Splines: A perfect fit for medical imaging

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 4684 I, Issue , 2002, Pages 225-236

  Unser, Michael ^a  

^a EPFL   (Switzerland)

Author keywords

Interpolation; Medical image processing; Registration; Splines

Indexed keywords

APPROXIMATION THEORY; COMPUTER AIDED DESIGN; COMPUTER GRAPHICS; IMAGE RECONSTRUCTION; INTERPOLATION; MATHEMATICAL MODELS; PROBLEM SOLVING; SIGNAL PROCESSING;

IMAGE REGISTRATION;

MEDICAL IMAGING;

EID: 0036034807     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.467162     Document Type: Conference Paper

References (49)

1. J.H. Ahlberg, E.N. Nilson and J.L. Walsh, The Theory of splines and their applications, Academic Press, New York, 1967.
2. A. Aldroubi and M. Unser, Wavelets in Medicine and Biology, CRC, Boca Raton, FL, 1996.
3. A. Aldroubi, M. Unser and M. Eden, "Cardinal spline filters: Stability and convergence to the ideal sinc interpolator", Signal Processing, Vol. 28, No. 2, pp. 127-138, August 1992.
4. G. Battle, "A block spin construction of ondelettes. Part I: Lemarié functions", Commun. Math. Phys., Vol. 110, pp. 601-615, 1987.
5. T. Blu, P. Thévenaz and M. Unser, "MOMS: Maximal-order interpolation of minimal support", IEEE Transactions on Image Processing, Vol. 10, No. 7, pp. 1069-1080, July 2001.
6. T. Blu and M. Unser, "Minimum support interpolators with optimum approximation properties", Proc. Int. Conf. Image Processing, Santa Barbara, CA, pp. 242-245, 1998.
7. T. Blu and M. Unser, "Quantitative Fourier analysis of approximation techniques: Part II - wavelets", IEEE Transactions on Signal Processing, Vol. 47, No. 10, pp. 2796-2806, October 1999.
8. T. Blu and M. Unser, "Quantitative Fourier analysis of approximation techniques: Part I - interpolators and projectors", IEEE Transactions on Signal Processing, Vol. 47, No. 10, pp. 2783-2795, October 1999.
9. T. Blu and M. Unser, "Wavelets, fractals and radial basis functions", IEEE Transactions on Signal Processing, in Press.
10. L.G. Brown, "A survey of image registration techniques", ACM Computing Surveys, Vol. 24, No. 4, pp. 325-376, 1992.
11. C.K. Chui and J.Z. Wang, "On compactly supported spline wavelets and a duality principle", Trans. Amer. Math. Soc., Vol. 330, No. 2, pp. 903-915, 1992.
12. A. Collignon, F. Maes, D. Delaere, D. Vandermeulen, P. Suetens and G. Marchal, "Automated multi-modality image registration based on information theory", in: Y. Bizais, ed., Information Processing in Medical Imaging, 1995, pp. 263-274.
13. I. Daubechies, Ten lectures on wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
14. C. De Boor, A practical guide to splines, Springer-Verlag, New York, 1978.
15. N.A. Dodgson, "Quadratic interpolation for image resampling", IEEE Trans. Image Processing, Vol. 6, No. 9, pp. 1322-1326, 1997.
16. R.G. Keys, "Cubic convolution interpolation for digital image processing", IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-29, No. 6, pp. 1153-1160, 1981.
17. J. Kybic, P. Thévenaz, A. Nirkko and M. Unser, "Unwarping of unidirectionally distorted EPI images", IEEE Transactions on Medical Imaging, Vol. 19, No. 2, pp. 80-93, February 2000.
18. J. Kybic and M. Unser, "Multidimensional Elastic Registration of Images Using Splines", Proc. IEEE International Conference on Image Processing, Vancouver BC, Canada, pp. 455-458, September 10-13, 2000.
19. T.M. Lehmann, C. Gönner and K. Spitzer, "Survey: Interpolation methods in medical image processing", IEEE Transactions on Medical Imaging, Vol. 18, No. 11, pp. 1049-1075, November 1999.
20. T.M. Lehmann, C. Gönner and K. Spitzer, "Addendum: B-spline interpolation in medical image processing", IEEE Transactions on Medical Imaging, Vol. 20, No. 7, pp. 660-665, November 2001.
21. P.-G. Lemarié, "Ondelettes à localisation exponentielle", J. Math. pures et appl., Vol. 67, No. 3, pp. 227-236, 1988.
22. E. Maeland, "On the comparison of interpolation methods", IEEE Transactions on Medical Imaging, Vol. 7, No. 3, pp. 213-217, September 1988.
23. S. Mallat, A wavelet tour of signal processing, Academic Press, San Diego, 1998.
