Abstract
Stationary points of multivariable function which represents some surface have an important role in many application such as computer vision, chemical physics, etc. Nevertheless, the dataset describing the surface for which a sampling function is not known is often given. Therefore, it is necessary to propose an approach for finding the stationary points without knowledge of the sampling function.
In this paper, an algorithm for determining a set of stationary points of given sampled surface and detecting the bindings between these stationary points (such as stationary points lie on line segment, circle, etc.) is presented. Our approach is based on the piecewise RBF interpolation of the given dataset.
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Banerjee, A., Adams, N., Simons, J., Shepard, R.: Search for stationary points on surfaces. J. Phys. Chem. 89(1), 52–57 (1985)
Tsai, C.J., Jordan, K.D.: Use of an eigenmode method to locate the stationary points on the potential energy surfaces of selected argon and water clusters. J. Phys. Chem. 97(43), 11227–11237 (1993)
Comaniciu, D., Meer, P.: Mean shift: a robust approach toward feature space analysis. IEEE Trans. Pattern Anal. Mach. Intell. 24, 603–619 (2002)
Strodel, B., Wales, D.J.: Free energy surfaces from an extended harmonic superposition approach and kinetics for alanine dipeptide. Chem. Phys. Lett. 466(4), 105–115 (2008)
Liu, Y., Burger, S.K., Ayers, P.W.: Newton trajectories for finding stationary points on molecular potential energy surfaces. J. Math. Chem. 49(9), 1915–1927 (2011)
Majdisova, Z., Skala, V.: Radial basis function approximations: comparison and applications. Appl. Math. Model. 51, 728–743 (2017)
Majdisova, Z., Skala, V.: Big geo data surface approximation using radial basis functions: a comparative study. Comput. Geosci. 109, 51–58 (2017)
Skala, V.: RBF interpolation with CSRBF of large data sets. Procedia Comput. Sci. 108, 2433–2437 (2017). International Conference on Computational Science, ICCS 2017, 12–14 June 2017, Zurich, Switzerland
Smolik, M., Skala, V.: Large scattered data interpolation with radial basis functions and space subdivision. Integr. Comput.-Aided Eng. 25(1), 49–62 (2018)
Bhatia, H., Gyulassy, A., Wang, H., Bremer, P.T., Pascucci, V.: Robust detection of singularities in vector fields. In: Topological Methods in Data Analysis and Visualization III, pp. 3–18. Springer (2014)
Wang, W., Wang, W., Li, S.: Detection and classification of critical points in piecewise linear vector fields. J. Vis. 21, 147–161 (2018)
Franke, R.: A critical comparison of some methods for interpolation of scattered data. Technical report NPS53-79-003, Naval Postgraduate School, Monterey, CA (1979)
Acknowledgments
The authors would like to thank their colleagues at the University of West Bohemia, Plzeň, for their discussions and suggestions, and the anonymous reviewers for their valuable comments. Special thanks belong to Jan Dvorak, Lukas Hruda and Martin Červenka for their independent experiments and valuable comments. The research was supported by the Czech Science Foundation GAČR project GA17-05534S and partially supported by the SGS 2016-013 project.
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Majdisova, Z., Skala, V., Smolik, M. (2019). Determination of Stationary Points and Their Bindings in Dataset Using RBF Methods. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds) Computational and Statistical Methods in Intelligent Systems. CoMeSySo 2018. Advances in Intelligent Systems and Computing, vol 859. Springer, Cham. https://doi.org/10.1007/978-3-030-00211-4_20
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DOI: https://doi.org/10.1007/978-3-030-00211-4_20
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