Quantitative evaluation of convolution-based methods for medical image interpolation

Medical Image Analysis

Volumn 5, Issue 2, 2001, Pages 111-126

  Meijering, Erik H W ^a   Niessen, Wiro J ^a   Viergever, Max A ^a  

^a UNIVERSITY MEDICAL CENTER UTRECHT   (Netherlands)

Author keywords

Convolution based interpolation; Geometrical transformation; Medical images; Piecewise polynomial kernels; Quantitative evaluation; Spline interpolation; Windowed sinc kernels

Indexed keywords

ACCURACY; ARTICLE; BRAIN ANGIOGRAPHY; COMPUTER ASSISTED TOMOGRAPHY; CONTROLLED STUDY; COST BENEFIT ANALYSIS; DIAGNOSTIC IMAGING; EVALUATION; GEOMETRY; IMAGE ANALYSIS; IMAGE PROCESSING; INTERMETHOD COMPARISON; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; POSITRON EMISSION TOMOGRAPHY; PRIORITY JOURNAL; QUANTITATIVE ANALYSIS; ROTATION; SINGLE PHOTON EMISSION COMPUTER TOMOGRAPHY; THREE DIMENSIONAL IMAGING; X RAY ANALYSIS;

BRAIN MAPPING; DIAGNOSTIC IMAGING; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; MATHEMATICS;

EID: 0035384145     PISSN: 13618415     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1361-8415(00)00040-2     Document Type: Article

References (61)