24. E.H.W. Meijering, W.J. Niessen and M.A. Viergever, "Quantitative evaluation of convolution-based methods for medical image interpolation", Medical Image Analysis, Vol. 5, pp. 111-126, 2001.
25. J.A. Parker, R.V. Kenyon and D.E. Troxel, "Comparison of interpolating methods for image resampling", IEEE Trans. Med. Imaging, Vol. MI-2, No. 1, pp. 31-39, 1983.
26. A. Schaum, "Theory and design of local interpolators", CVGIP: Graphical Models and Image Processing, Vol. 55, pp. 464-481, November 1993.
27. I.J. Schoenberg, "Contribution to the problem of approximation of equidistant data by analytic functions", Quart. Appl. Math., Vol. 4, pp. 45-99, 112-141, 1946.
28. I.J. Schoenberg, Cardinal spline interpolation, Society of Industrial and Applied Mathematics, Philadelphia, PA, 1973.
29. S. Schreiner, C.B. Paschal and R.L. Galloway, "Comparison of projection algorithms used for the construction of maximum intensity projection images", J. Computer Assisted Tomography, Vol. 20, No. 1, pp. 56-67, 1996.
30. L.L. Schumaker, Spline functions: basic theory, Wiley, New York, 1981.
31. J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients", IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 41, No. 12, pp. 3445-3462, December 1993.
32. G. Strang and T. Nguyen, Wavelets and filter banks, Wellesley-Cambridge, Wellesley, MA, 1996.
33. P. Thévenaz, T. Blu and M. Unser, "Image interpolation and resampling", in: I.N. Bankman, ed., Handbook of Medical Image Processing, Academic Press, San Diego, CA, 2000, pp. 393-420.
34. P. Thévenaz, T. Blu and M. Unser, "Interpolation revisited", IEEE Transactions on Medical Imaging, Vol. 19, No. 7, pp. 739-758, July 2000.
35. P. Thévenaz, U.E. Ruttimann and M. Unser, "A pyramid approach to subpixel registration based on intensity", IEEE Trans. Image Processing, Vol. 7, No. 1, pp. 27-41, January 1998.
36. P. Thévenaz and M. Unser, "Spline pyramids for inter-modal image registration using mutual information", Proc. Wavelet Applications in Signal and Image Processing V, San Diego, CA, pp. 236-247, September 16-19, 1997.
37. M. Unser, "Ten good reasons for using spline wavelets", Proc. SPIE Conf. Wavelet Applications in Signal and Image Processing V, San Diego, CA, pp. 422-431, August 6-9, 1997.
38. M. Unser, "Splines: A perfect fit for signal and image processing", IEEE Signal Processing Magazine, Vol. 16, No. 6, pp. 22-38, November 1999.
39. M. Unser and A. Aldroubi, "A review of wavelets in biomedical applications", Proceedings of the IEEE, Vol. 84, No. 4, pp. 626-638, April 1996.
40. M. Unser, A. Aldroubi and M. Eden, "Fast B-spline transforms for continuous image representation and interpolation", IEEE Trans. Pattern Anal. Machine Intell., Vol. 13, No. 3, pp. 277-285, March 1991.
41. M. Unser, A. Aldroubi and M. Eden, "On the asymptotic convergence of B-spline wavelets to Gabor functions", IEEE Trans. Information Theory, Vol. 38, No. 2, pp. 864-872, March 1992.
42. M. Unser, A. Aldroubi and M. Eden, "B-spline signal processing: Part II - efficient design and applications", IEEE Trans. Signal Processing, Vol. 41, No. 2, pp. 834-848, February 1993.
43. M. Unser, A. Aldroubi and M. Eden, "B-spline signal processing: Part I - theory", IEEE Trans. Signal Processing, Vol. 41, No. 2, pp. 821-833, February 1993.
44. M. Unser, A. Aldroubi and M. Eden, "A family of polynomial spline wavelet transforms", Signal Processing, Vol. 30, No. 2, pp. 141-162, January 1993.
45. M. Unser, A. Aldroubi and S.J. Schiff, "Fast implementation of the continuous wavelet transform with integer scales", IEEE Trans. Signal Processing, Vol. 42, No. 12, pp. 3519-3523, December 1994.
46. M. Unser, P. Thévenaz and L. Yaroslavsky, "Convolution-based interpolation for fast, high-quality rotation of images", IEEE Trans. Image Processing, Vol. 4, No. 10, pp. 1371-1381, October 1995.
47. P.A. van den Elsen, E.-J.D. Pol and M.A. Viergever, "Medical image matching: A review with classification", IEEE Engineering in Medicine and Biology, Vol. 12, No. 1, pp. 26-39, March 1993.
48. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, Englewood Cliffs, NJ, 1995.
49. J.B. Weaver, X. Yansun, D.M. Healy, Jr. and L.D. Cromwell, "Filtering noise from images with wavelet transforms", Magnetic Resonance in Medicine, Vol. 21, No. 2, pp. 288-95, 1991.