Fast evaluation of thin-plate splines on fine square grids. (English) Zbl 1249.65025

Summary: The paper deals with effective calculation of thin plate splines. We present a new modification of hierarchical approximation scheme. Unlike 2-D schemes published earlier, we propose an 1-D approximation. The new method yields lower computing complexity while it preserves the approximation accuracy.


65D07 Numerical computation using splines
41A15 Spline approximation
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[1] Arad N., Dyn N., Reisfeld, D., Yeshurun Y.: Image warping by radial basis functions: Application to facial expressions. CVGIP: Graphical Models and Image Processing 56 (1994), 161-172
[2] Arad N., Gotsman C.: Enhancement by image-dependent warping. IEEE Trans. Image Processing 8 (1999), 1063-1074 · doi:10.1109/83.777087
[3] Beatson R. K., Newsam G. N.: Fast evaluation of radial basis functions. Comput. Math. Appl. 24 (1992), 7-19 · Zbl 0765.65021 · doi:10.1016/0898-1221(92)90167-G
[4] Berman M.: Automated smoothing of image and other regularly spaced data. IEEE Trans. Pattern Anal. Mach. Intell. 16 (1994), 460-468 · doi:10.1109/34.291451
[5] Bookstein F. L.: Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans. Pattern Anal. Mach. Intell. 11 (1989), 567-585 · Zbl 0691.65002 · doi:10.1109/34.24792
[6] Carr J. C., Fright W. R., Beatson R.: Surface interpolation with radial basis functions for medical imaging. IEEE Trans. Medical Imaging 16 (1997), 96-107 · doi:10.1109/42.552059
[7] Duchon J.: Interpolation des fonctions de deux variables suivant le principle de la flexion des plaques minces. RAIRO Anal. Num. 10 (1976), 5-12
[8] Flusser J.: An adaptive method for image registration. Pattern Recognition 25 (1992), 45-54 · doi:10.1016/0031-3203(92)90005-4
[9] Goshtasby A.: Registration of images with geometric distortions. IEEE Trans. Geoscience and Remote Sensing 26 (1988), 60-64 · doi:10.1109/36.3000
[10] Greengard L., Rokhlin V.: A fast algorithm for particle simulations. J. Comput. Phys. 73 (1987), 325-348 · Zbl 0629.65005 · doi:10.1016/0021-9991(87)90140-9
[11] Grimson W. E. L.: A computational theory of visual surface interpolation. Philos. Trans. Roy. Soc. London Ser. B 298 (1982), 395-427 · doi:10.1098/rstb.1982.0088
[12] Harder R. L., Desmarais R. N.: Interpolation using surface splines. J. Aircraft 9 (1972), 189-191 · doi:10.2514/3.44330
[13] Kašpar R., Zitová B.: Weighted thin-plate spline image denoising. Pattern Recognition 36 (2003), 3027-3030 · Zbl 1059.68150 · doi:10.1016/S0031-3203(03)00133-X
[14] Powell M. J. D.: Tabulation of thin plate splines on a very fine two-dimensional grid. Numerical Methods of Approximation Theory, Volume 9 (D. Braess and L. L. Schumacher, Birkhäuser Verlag, Basel, 1992, pp. 221-244 · Zbl 0813.65014
[15] Powell M. J. D.: Tabulation of Thin Plate Splines on a Very Fine Two-Dimensional Grid. Numerical Analysis Report of University of Cambridge, DAMTP/1992/NA2, Cambridge 1992 · Zbl 0813.65014
[16] Rohr K., Stiehl H. S., Buzug T. M., Weese, J., Kuhn M. H.: Landmark-based elastic registration using approximating thin-plate splines. IEEE Trans. Medical Imaging 20 (2001), 526-534 · doi:10.1109/42.929618
[17] Wahba G.: Spline Models for Observational Data. SIAM, Philadelphia 1990 · Zbl 0813.62001
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