Summary
This chapter presents a methodology for automated cartographic data input, drawing and editing. This methodology is based on kinematic algorithms for point and line Delaunay triangulation and the Voronoi diagram. It allows one to automate some parts of the manual digitization process and the topological editing of maps that preserve map updates. The manual digitization process is replaced by computer assisted skeletonization using scanned paper maps. We are using the Delaunay triangulation and the Voronoi diagram in order to extract the skeletons that are guaranteed to be topologically correct. The features thus extracted as object centrelines can be stored as vector maps in a Geographic Information System after labelling and editing. This research work can also be used for updates from sources that are either paper copy maps or digital raster images. A prototype application that was developed as part of the research has been presented.
We also describe two reversible line-drawing methods for cartographic applications based on the kinetic (moving-point) Voronoi diagram. Our objectives were to optimize the user’s ability to draw and edit the map, rather than to produce the most efficient batch-oriented algorithm for large data sets, and all our algorithms are based on local operations (except for basic point location). Because the deletion of individual points or line segments is a necessary part of the manual editing process, incremental insertion and deletion is used. The original concept used here is that, as a curve (line) is the locus of a moving point, then segments are drawn by maintaining the topology of a single moving point (abbreviated as MP hereafter, or the “pen”) as it moves through the topological network (visualized as either the Voronoi diagram or Delaunay triangulation). This approach also has the interesting property that a “log file” of all operations may be preserved, allowing reversion to previous map states, or “dates”, as required.
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References
Amenta, N., Bern, M., Eppstein, D.: The crust and the β-skeleton: Combinatorial curve reconstruction. Graphical models and image processing: GMIP 60(2), 125–135 (1998)
Anton, F., Gold, C.: An iterative algorithm for the determination of Voronoi vertices in polygonal and non-polygonal domains. In: Proceedings of the Canadian Conference on Computational Geometry, Kingston, Canada, pp. 257–262 (1997)
Anton, F., Snoeyink, J., Gold, C.: An iterative algorithm for the determination of Voronoi vertices in polygonal and non-polygonal domains on the plane and the sphere. In: 14th European Workshop on Computational Geometry (1998)
Anton, F., Mioc, D., Fournier, A.: 2D image reconstruction using natural neighbour interpolation. The Visual Computer 17(3), 134–146 (2001)
Aurenhammer, F.: Voronoi diagramsa survey of a fundamental geometric data structure. ACM Computing Surveys (CSUR) 23(3), 345–405 (1991)
Bagli, S., Soille, P.: Morphological automatic extraction of coastline from pan-european landsat tm images. In: Proceedings of the Fifth International Symposium on GIS and Computer Cartography for Coastal Zone Management, vol. 3, pp. 58–59 (2003)
Bernard, T.M., Manzanera, A.: Improved low complexity fully parallel thinning algorithm. In: ICIAP 1999: Proceedings of the 10th International Conference on Image Analysis and Processing, p. 215. IEEE Computer Society, Washington (1999)
Bo, G., Delleplane, S., Laurentiis, R.D.: Coastline extraction in remotely sensed images by means of texture features analysis. In: Geoscience and Remote Sensing Symposium, IGARSS 2001, Sydney, NSW, Australia, vol. 3, pp. 1493–1495 (2001)
Borgefors, G.: Distance transformations in arbitrary dimensions. Computer Vision, Graphics, and Image Processing 27(3), 321–345 (1984)
