Abstract
The triangulation is a process by which the 3D point position can be calculated from two images where that point is visible. This process requires the intersection of two known lines in the space. However, in the presence of noise this intersection does not occur, then it is necessary to estimate the best approximation. One option towards achieving this goal is the usage of evolutionary algorithms. In general, evolutionary algorithms are very robust optimization techniques, however in some cases, they could have some troubles finding the global optimum getting trapped in a local optimum. To overcome this situation some authors suggested removing the local optima in the search space by means of a single-objective problem to a multi-objective transformation. This process is called multi-objectivization. In this paper we successfully apply this multi-objectivization to the triangulation problem.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Jebara, T., Azarbayejani, A., Pentland, A.: 3D Structure from 2D Motion. IEEE Signal Processing Magazine 6(3), 66–84 (1999)
Hartley, R.I., Zisserman, A. (eds.): Multiple View Geometry in Computer Vision, ISBN: 0521540518, 2nd edn. Cambridge University Press, Cambridge (2004)
Knowles, J.D., Watson, R.A., Corne, D.W.: Reducing Local Optima in Single-Objective Problems by Multi-Objectivization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 269–283. Springer-Verlag, Berlin Heidelberg New York (2001)
Jensen, M.T.: Guiding Single-Objective Optimization Using Multi-objective Methods. In: Raidl, G.R., Cagnoni, S., Cardalda, J.J.R., Corne, D.W., Gottlieb, J., Guillot, A., Hart, E., Johnson, C.G., Marchiori, E., Meyer, J.-A., Middendorf, M. (eds.) EvoIASP 2003, EvoWorkshops 2003, EvoSTIM 2003, EvoROB/EvoRobot 2003, EvoCOP 2003, EvoBIO 2003, and EvoMUSART 2003. LNCS, vol. 2611, pp. 199–210. Springer, Berlin Heidelberg New York (2003)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Hartley, R., Sturm, P.: Triangulation. Computer Vision and Image Understanding 68(2), 146–157 (1997)
Beardsley, P.A., Zisserman, A., Murray, D.W.: Navigation Using Affine Structure and Motion. In: Eklundh, J.-O. (ed.) ECCV 1994. LNCS, vol. 800, pp. 85–96. Springer-Verlag, Berlin Heidelberg New York (1994)
Beardsley, P.A., Zisserman, A., Murray, D.W.: Sequential Updating of Projective and Affine Structure from Motion. International Journal of Computer Vision 23(3), 235–259 (1997)
Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer, Berlin Heidelberg New York (2003)
Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann Publishers, San Mateo, CA (2001)
Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J.: PESA-II: Region-Based Selection in Evolutionary Multiobjective Optimization. In: Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), 7-11, pp. 283–290. Morgan Kaufmann, San Francisco, California, USA (2001)
Deb, K., Mohan, M., Mishra, S.: Evaluating the Epsilon-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions. Evolutionary Computation 13(4), 501–525 (2005)
Santana-Quintero, L.V., Coello, C.A.C.: An Algorithm Based on Differential Evolution for Multi-Objective Problems. International Journal of Computational Intelligence Research 1(2), 151–169 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vite-Silva, I., Cruz-Cortés, N., Toscano-Pulido, G., de la Fraga, L.G. (2007). Optimal Triangulation in 3D Computer Vision Using a Multi-objective Evolutionary Algorithm. In: Giacobini, M. (eds) Applications of Evolutionary Computing. EvoWorkshops 2007. Lecture Notes in Computer Science, vol 4448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71805-5_36
Download citation
DOI: https://doi.org/10.1007/978-3-540-71805-5_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71804-8
Online ISBN: 978-3-540-71805-5
eBook Packages: Computer ScienceComputer Science (R0)