Image warping using radial basis functions

Journal of Applied Statistics

Volumn 41, Issue 2, 2014, Pages 242-258

  Chen, Ting Li ^a   Geman, Stuart ^b  

^a INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

^b BROWN UNIVERSITY   (United States)

Author keywords

data interpolation; image morphing; image warping; optimization; thin plate spline

Indexed keywords

EID: 84889096336     PISSN: 02664763     EISSN: 13600532     Source Type: Journal    
DOI: 10.1080/02664763.2013.838667     Document Type: Article

References (42)

1. H. Akima, A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points, ACM Trans. Math. Software 4 (1978), pp. 148-159. doi: 10.1145/355780.355786
2. I. Amidror, Scattered data interpolation methods for electronic imaging systems: A survey, J. Electronic Imaging 2 (2002), pp. 157-176. doi: 10.1117/1.1455013
3. F.L. Bookstein, Principal warps: Thin-plate splines and decomposition of deformations, IEEE Trans. Pattern Anal. Mach. Intell. 11 (1989), pp. 567-585. doi: 10.1109/34.24792
4. F.L. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, Cambridge, 1991.
5. M.D. Buhmann, Radial Basis Functions: Theory and Implementations, Cambridge University Press, Cambridge, 2003.
6. R.W. Clough and J.L. Tocher, Finite element stiffness matrices for analysis of plates in bending, Proceedings of the Conference on Matrix Methods in Structural Mechanics Wright-Patterson A.F.B., Ohio, 1965, pp. 515-545.
7. I. Crain and K. Bhattacharyya, Treatment of nonequispaced two-dimensional data with a digital computer, Geoexploration 5 (1967), pp. 173-194. doi: 10.1016/0016-7142(67)90011-7
8. N.A. Cressie, Statistics for Spatial Data, Revised ed., Wiley and Sons, New York, 1993.
9. G.P. Cressman, An operational objective analysis system, Mon. Wea. Rev. 87 (1959), pp. 367-384. doi: 10.1175/1520-0493(1959)087<0367:AOOAS>2.0.CO;2
10. B. Delaunay, Sur la sphère vide, Bull. Acad. Science USSR VII: Class. Sci. Mat. Nat. (1934), pp. 793-800.
11. J. Duchon, Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces, Analyse Numeriques 10 (1976), pp. 5-12.
12. J. Duchon, Splines minimizing rotation-invariant semi-norms in Sobolev spaces, in Multivariate Approximation Theory, W. Schempp and K. Zeller, eds. Birkhäuser, Basel, 1977, pp. 85-100.
13. N. Dyn, Interpolation of scattered data by radial functions, in Topics in Multivariate Approximation, C.K. Chui, L.L. Schumaker, and F.I. Utreras, eds. Academic Press, New York, 1987, pp. 47-61.
14. N. Dyn, Interpolation and approximation by radial and related functions, in Approximation Theory VI: Volume 1, C.K. Chui, L.L. Schumaker, and J.D. Ward, eds., Academic Press, New York, 1989, pp. 211-234.
15. N. Dyn, D. Levin, and S. Rippa, Numerical procedures for surface fitting of scattered data by radial functions, SIAM J. Sci. Stat. Comput. 7 (1986), pp. 639-659. doi: 10.1137/0907043
16. R. Franke, Scattered data interpolation: Tests of some methods, Math. Comp. 38 (1982), pp. 181-200.
17. R. Franke and G.M. Nelson, Scattered data interpolation of large sets of scattered data, Int. J. Numer. Methods Eng. 15 (1980), pp. 1691-1704. doi: 10.1002/nme.1620151110
18. R. Franke and G.M. Nelson, Scattered data interpolation and applications: A tutorial and survey, in Geometric Modelling: Methods and Their Application, H. Hagen and D. Roller, eds., Springer-Verlag, Berlin, 1991, pp. 131-160.
19. C.A. Glasbey and K.V. Mardia, A review of image-warping methods, J. Appl. Stat. 25 (1988), pp. 155-172. doi: 10.1080/02664769823151