Cheng, Y.: Mean shift, mode seeking, and clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(8), 790–799 (1995)
Comaniciu, D., Meer, P.: Robust analysis of feature spaces: color image segmentation. In: Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR 1997), pp. 750–755. IEEE Computer Society, Washington (1997)
Comaniciu, D., Meer, P.: Mean shift: A robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis Machine Intelligence 24(5), 603–619 (2002)
Devillers, O.: On deletion in Delaunay triangulations. In: Proceedings of the fifteenth annual symposium on Computational geometry, pp. 181–188 (1999)
Di, K., Wang, J., Ma, R., Li, R.: Automatic shoreline extraction from high-resolution ikonos satellite imagery. In: Proceeding of ASPRS 2003 Annual Conference, vol. 3., Anchorage, Alaska (2003)
Gabriel, K.R., Sokal, R.R.: A new statistical approach to geographic variation analysis. Systematic Zoology 18(3), 259–278 (1969)
Gold, C.: Spatial Data Structures: the Extension from One to Two Dimensions. LF Pau (ad.), Mapping and Spatial Modelling for Navigation, NATO ASI Series F 65, 11–39 (1990)
Gold, C.M.: Crust and anti-crust: A one-step boundary and skeleton extraction algorithm. In: Symposium on Computational Geometry, pp. 189–196. ACM Press, New York (1999)
Gold, C.M.: An object-based dynamic spatial data model, and its applications in the development of a user-friendly digitizing system. In: Proceedings of the Fifth International Symposium on Spatial Data Handling, Charleston, pp. 495–504 (1992)
Gold, C.M.: Three approaches to automated topology, and how computational geometry helps. In: Proceedings of the Sixth International Seminar on Spatial Data Handling, Edinburgh, Scotland, pp. 145–158 (1994)
Gold, C., Remmele, P., Roos, T.: Voronoi diagrams of line segments made easy. Proc. 7th Canad. Conf. Comput. Geom, pp. 223–228 (1995)
Gold, C., Charters, T., Ramsden, J.: Automated contour mapping using triangular element data structures and an interpolant over each irregular triangular domain. In: Proceedings of the 4th annual conference on Computer graphics and interactive techniques, pp. 170–175 (1977)
Gold, C.M., Snoeyink, J.: A one-step crust and skeleton extraction algorithm. Algorithmica 30(2), 144–163 (2001)
Gold, C.M., Thibault, D.: Map generalization by skeleton retraction. In: Proceedings of the 20th International Cartographic Conference (ICC), Beijing, China, pp. 2072–2081 (August 2001)
Gonzalez, R.C., Woods, R.E.: Digital Image Procesisng, 2nd edn. Prentice Hall, Englewood Cliffs (2002)
Green, P., Sibson, R.: Computing dirichlet tessellations in the plane. The Computer Journal 21(2), 168–173 (1977)
Guibas, L., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of voronoi diagrams. ACM Transactions on Graphics 4(2), 74–123 (1985)
Guibas, L.: Kinetic data structures: A state of the art report (1998)
Guibas, L., Mitchell, J., Roos, T.: Voronoi diagrams of moving points in the plane. 570, 113–125 (1992)
Held, M.: VRONI: An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments. Computational Geometry: Theory and Applications 18(2), 95–123 (2001)
Imai, T.: A Topology Oriented Algorithm for the Voronoi Diagram of Polygons. In: Proceedings of the 8th Canadian Conference on Computational Geometry table of contents, pp. 107–112 (1996)
Jones, C., Bundy, G., Ware, J.: Map generalization with a triangulated data structure. CARTOGR GEOGRAPH INF SYST. 22(4), 317–331 (1995)
Jones, C., Ware, J.: Proximity Search with a Triangulated Spatial Model. The Computer Journal 41(2), 71 (1998)
Karavelas, M.: A robust and efficient implementation for the segment Voronoi diagram. In: International Symposium on Voronoi Diagrams in Science and Engineering (VD 2004), pp. 51–62 (2004)
Kasturi, R., Fernandez, R., Amlani, M.L., chun Feng, W.: Map data processing in geographic information systems. Computer 22(12), 10–21 (1989)
