Abstract
The correct connection of the topological relationships between critical points (or lines) is the basis of the earth’s surface description, terrain topological simplification, or geomorphic generalization of relief. However, the intersection of valley and ridge line at regular points often occurs in the existing algorithms of constructing terrain Morse complexes. In this paper, a novel universal algorithm of the constrained construction for terrain Morse complexes is presented. In our approach, the separatrix of descending (or ascending) Morse complex is regarded as the constrained boundary of extracting the separatrix of the dual Morse complex, and the terrain feature line starting from end (or start) saddle coincides exactly with the “macro-saddle line”. As a result, the intersections are prevented absolutely and the macro-saddles can be identified to achieve complete decomposition of the whole terrain surface. In the end, an experiment is done to validate the correctness and feasibility of this algorithm.
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References
Bajaj, C.L., Shikore, D.R.: Topology Preserving Data Simplification with Error Bounds. Computers and Graphics 22(1), 3–12 (1998)
Bremer, P.T., Edelsbrunner, H., Hamann, B., Pascucci, V.: A Multi-resolution Data Structure for Two-dimensional Morse Functions. In: Turk, G., van Wijk, J., Moorhead, R. (eds.) Proceedings of the IEEE Visualization 2003, pp. 139–146. IEEE Computer Society (2003)
Bieniek, A., Moga, A.: A Connected Component Approach to the Watershed Segmentation. In: Mathematical Morphology and its Application to Image and Signal Processing, pp. 215–222. Kluwer Acad. Publ., Dordrecht (1998)
Bremer, P.: Topology-based Multi-resolution Hierarchies, PhD. University of California (2004)
Čomić, L., De Floriani, L., Papaleo, L.: Morse-Smale Decompositions for Modeling Terrain Knowledge. In: Cohn, A.G., Mark, D.M. (eds.) COSIT 2005. LNCS, vol. 3693, pp. 426–444. Springer, Heidelberg (2005)
Danovaro, E., De Floriani, L., Mesmoudi, M.M.: Topological Analysis and Characterization of Discrete Scalar Fields. In: Asano, T., Klette, R., Ronse, C. (eds.) Geometry, Morphology, and Computational Imaging. LNCS, vol. 2616, pp. 386–402. Springer, Heidelberg (2003)
Danovaro, E., De Floriani, L., Papaleo, L., Vitali, M.: Multi-resolution Morse-Smale Complexes for representing terrain morphology. In: Proceedings of the 15th Annual ACM International Symposium on Advances in Geographic Information Systems, Seattle, Washington, Article No: 29 (2007)
De Floriani, L., Magillo, P., Vitali, M.: Modeling and Generalization of Discrete Morse Terrain Decompositions. In: 20th International Conference on Pattern Recognition, Istanbul, Turkey, pp. 999–1002 (2010)
Edelsbrunner, H., Harer, J., Zomorodian, A.: Hierarchical Morse Complexes for Piecewise Linear 2-manifolds. In: Proceedings 17th ACM Symposium on Computational Geometry, pp. 70–79. ACM Press (2001)
Magillo, P., Danovaro, E., De Floriani, L., Papaleo, L., Vitali, M.: A Discrete Approach to Compute Terrain Morphology. Computer Vision and Computer Graphics. Theory and Applications 21, 13–26 (2009)
Milnor, J.: Morse Theory. Princeton Univ. Press (1963)
Pascucci, V.: Topology Diagrams of Scalar Fields in Scientific Visualization. In: Rana, S. (ed.) Topological Data Structures for Surfaces, pp. 121–129. John Wiley and Sons Ltd. (2004)
Pfaltz, J.L.: Surface Networks. Geographical Analysis 8, 77–93 (1976)
Stoer, S.L., Strasser, W.: Extracting Regions of Interest Applying A Local Watershed Transformation. In: Proc. IEEE Visualization 2000, pp. 21–28. IEEE Computer Society (2000)
Schneider, B.: Extraction of Hierarchical Surface Networks from Bilinear Surface Patches. Geographical Analysis 37, 244–263 (2005)
Schneider, B., Wood, J.: Construction of Metric Surface Networks from Raster-based DEMs. In: Rana, S. (ed.) Topological Data Structures for Surfaces. John Wiley and Sons Ltd., Chichester (2004)
Smale, S.: Morse Inequalities for a Dynamical System. Bulletin of American Mathematical Society 66, 43–49 (1960)
Takahashi, S., Ikeda, T., Kunii, T.L., Ueda, M.: Algorithms for Extracting Correct Critical Points and Constructing Topological Graphs from Discrete Geographic Elevation Data. Computer Graphics Forum 14(3), 181–192 (1995)
Vitali, M., Floriani, L.D., Magillo, P.: Analysis and Comparison of Algorithms for Morse Decompositions on Triangulated Terrains. Technical report DISI-TR-12-03. DISI, University of Genova (2012)
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Wang, H., Zhao, X., Zhang, C., Xiong, T. (2013). An Algorithm of the Constrained Construction for Terrain Morse Complexes. In: Bian, F., Xie, Y., Cui, X., Zeng, Y. (eds) Geo-Informatics in Resource Management and Sustainable Ecosystem. GRMSE 2013. Communications in Computer and Information Science, vol 399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41908-9_20
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DOI: https://doi.org/10.1007/978-3-642-41908-9_20
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