B-spline snakes: A flexible tool for parametric contour detection

IEEE Transactions on Image Processing

Volumn 9, Issue 9, 2000, Pages 1484-1496

  Brigger, Patrick ^a,b   Hoeg, Jeff ^c   Unser, Michael ^a,d  

^a IEEE   (Switzerland)

^b getAbstractcom   (Switzerland)

^c NATIONAL INSTITUTES OF HEALTH   (United States)

^d EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CURVE FITTING; EDGE DETECTION; FEATURE EXTRACTION; FOURIER TRANSFORMS; IMAGE ENHANCEMENT; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MEDICAL APPLICATIONS; OPTIMIZATION; SPURIOUS SIGNAL NOISE;

B-SPLINE SNAKES; NOISY IMAGE; PARAMETRIC CONTOUR DETECTION;

IMAGE ANALYSIS;

EID: 0034258794     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.862624     Document Type: Article

References (51)

1. J. H. Ahlberg, E. N. Nilson, and J. L. Wash, The Theory of Splines and Their Applications. New York: Academic, 1967.
2. A. Amini, T. Weymouth, and R. Jain, "Using dynamic programming for solving variational problems in vision," IEEE Trans. Pattern Anal. Machine Intell., vol. 12, pp. 855-867, Sept. 1990.
3. R. Bartels, J. Beatty, and B. Barsky, An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Los Altos, CA: Morgan Kaufmann, 1987.
4. P. Brigger, S. L. Bacharach, G. Srinivasan, K. A. Nour, J. Carson, V. Dilsizian, A. Aldroubi, and M. Unser, "Segmentation of gated Tl-201-SPECT images and computation of ejection fraction: A different approach," J. Nucl. Cardiol., vol. 6, no. 3, pp. 286-297, 1999.
5. P. Brigger, F. Mueller, K. Illgner, and M. Unser, "Centered pyramids," IEEE Trans. Image Processing, vol. 6, no. 9, pp. 1254-1264, 1999.
6. C. M. Brislawn, "Preservation of subband symmetry in multirate signal coding," IEEE Trans. Signal Processing, vol. 43, pp. 3046-3050, Dec. 1995.
7. P. J. Burt and E. H. Adelson, "The Laplacian pyramid as a compact code," IEEE Trans. Commun., vol. COM-31, pp. 337-345, Apr. 1983.
8. J. F. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.
9. V. Caselles, F. Catte, T. Coll, and F. Dibos, "A geometric model for active contours in image processing," Num. Math., vol. 66, pp. 1-31, 1993.
10. G. Chuang and C. Kuo, "Wavelet descriptor of planar curves: Theory and applications," IEEE Trans. Image Processing, vol. 5, pp. 56-70, Jan. 1996.
11. F. S. Cohen and W. Jin-Yinn, "Part I: Modeling image curves using invariant 3-D object curve models - A path to 3-D recognition and shape estimation from image contours," IEEE Trans. Pattern Anal. Machine Intell., vol. 16, pp. 1-12, Jan. 1994.
12. F. S. Cohen, Y. Zhengwei, Z. Huang, and J. Nianov, "Automatic matching of homologous hisological sections," IEEE Trans. Biomed. Eng., vol. 45, no. 5, pp. 642-649, 1998.
13. L. D. Cohen and I. Cohen, "A finite element method applied to new acitve contour models and 3D reconstruction from cross sections," in Proc. 3rd Int. Conf. Computer Vision, Los Alamitos, CA, 1990, pp. 587-591.
14. _, "Finite-element methods for active contour models and balloons for 2-D and 3-D images," IEEE Trans. Pattern Anal. Machine Intell., vol. 15, pp. 1131-1147, Nov. 1993.
15. C. Davatzikos, M. Vaillant, S. M. Resnick, J. L. Prince, S. Letovsky, and R. N. Bryan, "A computerized approach for morphological analysis of the corpus callosum," J. Comput. Assist. Tomogr., vol. 20, no. 1, pp. 88-97, 1996.
16. C. de Boor, A Practical Guide to Splines. New York: Springer-Verlag, 1978.
17. H. Eviatar and R. Somorjai, "A fast, simple active contour algorithm for biomedical images," Pattern Recognit. Lett., vol. 17, pp. 969-974, 1996.
18. M. Flickner, H. Sawhney, D. Pryor, and J. Lotspiech, "Intelligent interactive image outlining using spline snakes," in 28th Asilomar Conf. Signals, Systems, Computers, vol. 1, 1994, pp. 731-735.
19. M. Hoch and P. Litwinowicz, "A semi-automatic system for edge tracking with snakes," Vis. Comput., vol. 12, pp. 75-83, 1996.
20. M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models,"Int. J. Comput. Vis., pp. 321-331, 1988.
21. A. Klein, T. K. Egglin, J. S. Pollak, F. Lee, and A. Amini, "Identifying vascular features with orientation specific filters and B-spline snakes," Comput. Cardiol., pp. 113-116, 1994.
