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Performance Evaluation of GPU-Accelerated Spatial Interpolation Using Radial Basis Functions for Building Explicit Surfaces

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Abstract

This paper focuses on evaluating the computational performance of parallel spatial interpolation with Radial Basis Functions (RBFs) that is developed by utilizing modern GPUs. The RBFs can be used in spatial interpolation to build explicit surfaces such as Discrete Elevation Models. When interpolating with large-size of data points and interpolated points for building explicit surfaces, the computational cost would be quite expensive. To improve the computational efficiency, we specifically develop a parallel RBF spatial interpolation algorithm on many-core GPUs, and compare it with the parallel version implemented on multi-core CPUs. Five groups of experimental tests are conducted on two machines to evaluate the computational efficiency of the presented GPU-accelerated RBF spatial interpolation algorithm. Experimental results indicate that: in most cases, the parallel RBF interpolation algorithm on many-core GPUs does not have any significant advantages over the parallel version on multi-core CPUs in terms of computational efficiency. This unsatisfied performance of the GPU-accelerated RBF interpolation algorithm is due to: (1) the limited size of global memory residing on the GPU, and (2) the need to solve a system of linear equations in each GPU thread to calculate the weights and prediction value of each interpolated point.

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References

  1. Barlas, G.: Chapter 7–The Thrust Template Library, pp. 527–573. Morgan Kaufmann, Boston (2015). https://doi.org/10.1016/B978-0-12-417137-4.00007-1

    Chapter  Google Scholar 

  2. Bell, N., Hoberock, J., Rodrigues, C.: Chapter 16—Thrust: A Productivity-Oriented Library for CUDA, pp. 339–358. Morgan Kaufmann, Boston (2013). https://doi.org/10.1016/B978-0-12-415992-1.00016-X

    Chapter  Google Scholar 

  3. Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C., Evans, T.R., Acm, Acm: Reconstruction and representation of 3D objects with radial basis functions. In: Computer Graphics. Assoc Computing Machinery, New York, pp. 67–76. (2001). https://doi.org/10.1145/383259.383266

  4. Chianese, A., Piccialli, F.: Smach: A framework for smart cultural heritage spaces. In: 10th International Conference on Signal-image Technology and Internet-Based Systems Sitis 2014, pp. 477–484. IEEE, 345 E 47TH ST, New York, NY 10017 USA (2014). https://doi.org/10.1109/SITIS.2014.16

  5. Cuomo, S., De Michele, P., Piccialli, F.: 3D data denoising via nonlocal means filter by using parallel GPU strategies. Comput. Math. Methods Med. (2014). https://doi.org/10.1155/2014/523862

    Article  Google Scholar 

  6. Cuomo, S., De Michele, P., Piccialli, F., Farina, R.: A smart GPU implementation of an elliptic kernel for an ocean global circulation model. Appl. Math. Sci. 7, 3007–3021 (2013). https://doi.org/10.12988/ams.2013.13266

    Article  Google Scholar 

  7. Cuomo, S., De Michele, P., Piccialli, F., Galletti, A., Jung, J.E.: IoT-based collaborative reputation system for associating visitors and artworks in a cultural scenario. Expert Syst. Appl. 79, 101–111 (2017). https://doi.org/10.1016/j.eswa.2017.02.034

    Article  Google Scholar 

  8. Cuomo, S., Galletti, A., Giunta, G., Marcellino, L.: Reconstruction of implicit curves and surfaces via RBF interpolation. Appl. Numer. Math. 116, 157–171 (2017). https://doi.org/10.1016/j.apnum.2016.10.016

    Article  MathSciNet  MATH  Google Scholar 

  9. Cuomo, S., Galletti, A., Giunta, G., Starace, A.: Surface reconstruction from scattered point via RBF interpolation on GPU. In: Federated Conference on Computer Science and Information Systems, pp. 433–440. IEEE, New York (2013). https://doi.org/10.1145/383259.383266

  10. D’Amore, L., Casaburi, D., Marcellino, L., Murli, A.: Numerical solution of diffusion models in biomedical imaging on multicore processors. Int. J. Biomed. Imaging 2011, 680, 765 (2011). https://doi.org/10.1155/2011/680765

    Article  Google Scholar 

  11. D’Amore, L., Marcellino, L., Mele, V., Romano, D.: Deconvolution of 3d fluorescence microscopy images using graphics processing units. In: Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science, vol. 7203, pp. 690–699. Springer-Verlag Berlin, Heidelberger Platz 3, D-14197 Berlin, Germany (2012). https://doi.org/10.1007/978-3-642-31464-3_70

