Summary
This chapter surveys existing research and main achievements of simulated annealing and genetic algorithms for triangulation based problems, such as generation of an optimal triangulation, improvement of a shape of triangles or tetrahedra and positions of their vertices, the use of triangulations for digital image representation, registration of 3D models and their textures, etc. Main features of the methods, their results and typical problems are pointed out.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Acikgoz, N., Bottaso, C.L.: Metric-driven mesh optimization using a local simulated annealing algorithm. International Journal for Numerical Methods in Engineering 71, 201–223 (2007)
Bartánus, M., Ferko, A., Mag, R., Niepel, L., Plachetka, T., Sikudová, E.: New heuristics for minimum weight triangulation. In: Proceedings from the 4th International Conference in Central Europe on Computer Graphics and Visualization 1996, pp. 31–40. University of West Bohemia, Pilsen (1996)
Bærentzen J.A.: Optimizing 3D triangulations to recapture sharp edges. IMM-Technical Report-2006-11 (2006)
Bobáková, G., Ferko, A., Niepel, L.: On minimum weight triangulation. In: Proceedings of the 10th International Conference Spring School of Computer Graphics, Bratislava, pp. 226–232 (1994)
Bottaso, C.L.: Anisotropic mesh adaptation by metric-driven optimization. International Journal for Numerical Methods in Engineering 60, 597–639 (2004)
Bremer, P.T., Hamann, B., Kreylos, O., Wolter, F.E.: Simplification of closed triangulated surfaces using simulated annealing. In: Lynch, T., Schumaker, L.L. (eds.) Mathematical methods in CAGD, pp. 1–8 (2001)
Capp, C., Julstrom, B.A.: A weight-coded genetic algorithm for the minimum weight triangulation problem. In: Proceedings of the 1998 ACM Symposium on Applied Computing, pp. 327–331. New York (1998)
Cazals, F., Giesen, J.: Delaunay Triangulation Based Surface Reconstruction. In: Boissonnat, J.-D., Teillaud, M. (eds.) Effective Computational Geometry for Curves and Surfaces, pp. 231–276. Springer, Heidelberg (2006)
Chen, K.C., Hsieh, I., Wang, C.A.: A genetic algorithm for minimum tetrahedralization of a convex polyhedron. In: Proceedings of the Canadian conference on computational geometry, Halifax, Nova Scotia, pp. 1–5 (2003)
Chen, Y.H., Wang, Y.Z.: Genetic algorithms for optimized re-triangulation in the context of reverse engineering. Computer-Aided Design 31, 261–271 (1999)
Chetverikov, D., Stepanov, D., Krsek, P.: Robust Euclidean alignment of 3D point sets: the Trimmed Iterative Closest Point algorithm. Image and Vision Computing 23, 299–309 (2005)
Chetverikov, D., Jankó, Z., Lomonosov, E., Ekárt, A.: Creating photorealistic models by data fusion with genetic algorithms. In: A chapter of the edited volume Soft Computing in Image Processing: Recent Advances. Studies in Fuzziness and Soft Computing, vol. 210, pp. 239–266. Springer, Heidelberg (2007)
Cignoni, P., Montani, C., Scopigno, R.: A merge-first divide & conquer algorithm for Ed Delaunay triangulations, Internal Rep. C92/16, CNUCE/CNR, Pisa, Italy (1992)
Cooper, O., Campbell, N., Gibson, D.: Automatic augmentation and meshing of sparse 3D scene structure. In: Proceedings of the 7th IEEE workshop on applications of computer vision, pp. 287–293, Breckenridge (2005)
Eppstein, D., Paterson, M.S., Yao, F.: On nearest-neighbor graphs. Discrete and Computational Geometry 17(3), 263–282 (1997)
Goffe, W.L., Ferrier, G.D., Rogers, J.: Global optimization of statistical functions with simulated annealing. Journal of Econometrics 60, 65–100 (1994)
Goldberg, P.D.: Genetic algorithms in search, optimization and machine learning. Addison-Wesley Pub., Reading (1989)
Holder, M., Karr, C.L.: Quadrilateral mesh smoothing using a steady state genetic algorithm. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 2400–2401. Springer, Heidelberg (2003)
Jankó, Z., Chetverikov, D., Ekárt, A.: Using genetic algorithms in computer vision: Registering images to 3D surface model. Acta Cybernetica 18, 193–212 (2007)
Kallman, M.: Path planning in triangulations. In: Proceedings of the Workshop on Reasoning, Representation and Learning in Computer Games. In: International Joint Conference on Artficial Intelligence (IJCAI), Edinburg, Scotland, pp. 49–54 (2005)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.O.: Optimization by simulated annealing. Science 220, 671–680 (1983)
Kolingerová, I.: Genetic optimization of the triangulation weight. In: Proceedings of the 2nd international conference Computer Graphics and Artificial Intelligence, Limoges, pp. 23–34 (1998)
Kolingerová, I.: Genetic approach to triangulations. In: Proceedings of the 4th international conference Computer graphics and artificial intelligence, Limoges, pp. 11–23 (2000)