22. K. Lam and H. Yan, "Fast greedy algorithm for active contours," Electron. Lett., vol. 30, no. 1, pp. 21-23, 1994.
23. C. W. Liao and G. Medioni, "Surface approximation of a cloud of 3D points," Graph. Models Image Process., vol. 57, no. 1, pp. 67-74, 1995.
24. W. A. Light, "Recent developments in the Strang-Fix theory for approximation orders," in Curves and Surfaces, P. J. Laurent, A. L. Méhauté, and L. L. Schumaker, Eds. New York: Academic, 1991, pp. 285-292.
25. R. Malladi, J. Sethian, and B. Vemuri, "Shape modeling with fron propagation: A level set approach," IEEE Trans. Pattern Anal. Machine Intell., vol. 17, pp. 158-175, 1995.
26. T. McInerney and D. Terzopoulos, "Topologically adaptable snakes," in 5th Int. Conf. Computer Vision, 1995, pp. 840-845.
27. S. Menet, P. Saint-Marc, and G. Medioni, "B-snakes: Implementation and application to stereo," in Image Understanding Workshop, Sept. 1990, pp. 720-726.
28. E. Persoon and K. Fu, "Shape discrimination using Fourier descriptors," IEEE Trans. Syst., Man, Cybern., vol. SMC-7, pp. 170-179, Mar. 1977.
29. B. Pinkowski, "Multiscale Fourier descriptors for classifying semivowels in spectrograms," Pattern Recognit., vol. 26, no. 10, pp. 1593-1602, 1993.
30. E. Polak, Computational Methods in Optimization. New York: Academic, 1971.
31. S. Ranganath, "Contour extraction from cardiac MRI studies using snakes,"IEEE Trans. Med. Imag., vol. 14, pp. 328-338, June 1995.
32. C. H. Reinsh, "Smoothingby spline functions," Numer. Math., vol. 10, pp. 177-183, 1967.
33. A. Rosenfeld, Multiresolution Image Processing. New York: Springer-Verlag, 1984.
34. I. J. Schoenberg, "Contribution to the problem of approximation of equidistant data by analytic functions," Quart. Appl. Math., vol. 4, pp. 112-141, 1946.
35. _, "Spline functions and the problem of graduation," Proc. Nat. Acad. Sci., vol. 52, pp. 947-950, 1964.
36. _, Cardinal Spline Interpolation. Philadelphia, PA: SIAM, 1973.
37. L. L. Schumaker, Spline Functions: Basic Theory. New York: Wiley, 1981.
38. J. A. Sethian, Level Set Methods. Cambridge, U.K.: Cambridge Univ. Press, 1996.
39. L. Staib, "Boundary finding with parametrically deformable models," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, pp. 1061-1075, Nov. 1992.
40. G. Strang and G. Fix, A Fourier Analysis of Finite Element Variational Method. Rome, Italy: Edizioni Cremonese, 1971, pp. 796-830.
41. R. Tello, "Fourier descriptors for computer graphics," IEEE Trans. Syst., Man, Cybern., vol. 25, pp. 861-865, May 1995.
42. M. Unser, A. Aldroubi, and M. Eden, "Polynomial spline signal approximations: Filter design and asymptotic equivalence with Shannon's sampling theorem," IEEE Trans. Inform. Theory, vol. 38, pp. 95-103, Jan. 1992.
43. _, "B-spline signal processing. Part I: Theory," IEEE Trans. Signal Processing, vol. 41, pp. 821-833, Feb. 1993.
44. _, "B-spline signal processing. Part II: Efficient design and applications," IEEE Trans. Signal Processing, vol. 41, pp. 834-848, Feb. 1993.
45. M. Unser and I. Daubechies, "On the approximation power of convolution-based least squares versus interpolation," IEEE Trans. Signal Processing, vol. 45, pp. 1697-1711, July 1997.
46. G. Wahba, Spline Models for Observational Data. Philadelphia, PA: SIAM, 1990.
47. J. Wang and F. Cohen, "Part II: 3-D object recognition and shape estimation from image contours using B-splines, shape invariant matching, and neural networks," IEEE Trans. Pattern Anal. Machine Intell., vol. 16, pp. 13-23, Jan. 1994.
48. M. Wang, J. Evans, L. Hassebrook, and C. Knapp, "A multistage, optimal active contour model," IEEE Trans. Image Processing, vol. 5, pp. 1586-1591, Nov. 1996.
49. D. Williams and M. Shah, "A fast algorithm for active contours and curvature estimation," Comput. Vis. Graph. Image Process., vol. 55, no. 1, pp. 14-26, 1992.
50. G. Xu, E. Segawa, and S. Tsuji, "Robust active contours with insensitive parameters," Pattern Recognit., vol. 27, no. 7, pp. 879-884, 1994.
51. F. Yamaguchi, Curves and Surfaces in Computer Aided Geometric Design. Berlin, Germany: Springer-Verlag, 1988.