    Chapter  Google Scholar 

  12. Franke, R.: Scattered data interpolation—tests of some methods. Math. Comput. 38(157), 181–200 (1982). https://doi.org/10.2307/2007474

    Article  MathSciNet  MATH  Google Scholar 

  13. Hardy, R.L.: Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res. 76(8), 1905–1915 (1971). https://doi.org/10.1029/JB076i008p01905

    Article  Google Scholar 

  14. Hillier, M.J., Schetselaar, E.M., de Kemp, E.A., Perron, G.: Three-dimensional modelling of geological surfaces using generalized interpolation with radial basis functions. Math. Geosci. 46(8), 931–953 (2014). https://doi.org/10.1007/s11004-014-9540-3

    Article  MathSciNet  MATH  Google Scholar 

  15. Hoberock, J., Bell, N.: Thrust library (2017). http://thrust.github.io/

  16. Huang, F., Bu, S.S., Tao, J., Tan, X.C.: OpenCL implementation of a parallel universal kriging algorithm for massive spatial data interpolation on heterogeneous systems. ISPRS Int. J. Geo-Inf. 5(6), 22 (2016). https://doi.org/10.3390/ijgi5060096

    Article  Google Scholar 

  17. Huang, F., Liu, D.S., Tan, X.C., Wang, J.A., Chen, Y.P., He, B.B.: Explorations of the implementation of a parallel IDW interpolation algorithm in a Linux cluster-based parallel GIS. Comput. Geosci. 37(4), 426–434 (2011). https://doi.org/10.1016/j.cageo.2010.05.024

    Article  Google Scholar 

  18. Izquierdo, D., de Silanes, M.C.L., Parra, M.C., Torrens, J.J.: CS-RBF interpolation of surfaces with vertical faults from scattered data. In: 4th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources—PART II, Mathematics and Computers in Simulation 102, 11–23 (2014). https://doi.org/10.1016/j.matcom.2013.05.015

    Article  MathSciNet  Google Scholar 

  19. Karkouch, A., Mousannif, H., Al Moatassime, H., Noel, T.: Data quality in internet of things: a state-of-the-art survey. J. Netw. Comput. Appl. 73, 57–81 (2016). https://doi.org/10.1016/j.jnca.2016.08.002

    Article  Google Scholar 

  20. Lin, Y., Chen, C., Song, M., Liu, Z.: Dual-RBF based surface reconstruction. Vis. Comput. 25(5), 599–607 (2009). https://doi.org/10.1007/s00371-009-0349-x

    Article  Google Scholar 

  21. Lu, G., Ren, L., Kolagunda, A., Wang, X., Turkbey, I.B., Choyke, P.L., Kambhamettu, C.: Representing 3D shapes based on implicit surface functions learned from RBF neural networks. J. Vis. Commun. Image Represent. 40, 852–860 (2016). https://doi.org/10.1016/j.jvcir.2016.08.014

    Article  Google Scholar 

  22. Luo, S.H., Wang, J.X., Wu, S.L., Xiao, K.: Chaos RBF dynamics surface control of brushless DC motor with time delay based on tangent barrier lyapunov function. Nonlinear Dyn. 78(2), 1193–1204 (2014). https://doi.org/10.1007/s11071-014-1507-x

    Article  MATH  Google Scholar 

  23. Macêdo, I., Gois, J.a.P., Velho, L.: Hermite interpolation of implicit surfaces with radial basis functions. In: Proceedings of the 2009 XXII Brazilian Symposium on Computer Graphics and Image Processing, SIBGRAPI ’09, pp. 1–8. IEEE Computer Society, Washington, DC, USA (2009). https://doi.org/10.1109/SIBGRAPI.2009.11

  24. Mallet, J.L.: Discrete smooth interpolation in geometric modeling. Comput. Aided Des. 24(4), 178–191 (1992). https://doi.org/10.1016/0010-4485(92)90054-e

    Article  MATH  Google Scholar 

  25. Mallet, J.L.: Discrete modeling for natural objects. Math. Geol. 29(2), 199–219 (1997). https://doi.org/10.1007/bf02769628

    Article  MathSciNet  MATH  Google Scholar 

  26. Matheron, G.: Principles of geostatistics. Econ. Geol. 58(8), 1246–1266 (1963). https://doi.org/10.2113/gsecongeo.58.8.1246