1. Aldroubi, A., Unser, M., Eden, M., 1992. Cardinal spline filters: Stability and convergence to the ideal sinc interpolator. Signal Processing 28 (2), 127-138.
2. Altman, D.G., 1991. Practical Statistics for Medical Research. Chapman & Hall, London, UK.
3. Blu, T., Unser, M., 1999. Quantitative Fourier analysis of approximation techniques: Part I - Interpolators and projectors. IEEE Trans. Signal Processing 47 (10), 2783-2795.
4. Catmull, E., Rom, R., 1974. A class of local interpolating splines. In: Barnhill, R.E., Riesenfeld, R.F. (Eds.), Computer Aided Geometric Design. Academic Press, New York, NY, pp. 317-326.
5. Chuang, K.-S., 1990. Comparison of interpolation methods in three-dimensional surface display. In: Medical Imaging IV: Image Processing, Vol. 1233 of Proc. SPIE, The International Society for Optical Engineering, Bellingham, Washington, USA, pp. 443-452.
6. Danielsson, P.-E., Hammerin, M., 1992. High-accuracy rotation of images. CVGIP: Graphical Models and Image Processing 54 (4), 340-344.
7. Dodgson, N.A., 1997. Quadratic interpolation for image resampling. IEEE Trans. on Image Processing 6 (9), 1322-1326.
8. Du, Y.P., Parker, D.L., Davis, W.L., Cao, G., 1994. Reduction of partial-volume artifacts with zero-filled interpolation in three-dimensional MR angiography. J. of Magnetic Resonance Imaging 4 (5), 733-741.
9. Eddy, W.F., Fitzgerald, M., Noll, D.C., 1996. Improved image registration by using Fourier interpolation. Magnetic Resonance in Medicine 36 (6), 923-931.
10. Grevera, G.J., Udupa, J.K., 1996. Shape-based interpolation of multi-dimensional grey-level images. IEEE Trans. on Medical Imaging 15 (6), 881-892.
11. Grevera, G.J., Udupa, J.K., 1998. An objective comparison of 3-D image interpolation methods. IEEE Trans. on Medical Imaging 17 (4), 642-652.
12. Guo, J.-F., Cai, Y.-L., Wang, Y.-P., 1995. Morphology-based interpolation for 3D medical image reconstruction. Computerized Medical Imaging and Graphics 19 (3), 267-279.
13. Hajnal, J.V., Saeed, N., Soar, E.J., Oatridge, A., Young, I.R., Bydder, G.M., 1995. A registration and interpolation procedure for subvoxel matching of serially acquired MR images. J. of Computer Assisted Tomography 19 (2), 289-296.
14. Hamming, R.W., 1989. Digital Filters, 3rd Edition. Signal Processing Series. Prentice-Hall, Engelwood Cliffs, NJ.
15. Harris, F.J., 1978. On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66 (1), 51-83.
16. Herman, G.T., Rowland, S.W., Yau, M., 1979. A comparative study of the use of linear and modified cubic spline interpolation for image reconstruction. IEEE Trans. Nuclear Sci. 26 (2), 2879-2894.
17. Herman, G.T., Zheng, J., Bucholtz, C.A., 1992. Shape-based interpolation. IEEE Computer Graphics and Applications 12 (3), 69-79.
18. Higgins, W.E., Morice, C., Ritman, E.L., 1993. Shape-based interpolation of tree-like structures in three-dimensional images. IEEE Trans. Med. Imaging 12 (3), 439-450.
19. Higgins, W.E., Orlick, C.J., Ledell, B.E., 1996. Nonlinear filtering approach to 3-D gray-scale image interpolation. IEEE Trans. Med. Imaging 15 (4), 580-587.
20. Hou, H.S., Andrews, H.C., 1978. Cubic splines for image interpolation and digital filtering. IEEE Trans. Acoustics, Speech, and Signal Processing 26 (6), 508-517.
21. Hylton, N.M., Simovsky, I., Li, A.J., Hale, J.D., 1992. Impact of section doubling on MR angiography. Radiology, 185 (3), 899-902.
22. Jain, A.K., 1989. Fundamentals of Digital Image Processing. Prentice-Hall, Englewood Cliffs, NJ.
23. Jerri, A.J., 1977. The Shannon sampling theorem - Its various extensions and applications: A tutorial review. Proc. IEEE 65 (11), 1565-1596.
24. Keys, R.G., 1981. Cubic convolution interpolation for digital image processing. IEEE Trans. Acoustics, Speech, and Signal Processing 29 (6), 1153-1160.
25. Kramer, D., Li, A., Simovsky, I., Hawryszko, C., Hale, J., Kaufman, L., 1990. Applications of voxel shifting in magnetic resonance imaging. Investigative Radiol. 25 (12), 1305-1310.
26. Kwakernaak, H., Sivan, R., 1991. Modern Signals and Systems. Information and System Sciences Series. Prentice-Hall, Englewood Cliffs, NJ.
27. Lee, C.-H., 1983. Restoring spline interpolation of CT images. IEEE Trans. Med. Imaging 2 (3), 142-149.
28. Machiraju, R., Yagel, R., 1996. Reconstruction error characterization and control: A sampling theory approach. IEEE Trans. Visualization and Computer Graphics 2 (4), 364-378.
29. Maeland, E., 1988. On the comparison of interpolation methods. IEEE Trans. Med. Imaging 7 (3), 213-217.
30. Marschner, S.R., Lobb, R.J., 1994. An evaluation of reconstruction filters for volume rendering. In: Bergerson, R.D., Kaufman, A.E. (Eds.), Proc. IEEE Conf. Visualization (Visualization '94). IEEE Computer Society Press, Los Alamitos, CA, pp. 100-107.
31. Meijering, E.H.W., Niessen, W.J., Viergever, M.A., 1999a. Piecewise polynomial kernels for image interpolation: A generalization of cubic convolution. In: IEEE Int. Conf. Image Processing (ICIP'99), Vol. III. IEEE Computer Society Press, Los Alamitos, CA, pp. 647-651.
