A Radial Basis Function Approximation for Large Datasets

Zuzana Majdisova
Department of Computer Science and Engineering, Faculty of Applied Sciences, University of West Bohemia, Czech Republic

Vaclav Skala
Department of Computer Science and Engineering, Faculty of Applied Sciences, University of West Bohemia, Czech Republic

Ladda ner artikel

Ingår i: Proceedings of SIGRAD 2016, May 23rd and 24th, Visby, Sweden

Linköping Electronic Conference Proceedings 127:2, s. 9-14

Visa mer +

Publicerad: 2016-05-30

ISBN: 978-91-7685-731-1

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is based on a distance between two points. This method leads to a solution of overdetermined linear system of equations. In this paper a new approach to the RBF approximation of large datasets is introduced and experimental results for different real datasets and different RBFs are presented with respect to the accuracy of computation. The proposed approach uses symmetry of matrix and partitioning matrix into blocks.


Radial basis function RBF approximation LiDAR data


[CBC*01] CARR J. C., BEATSON R. K., CHERRIE J. B., MITCHELL T. J., FRIGHT W. R., MCCALLUM B. C., EVANS T. R.: Reconstruction and representation of 3d objects with radial basis functions. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2001, Los Angeles, California, USA, August 12-17, 2001 (2001), pp. 67–76. 1

[Dar00] DARVE E.: The fast multipole method: Numerical implementation. Journal of Computational Physics 160, 1 (2000), 195–240. 1

[Fas07] FASSHAUER G. E.: Meshfree Approximation Methods with MATLAB, vol. 6. World Scientific Publishing Co., Inc., River Edge, NJ, USA, 2007. 2

[Har71] HARDY R. L.: Multiquadratic Equations of Topography and Other Irregular Surfaces. Journal of Geophysical Research 76 (1971), 1905–1915. 1

[HSfY15] HON Y.-C., SARLER B., FANG YUN D.: Local radial basis function collocation method for solving thermo-driven fluid-flow problems with free surface. Engineering Analysis with Boundary Elements 57 (2015), 2 – 8. {RBF} Collocation Methods. 1

[LCC13] LI M., CHEN W., CHEN C.: The localized {RBFs} collocation methods for solving high dimensional {PDEs}. Engineering Analysis with Boundary Elements 37, 10 (2013), 1300 – 1304. 1

[PRF14] PEPPER D. W., RASMUSSEN C., FYDA D.: A meshless method using global radial basis functions for creating 3-d wind fields from sparse meteorological data. Computer Assisted Methods in Engineering and Science 21, 3-4 (2014), 233–243. 1

[PS11] PAN R., SKALA V.: A two-level approach to implicit surface modeling with compactly supported radial basis functions. Eng. Comput. (Lond.) 27, 3 2011), 299–307. 1

[Ska13] SKALA V.: Fast Interpolation and Approximation of Scattered Multidimensional and Dynamic Data Using Radial Basis Functions. WSEAS Transactions on Mathematics 12, 5 (2013), 501–511. 2

[Ska15] SKALA V.: Meshless interpolations for computer graphics, visualization and games. In Eurographics 2015 - Tutorials, Zurich, Switzerland, May 4-8, 2015 (2015), Zwicker M., Soler C., (Eds.), Eurographics Association. 1, 2

[SPN13] SKALA V., PAN R., NEDVED O.: Simple 3d surface reconstruction using flatbed scanner and 3d print. In SIGGRAPH Asia 2013, Hong Kong, China, November 19-22, 2013, Poster Proceedings (2013), ACM, p. 7. 1

[SPN14] SKALA V., PAN R., NEDVED O.: Making 3d replicas using a flatbed scanner and a 3d printer. In Computational Science and Its Applications - ICCSA 2014 - 14th International Conference, Guimarães, Portugal, June 30 - July 3, 2014, Proceedings, Part VI (2014), vol. 8584 of Lecture Notes in Computer Science, Springer, pp. 76–86. 1

[TO02] TURK G., O’BRIEN J. F.: Modelling with implicit surfaces that interpolate. ACM Trans. Graph. 21, 4 (2002), 855–873. 1

[Wen06] WENDLAND H.: Computational aspects of radial basis function approximation. Studies in Computational Mathematics 12 (2006), 231–256. 1

Citeringar i Crossref