
   Google Scholar