32. Meijering, E.H.W., Niessen, W.J., Viergever, M.A., 1999b. The sinc-approximating kernels of classical polynomial interpolation. In: IEEE Int. Conf. on Image Processing (ICIP'99), Vol. III. IEEE Computer Society Press, Los Alamitos, CA, pp. 652-656.
33. Meijering, E.H.W., Zuiderveld, K.J., Viergever, M.A., 1999c. Image reconstruction by convolution with symmetrical piecewise nth-order polynomial kernels. IEEE Trans. Image Processing 8 (2), 192-201.
34. Mitchell, D.P., Netravali, A.N., 1988. Reconstruction filters in computer graphics. Computer Graphics (SIGGRAPH'88 Conference Proceedings) 22 (4) 221-228.
35. Möller, T., Machiraju, R., Mueller, K., Yagel, R., 1997. Evaluation and design of filters using a Taylor series expansion. IEEE Trans. on Visualization and Computer Graphics 3 (2), 184-199.
36. Nyquist, H., 1928. Certain topics in telegraph transmission theory. Trans. Am. Inst. Electr. Eng. 47, 617-644.
37. Oppenheim, A.V., Schafer, R.W., 1975. Digital Signal Processing. Prentice-Hall, Englewood Cliffs, NJ.
38. Ostuni, J.L., Santha, A.K.S., Mattay, V.S., Weinberger, D.R., Levin, R.L., Frank, J.A., 1997. Analysis of interpolation effects in the reslicing of functional MR images. J. Computer Assisted Tomography 21 (5), 803-810.
39. Park, S.K., Schowengerdt, R.A., 1982. Image sampling, reconstruction, and the effect of sample-scene phasing. Applied Optics 21 (17), 3142-3151.
40. Park, S.K., Schowengerdt, R.A., 1983. Image reconstruction by parametric cubic convolution. Computer Vision, Graphics and Image Processing 23 (3), 258-272.
41. Parker, J.A., Kenyon, R.V., Troxel, D.E., 1983. Comparison of interpolating methods for image resampling. IEEE Trans. Med. Imaging 2 (1), 31-39.
42. Pluim, J.P.W, Maintz, J.B.A., Viergever, M.A., 2000. Interpolation artefacts in mutual information-based image registration. Computer Vision and Image Understanding 77 (2), 211-232.
43. Raya, S.P., Udupa, J.K., 1990. Shape-based interpolation of multidimensional objects. IEEE Trans. Med. Imaging 9 (1), 32-42.
44. Rifman, S.S., 1973. Digital rectification of ERTS multispectral imagery. In: Proc. Symp. Significant Results Obtained from the Earth Resources Technology Satellite-1, Vol. 1, Section B. NASA SP-327, pp. 1131-1142.
45. Schafer, R.W., Rabiner, L.R., 1973. A digital signal processing approach to interpolation. Proc. IEEE 61 (6), 692-702.
46. Schanze, T., 1995. Sinc interpolation of discrete periodic signals. IEEE Trans. Signal Processing 43 (6), 1502-1503.
47. Schaum, A., 1993. Theory and design of local interpolators. CVGIP: Graphical Models and Image Processing 55 (6), 464-481.
48. Schoenberg, I.J., 1946. Contributions to the problem of approximation of equidistant data by analytic functions. Quarterly of Applied Mathematics 4 (1, 2) 45-99 and 112-141.
49. Schoenberg, I.J., 1969. Cardinal interpolation and spline functions. J. Approximation Theory 2 (2), 167-206.
50. Schoenberg, I.J., 1973. Notes on spline functions III: On the convergence of the interpolating cardinal splines as their degree tends to infinity. Israel J. Math. 16, 87-93.
51. Schreiber, W.F., Troxel, D.E., 1985. Transformation between continuous and discrete representations of images: A perceptual approach. IEEE Trans. Pattern Anal. Machine Intell. 7 (2), 178-186.
52. Schreiner, S., Paschal, C.B., Galloway, R.L., 1996. Comparison of projection algorithms used for the construction of maximum intensity projection images. J. Computer Assisted Tomography 20 (1), 56-67.
53. Shannon, C.E., 1949. Communication in the presence of noise. Proc. Inst. Radio Eng. 37 (1), 10-21.
54. Simon, K.W., 1975. Digital image reconstruction and resampling for geometric manipulation. In: McGillem, C.D., Morrison, D.B. (Eds.), Symp. Machine Processing of Remotely Sensed Data. IEEE Press, New York, NY, pp. 3A1-3A11.
55. Unser, M., Aldroubi, A., Eden, M., 1991. Fast B-spline transforms for continuous image representation and interpolation. IEEE Trans. Pattern Anal. Machine Intelligence 13 (3), 277-285.
56. Unser, M., Aldroubi, A., Eden, M., 1993a. B-spline signal processing: Part I-Theory. IEEE Trans. Signal Processing 41 (2), 821-833.
57. Unser, M., Aldroubi, A., Eden, M., 1993b. B-spline signal processing: Part II-Efficient design and applications. IEEE Trans. Signal Processing 41 (2), 834-848.
58. Unser, M., Thévenaz, P., Yaroslavsky, L., 1995. Convolution-based interpolation for fast, high-quality rotation of images. IEEE Trans. Image Processing 4 (10), 1371-1381.
59. Whittaker, E.T., 1915. On the functions which are represented by the expansions of interpolation-theory. Proc. Roy. Soc. Edinburgh 35, 181-194.
60. Whittaker, J.M., 1935. Interpolatory Function Theory. No. 33 in Cambridge Tracts in Mathematics and Mathematical Physics. Cambridge University Press, Cambridge, UK.
61. Wolberg, G., 1990. Digital Image Warping. IEEE Computer Society Press, Washington, USA.