Kolingerová, I.: Probabilistic methods for triangulated models. In: Proceedings of the 8th international conference on Computer Graphics and Artificial Intelligence, Limoges, pp. 93–106 (2005)
Kolingerová, I., Ferko, A.: Multicriteria-optimized triangulations. The Visual Computer 17, 380–395 (2001)
Kreylos, O., Hamann, B.: On simulated annealing and the construction of linear spline approximations for scattered data. IEEE Transactions on Visualization and Computer Graphics 7, 17–31 (2001)
Lawson, C.L.: Software for C 1 Surface interpolation. In: Price, J.R. (ed.) Mathematical Sofware III, pp. 161–194. Academic Press, New York (2007)
Lehner, B., Umlauf, G., Hamann, B.: Image compression using data-dependent triangulations. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Paragios, N., Tanveer, S.-M., Ju, T., Liu, Z., Coquillart, S., Cruz-Neira, C., Müller, T., Malzbender, T. (eds.) ISVC 2007, Part I. LNCS, vol. 4841, pp. 351–362. Springer, Heidelberg (2007)
Lomonosov, E., Chetverikov, D., Ekárt, A.: Pre-registration of arbitrarily oriented 3D surfaces using a genetic algorithm, Pattern Recognition Letters. Special Issue on Evolutionary Computer Vision and Image Understanding 27, 1201–1208 (2006)
Mallampati, D.R., Mutalik, P.P., Wainwright, R.L.: A parallel multi-phase implementation of simulated annealing for the travelling salesman problem. In: Proceedings of the 6th Distributed memory computing conference, pp. 488–491 (1991)
Manacher, K., Zobrist, A.L.: Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation. Information Processing Letters 9(1), 31–34 (1979)
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculation by fast computing machines. J. Chem. Phys. 21, 1087 (1953)
Michalewitz, Z.: Genetic algorithms + data structures = Evolution programs. Springer, Heidelberg (1996)
Morris, D., Kanade, T.: Image-consistent surface triangulation, In: Proceedings of the IEEE conference on computer vision and pattern recognition, vol.1, pp. 332–338 (2000)
Mulzer, W., Rote, G.: Minimum Weight Trianglation is NP-hard. In: Proceedings of the 22nd Annual Symposium on Computational Geometry, Sedona, Association for Computing Machinery, pp. 1–10 (2006)
Mutalik, P.P., Knight, L.R., Blanton, J.L., Wainwright, R.L.: Solving combinatorial optimization problems using parallel simulated annealing and parallel genetic algorithms. In: Proceedings of the 1992 ACM/SIGAPP symposium on Applied computing: technological challenges of the 1990, pp. 1031–1038 (1992)
Prestifilippo, G., Sprave, J.: Optimal triangulation by means of evolutionary algorithms. In: Genetic Algorithms in Engineering Systems: Innovations and Applications, GALESIA 1997, pp. 492–497 (1997)
Rila, L., Constantinides, A.G.: Image coding using data-dependent triangulation. In: Digital Signal Processing Proceedings, vol.2, pp. 531–534 (1997)
Renner, G., Ekárt, A.: Genetic algorithms in computer aided design. Computer-Aided Design 35, 709–726 (2003)
Schumaker, L.L.: Computing optimal triangulations using simulated annealing. Computer Aided Geometric Design 10, 329–345 (1993)
Sen, S., Zheng, S.: Near-optimal triangulation of a point set by simulated annealing. In: Symposium on Applied Computing, pp. 1000–1008 (1992)
Seneviratne, L.D., Ko, W.-S., Earles, S.W.E.: Triangulation-based path planning for a mobile robot. In: Journal Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Professional Engineering Publishing, vol. 211(5), pp. 365–371 (1997)
Shikhare, D., Gopalsamy, S., Modur, S.P.: A two phase technique for optimal tessellation of complex geometric models. In: 8th International conference on engineering computer graphics and descriptive geometry (1998)
Toussaint, G.T.: The relative neighbourhood graph of a finite planar set. Pattern Recognition 12, 261–268 (1980)
Vigo, M., Pla, N., Cotrina, J.: Regular triangulations of dynamic sets of points. Computer Aided Geometric Design 19(2), 127–149 (2002)
Wagner, T., Michelitsch, T., Sacharow, A.: On the design of optimisers for surface reconstruction. In: Genetic and Evolutionary Commputation Conference (GECCO 2007), pp. 2195–2202 (2007)
Weinert, K.: Optimal surface reconstruction from digitized point data using CI methods. Technical Report CI5 /97, SFB 531, University of Dortmund (1997)
Wu, Y., Wainwright, R.L.: Near-optimal triangulation of a point set using genetic algorithms. In: Proceedings of the 7th Oklahoma symposium on AI, pp. 122–131 (1993)
Yu, X., Morse, B.S., Sederberg, T.W.: Image Reconstruction Using Data-Dependent Triangulation. IEEE Computer Graphics and Applications 21(3), 62–68 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kolingerová, I. (2009). Simulated Annealing and Genetic Algorithms in Quest of Optimal Triangulations. 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_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-85126-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85125-7
Online ISBN: 978-3-540-85126-4
eBook Packages: EngineeringEngineering (R0)