Title:
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Fast evaluation of thin-plate splines on fine square grids (English) |
Author:
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Luner, Petr |
Author:
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Flusser, Jan |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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41 |
Issue:
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1 |
Year:
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2005 |
Pages:
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[97]-112 |
Summary lang:
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English |
. |
Category:
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math |
. |
Summary:
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The paper deals with effective calculation of Thin-Plate Splines (TPS). 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. (English) |
Keyword:
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Thin-Plate Spline |
Keyword:
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fast evaluation |
Keyword:
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subtabulation |
MSC:
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41A15 |
MSC:
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65D07 |
MSC:
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65D17 |
MSC:
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65D18 |
idZBL:
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Zbl 1249.65025 |
idMR:
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MR2131128 |
. |
Date available:
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2009-09-24T20:07:18Z |
Last updated:
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2015-03-23 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/135642 |
. |
Reference:
|
[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 |
Reference:
|
[2] Arad N., Gotsman C.: Enhancement by image-dependent warping.IEEE Trans. Image Processing 8 (1999), 1063–1074 10.1109/83.777087 |
Reference:
|
[3] Beatson R. K., Newsam G. N.: Fast evaluation of radial basis functions.Comput. Math. Appl. 24 (1992), 7–19 Zbl 0765.65021, MR 1190302, 10.1016/0898-1221(92)90167-G |
Reference:
|
[4] Berman M.: Automated smoothing of image and other regularly spaced data.IEEE Trans. Pattern Anal. Mach. Intell. 16 (1994), 460–468 10.1109/34.291451 |
Reference:
|
[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, 10.1109/34.24792 |
Reference:
|
[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 10.1109/42.552059 |
Reference:
|
[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 MR 0470565 |
Reference:
|
[8] Flusser J.: An adaptive method for image registration.Pattern Recognition 25 (1992), 45–54 10.1016/0031-3203(92)90005-4 |
Reference:
|
[9] Goshtasby A.: Registration of images with geometric distortions.IEEE Trans. Geoscience and Remote Sensing 26 (1988), 60–64 10.1109/36.3000 |
Reference:
|
[10] Greengard L., Rokhlin V.: A fast algorithm for particle simulations.J. Comput. Phys. 73 (1987), 325–348 Zbl 0629.65005, MR 0918448, 10.1016/0021-9991(87)90140-9 |
Reference:
|
[11] Grimson W. E. L.: A computational theory of visual surface interpolation.Philos. Trans. Roy. Soc. London Ser. B 298 (1982), 395–427 10.1098/rstb.1982.0088 |
Reference:
|
[12] Harder R. L., Desmarais R. N.: Interpolation using surface splines.J. Aircraft 9 (1972), 189–191 10.2514/3.44330 |
Reference:
|
[13] Kašpar R., Zitová B.: Weighted thin-plate spline image denoising.Pattern Recognition 36 (2003), 3027–3030 Zbl 1059.68150, 10.1016/S0031-3203(03)00133-X |
Reference:
|
[14] Powell M. J. D.: Tabulation of thin plate splines on a very fine two-dimensional grid.In: Numerical Methods of Approximation Theory, Volume 9 (D. Braess and L. L. Schumacher, eds.), Birkhäuser Verlag, Basel, 1992, pp. 221–244 Zbl 0813.65014, MR 1269364 |
Reference:
|
[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, MR 1269364 |
Reference:
|
[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 10.1109/42.929618 |
Reference:
|
[17] Wahba G.: Spline Models for Observational Data.SIAM, Philadelphia 1990 Zbl 0813.62001, MR 1045442 |
Reference:
|
[18] Wolberg G.: Digital Image Warping.IEEE Computer Society Press, 1990 |
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