Shape analysis and symmetry detection in gray-level objects using the analytical Fourier-Mellin representation

Signal Processing

Volumn 84, Issue 1, 2004, Pages 25-39

  Derrode, Stéphane ^a   Ghorbel, Faouzi ^b  

^a AIX MARSEILLE UNIVERSITÉ   (France)

^b Laboratoire Cristal   (Tunisia)

Author keywords

Analytical Fourier Mellin transform; Gray levels object; Hausdorff distance; Rotational and reflectional symmetries estimation; Scale and rotation parameters estimation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FOURIER TRANSFORMS; HARMONIC ANALYSIS; INVARIANCE; PARAMETER ESTIMATION; ROTATION;

GRAY LEVEL OBJECTS;

SIGNAL DETECTION;

EID: 0344494101     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2003.07.006     Document Type: Article

References (28)

1. L. Benyoussef, Y. Delignon, F. Ghorbel, An optimal matched filter for target detection in images distorted by noise, Proceedings of the International Conference on Geoscience and Remote Sensing, Vol. 2, Seatle (USA), 6-10 July 1998, pp. 1001-1003.
2. Chen Q., Defrise M., Deconinck F. Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition. IEEE Trans. Pattern Anal. Machine Intell. 16(12):1994;1156-1168.
3. Daoudi M., Ghorbel F., Mokadem A., Avaro O., Sanson H. Shape distances for contour tracking and motion estimation. Pattern Recognition. 32:June 1999;1297-1306.
4. De Bougrenet de la Tocnaye J.L., Ghorbel F. Scale-rotation invariant pattern recognition applied to image data compression. Pattern Recognition Lett. 8:July 1988;55-58.
5. Derrode S., Ghorbel F. Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description. Comput. Vision Image Understand. 83(1):July 2001;57-78.
6. Dieudonné J. Éléments d'analyse, Tome II. 3rd Edition:1983;Gauthier-Villars, Cahiers Scientifiques, Paris (Fr.).
7. Ghorbel F. A complete invariant description for gray-level images by the harmonic analysis approach. Pattern Recognition Lett. 15:October 1994;1043-1051.
8. Ghorbel F. Towards a unitary formulation for invariant image description, Application to image coding. Ann. Telecommun. 53(3):May 1998;143-153.
9. Grace A.E., Spann M. A comparison between Fourier-Mellin descriptors and moment based features for invariant object recognition using neural networks. Pattern Recognition Lett. 12:October 1991;635-643.
10. Hagedoorn M., Veltkamp R.C. Reliable and efficient pattern matching using an affine invariant metric. Internat. J. Comput. Vision. 31(2/3):April 1999;203-225.
11. Huttenlocher D.P., Klanderman G.A., Rucklidge W.J. Comparing images using the Hausdorff distance. IEEE Trans. Pattern Anal. Machine Intell. 15(9):September 1993;850-863.
12. Huttenlocher D.P., Ullman S. Recognizing solid objects by alignment with an image. Internat. J. Comput. Vision. 5(2):1990;195-212.
13. T.M. Lehmann, A two-stage algorithm for model-based registration of medical images, in: Proceedings of the Fourth International Conference on Pattern Recognition, Vol. 1, 1998, pp. 344-351.
14. Lenz R. Describing and recognizing group-invariant pattern classes with group-sampling. Pattern Recognition Lett. 9:April 1989;169-173.
15. Lenz R. Goos G., Hartmanis J. Group Theoretical Methods in Image Processing. Lecture Notes in Computer Science. Vol. 413:1990;Springer, Berlin, Germany.
16. Milanese R., Cherbuliez M. A rotation-, translation-, and scale-invariant approach to content-based image retrieval. J. Visual Commun. Image Represent. 10:June 1999;186-196.
17. M. Pavel, Fundamentals of pattern recognition, in: Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1989.
18. Press W.H., Teukolsky S.A., Vetterling A.T., Flannery B.P. Numerical Recipes in C, the Art of Scientific Computing. 2nd Edition:1983;Cambridge University Press, Cambridge.
19. Rothe I., Voss K., Suesse H. The method of normalization to determine invariants. IEEE Trans. Pattern Anal. Machine Intell. 18(4):April 1996;366-375.
20. Rucklidge W.J. Efficient visual recognition using the Hausdorff distance. Lecture Notes in Computer Science. Vol. 1173:1996;Springer, Berlin, Germany.
21. Rudin W. Fourier Analysis on Groups. 1990;Wiley Classics, New York.
22. Shen D., Ip H.H.S., Cheung K.K.T., Teoh E.K. Symmetry detection by generalized complex (GC) moments. A close-form solution IEEE Trans. Pattern Anal. Machine Intell. 21(5):May 1999;466-475.
23. Shen D., Ip H.H.S., Teoh E.K. An energy of asymmetry for accurate detection of global reflection axes. Image Vision Comput. 19:2001;283-297.
24. Sheng Y., Arsenault H.H. Experiments on pattern recognition using invariant Fourier-Mellin descriptors. J. Opt. Soc. Amer. A. 3(6):June 1986;771-776.
25. Turski J. Projective Fourier analysis for patterns. Pattern Recognition. 33:2000;2033-2043.
26. G. Tzanetakis, M. Traka, G. Tziritas, Motion estimation based on affine moment invariants, in: IX European Signal Processing Conference (Eusipco98), Vol. 2, Island of Rhodes, Greece, September 8-11 1998, pp. 925-929.
27. X. Yi, O.I. Camps, Line feature based recognition using Hausdorff distance, in: Proceedings of the First International Symposium on Computer Vision, Coral Gables (Fl.), November 1995, pp. 79-84.
28. Zwicke P.E., Kiss Z. A new implementation of the Mellin transform and its application to radar classification. IEEE Trans. Pattern Anal. Mach. Intell. 5(2):March 1983;191-199.