    Article  Google Scholar 

  27. Mei, G., Tipper, J.C., Xu, N.: A generic paradigm for accelerating Laplacian-based mesh smoothing on the GPU. Arab. J. Sci. Eng. 39(11), 7907–7921 (2014). https://doi.org/10.1007/s13369-014-1406-y

    Article  Google Scholar 

  28. Mei, G., Xu, L., Xu, N.: Accelerating adaptive inverse distance weighting interpolation algorithm on a graphics processing unit. R. Soc. Open Sci. (2017). https://doi.org/10.1098/rsos.170436

    Article  MathSciNet  Google Scholar 

  29. Mei, G., Xu, N.X., Xu, L.L.: Improving GPU-accelerated adaptive IDW interpolation algorithm using fast kNN search. Springerplus 5, 22 (2016). https://doi.org/10.1186/s40064-016-3035-2

    Article  Google Scholar 

  30. Mirzaei, D.: Analysis of moving least squares approximation revisited. J. Comput. Appl. Math. 282, 237–250 (2015). https://doi.org/10.1016/j.cam.2015.01.007

    Article  MathSciNet  MATH  Google Scholar 

  31. Piccialli, F., Cuomo, S., De Michele, P.: A regularized MRI image reconstruction based on hessian penalty term on CPU/GPU systems. In: 2013 International Conference on Computational Science, Procedia Computer Science, vol. 18, pp. 2643–2646. Elsevier Science BV, Sara Burgerhartstraat 25, Po Box 211, 1000 Ae Amsterdam, Netherlands (2013). https://doi.org/10.1016/j.procs.2013.06.001

    Article  Google Scholar 

  32. Shankar, V., Wright, G.B., Kirby, R.M., Fogelson, A.L.: A radial basis function (RBF)-finite difference (FD) method for diffusion and reaction–diffusion equations on surfaces. J. Sci. Comput. 63(3), 745–768 (2015). https://doi.org/10.1007/s10915-014-9914-1

    Article  MathSciNet  MATH  Google Scholar 

  33. Shepard, D.: A two-dimensional interpolation function for irregularly-spaced data (1968). https://doi.org/10.1145/800186.810616

  34. Wang, J.G., Liu, G.R.: On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Comput. Methods Appl. Mech. Eng. 191(23–24), 2611–2630 (2002). https://doi.org/10.1016/s0045-7825(01)00419-4

    Article  MathSciNet  MATH  Google Scholar 

  35. Wang, J.G., Liu, G.R.: A point interpolation meshless method based on radial basis functions. Int. J. Numer. Methods Eng. 54(11), 1623–1648 (2002). https://doi.org/10.1002/nme.489

    Article  MATH  Google Scholar 

  36. Wang, Q., Pan, Z., Bu, J., Chen, C.: Parallel RBF-based reconstruction from contour dataset. In: 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics, pp. 82–85 (2007). https://doi.org/10.1109/CADCG.2007.4407860

  37. Yang, R., Er, P.V., Wang, Z., Tan, K.K.: An RBF neural network approach towards precision motion system with selective sensor fusion. Neurocomputing 199, 31–39 (2016). https://doi.org/10.1016/j.neucom.2016.01.093

    Article  Google Scholar 

  38. Yokota, R., Barba, L.A., Knepley, M.G.: PetRBF—a parallel \(o(n)\) algorithm for radial basis function interpolation with gaussians. Comput. Methods Appl. Mech. Eng. 199(25–28), 1793–1804 (2010). https://doi.org/10.1016/j.cma.2010.02.008

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This research was jointly supported by the Natural Science Foundation of China (Grant Nos. 11602235 and 51674058), the China Postdoctoral Science Foundation (2015M571081), and the Fundamental Research Funds for China Central Universities (2652016105, 2652015065, and 2652017086).

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Authors and Affiliations

  1. School of Engineering and Technology, China University of Geosciences, Beijing, China

    Zengyu Ding, Gang Mei & Nengxiong Xu

  2. Department of Mathematics and Applications ”R. Caccioppoli”, University of Naples Federico II, Naples, Italy

    Salvatore Cuomo

  3. Faculty of Engineering, China University of Geosciences, Wuhan, China

    Hong Tian

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  1. Zengyu Ding
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Correspondence to Gang Mei.

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Ding, Z., Mei, G., Cuomo, S. et al. Performance Evaluation of GPU-Accelerated Spatial Interpolation Using Radial Basis Functions for Building Explicit Surfaces. Int J Parallel Prog 46, 963–991 (2018). https://doi.org/10.1007/s10766-017-0538-6

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