×

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.

MSC:

65D07 Numerical computation using splines
41A15 Spline approximation
PDFBibTeX XMLCite
Full Text: EuDML Link

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.