20. W.J. Gordon and J. Wixom, On Shepard's method of metric interpolation to scattered bivariate and multivariate data interpolation, Math. Comp. 32 (1978), pp. 253-264.
21. A. Goshtasby, Piecewise cubic mapping functions for image registration, Pattern Recognit. 20 (1987), pp. 525-533. doi: 10.1016/0031-3203(87)90079-3
22. R.L. Harder and R.N. Desmarais, Interpolation using surface splines, J. Aircraft 9 (1972), pp. 189-191.
23. R.L. Hardy, Multiquadratic equations of topography and other irregular surfaces, J. Geoph. Res. 76 (1971), pp. 1905-1915. doi: 10.1029/JB076i008p01905
24. R.L. Hardy, Theory and applications of the multiquadratic-biharmonic method, Comp. Math. Appl. 19 (1990), pp. 163-208. doi: 10.1016/0898-1221(90)90272-L
25. J.T. Kent and K.V. Mardia, The link between kriging and thin-plate splines, in Probability, Statistics and Optimization, F.P. Kelly eds., Wiley, New York, 1994, pp. 325-339.
26. 1 surface interpolation, in Mathematical Software III, J.R. Rice, eds., Academic Press, London, 1977, pp. 161-194.
27. D. Levin, The approximation power of moving least-squares, Math. Comput. 67 (1998), pp. 1517-1531. doi: 10.1090/S0025-5718-98-00974-0
28. D. Levin, Mesh-independent surface interpolation, in Geometric Modeling for Scientific Visualization, G. Brunnett, B. Hamann, H. Müller, and L. Linsen, eds., Springer-Verlag, New York, 2003, pp. 37-49.
29. S.K. Lodha and R. Franke, Scattered data techniques for Surfaces, in Proceedings of Dagstuhl Conference on Scientific Visualization, H. Hagen, G. Nielson and F. Post, eds., IEEE Computer Society Press, 1999, pp. 182-222.
30. S. Mann, C. Loop, M. Lounsbery, D. Meyers, J. Painter, T. DeRose, and K. Sloan, A survey of parametric scattered data fitting using triangular interpolations, in Curve and Surface Design, H. Hagen, eds., SIAM, Philadelphia, 1992, pp. 145-172.
31. J. Manson and S. Schaefer, Moving least squares coordinates, Comput. Graph. Forum 29 (2010), pp. 1517-1524. doi: 10.1111/j.1467-8659.2010.01760.x
32. G.M. Nielson and R. Franke, Surface Construction Based upon Triangulations, in Surfaces in CAGD, R.E. Barnhill and W. Boehm, eds., North-Holland, Amsterdam, 1982, pp. 163-179.
33. P. Percell, On cubic and quartic Clough-Tocher finite elements, SIAM J. Numer. Anal. 31 (1976), pp. 100-103. doi: 10.1137/0713011
34. M.J.D. Powell and M.A. Sabin, Piecewise quadratic approximations on triangles, ACM Trans. Math. Software 3 (1977), pp. 316-325. doi: 10.1145/355759.355761
35. R.L. Renka, Quadratic Shepard method for bivariate interpolation of scattered data, ACM Trans. Math. Software 14 (1988), pp. 149-150. doi: 10.1145/45054.356231
36. D. Ruprecht and H. Müller, Free form deformation with scattered data interpolation methods, G. Farin, H. Hagen, H. Noltemeier, (Eds.) Geometric Modelling, Computing Suppl. 8, Springer-Verlag, Wien, 1993, pp. 267-281.
37. D. Ruprecht and H. Müller, Image warping with scattered data interpolation, IEEE Comput. Graph. Appl. 15 (1995), pp. 37-43. doi: 10.1109/38.365004
38. L.L. Schumaker, Triangulation methods, in Topics in Multivariate Approximation, C.K. Chui, L.L. Schumaker, and F. Utreras, eds., Academic Press, New York, 1987, pp. 219-232.
39. D. Shepard, A Two Dimensional Interpolation Function for Irregularly Spaced Data, Proceedings of 23rd National Conference ACM, New York, 1968, pp. 517-524.
40. H. Wendland, Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, 2005.
41. G. Wolberg, Digital Image Warping, IEEE Computer Society Press, Los Alamitos, CA, 1994.
42. G. Wolberg, Image morphing: A survey, The Visual Computer 14 (1998), pp. 360-372 doi: 10.1007/s003710050148