Lee, K.H., Cho, S.B., Choy, Y.C.: A knowledge-based automated vectorizing system for geographic information system. In: ICPR 1998: Proceedings of the 14th International Conference on Pattern Recognition, vol. 2, p. 1546. IEEE Computer Society, Washington (1998)
Liu, H., Jezek, K.C.: A complete high-resolution coastline of antarctica extracted from orthorectified radarsat sar imagery. Photogrammetric Engineering and Remote Sensing 70(5), 605–616 (2004)
Mioc, D., Anton, F., Gold, C., Moulin, B.: Spatio-temporal change representation and map updates in a dynamic Voronoi data structure. In: Proceedings of the Eight International Symposium on Spatial Data Handling, Vancouver, Canada, pp. 441–452 (1998)
Mioc, D., Anton, F., Gold, C., Moulin, B.: Time Travel. Visualization in a Dynamic Voronoi Data Structure. Cartography and Geographic Information Science 26(2) (1999)
Mostafavi, M., Gold, C., Dakowicz, M.: Dynamic Voronoi/Delaunay Methods and Applications. Computers and Geosciences 29(4), 523–530 (2003)
Mioc, D., Anton, F., Gold, C.M., Moulin, B.: Map updates in a dynamic Voronoi data structure. In: ISVD, pp. 264–269 (2006)
Ogniewicz, R.L.: Skeleton-space: A multiscale shape description combining region and boundary information. In: Proceedings of Computer Vision and Pattern Recognition 1994, pp. 746–751 (1994)
Ogniewicz, R.L., Kübler, O.: Hierarchic Voronoi skeletons. Pattern Recognition 28(3), 343–359 (1995)
Ogniewicz, R.: Automatic medial axis pruning by mapping characteristics of boundaries evolving under the euclidean geometric heat flow onto Voronoi skeletons. Technical Report 95-4, Harvard Robotics Laboratory (1995)
Okabe, A., Boots, B., Sugihara, K.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. Wiley & Sons, Chichester (1992)
Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial tessellations: concepts and applications of Voronoi diagrams, 2nd edn. John Wiley & Sons Ltd, Chichester (2000)
Paul Chew, L.: Constrained delaunay triangulations. Algorithmica 4(1), 97–108 (1989)
Quek, F.K.H., Petro, M.C.: Human-machine perceptual cooperation. In: CHI 1993: Proceedings of the SIGCHI conference on Human factors in computing systems, pp. 123–130. ACM Press, New York (1993)
Rognant, L., Chassery, J.M., Goze, S., Planès, J.G.: The delaunay constrained triangulation: The delaunay stable algorithms. In: IV, pp. 147–152 (1999)
Roos, T.: Voronoi diagrams over dynamic scenes. Discrete Appl. Math. 43(3), 243–259 (1993)
Shewchuk, J.R.: Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In: Lin, M.C., Manocha, D. (eds.) FCRC-WS 1996 and WACG 1996. LNCS, vol. 1148, pp. 203–222. Springer, Heidelberg (1996)
Shewchuk, J.R.: Adaptive precision floating-point arithmetic and fast robust geometric predicates. In: Discrete and Computational Geometry, vol. 18, pp. 305–363 (1997)
Sonka, M., Hlavac, V., Boyle, R.: Image Processing, Analysis, and Machine Vision. PWS publishing (1999)
Sugihara, K., Iri, M., Inagaki, H., Imai, T.: Topology-Oriented Implementation–An Approach to Robust Geometric Algorithms. Algorithmica 27(1), 5–20 (2000)
Ware, J., Jones, C.: Conflict Reduction in Map Generalization Using Iterative Improvement. GeoInformatica 2(4), 383–407 (1998)
Yang, W., Gold, C.: Dynamic spatial object condensation based on the Voronoi diagram. In: Proceedings, Fourth International Symposium of LIESMARS, vol. 95, pp. 134–145 (1995)
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Gold, C.M., Mioc, D., Anton, F., Sharma, O., Dakowicz, M. (2009). A Methodology for Automated Cartographic Data Input, Drawing and Editing Using Kinetic Delaunay/Voronoi Diagrams. In: Gavrilova, M.L. (eds) Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence. Studies in Computational Intelligence, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85126-4_7
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