Two-dimensional directional wavelets in image processing

International Journal of Imaging Systems and Technology

Volumn 7, Issue 3, 1996, Pages 152-165

  Antoine, J P ^a   Vandergheynst, P ^a   Murenzi, R ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b CLARK ATLANTA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EDGE DETECTION; IMAGE ANALYSIS; WAVELET TRANSFORMS;

TWO DIMENSIONAL CONTINUOUS WAVELET TRANSFORM; TWO DIMENSIONAL DIRECTIONAL WAVELETS; WAVELET CALIBRATION;

IMAGE PROCESSING;

EID: 0030230668     PISSN: 08999457     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-1098(199623)7:3<152::AID-IMA1>3.0.CO;2-7     Document Type: Article

References (39)

1. I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia), 1992.
2. Y. Meyer, Les Ondelettes, Algorithmes et Applications (Armand Colin, Paris), 1992; English translation: Wavelets (Cambridge University Press, New York, 1993.
3. Y. Meyer, Les Ondelettes, Algorithmes et Applications (Armand Colin, Paris), 1992; English translation: Wavelets (Cambridge University Press, New York, 1993.
4. J.-M. Combes, A. Grossmann, and Ph. Tchatmitchian (eds.), Wavelets, Time-Frequency Methods and Phase Space (Proceedings of Marseille 1987). Springer-Verlag, Berlin, 1989.
5. Y. Meyer (ed.), Wavelets and Applications (Proceedings of Marseille 1989) (Springer-Verlag, Berlin), 1991.
6. Y. Meyer and S. Roques (eds.), Progress in Wavelet Analysis and Applications (Proceedings of Toulouse 1992) (Frontières, Gif-sur-Yvette), 1993.
7. S. G. Mallat, "Multifrequency channel decompositions of images and wavelet models," IEEE Trans. Acoust. Speech Signal Process. 37, 2091-2110 (1989).
8. S. G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Machine Intell. 11, 674-693 (1989).
9. R. Murenzi, "Wavelet transforms associated to the n-dimensional Euclidean group with dilations: Signals in more than one dimension," in Wavelets, Time-Frequency Methods and Phase Space (Proceedings of Marseille 1987. J. M. Combes, A. Grossman, and Ph. Tchamitchian (eds.), Springer-Verlag, Berlin, 1989, pp. 239-246.
10. R. Murenzi, Ondelettes multidimensionnelles et applications à l' analyse d'images, Thèse de Doctorat, Université Catholique de Louvain, Louvain-la-Neuve, 1990.
11. D. Marr and E. Hildreth, "Theory of edge detection," Proc. R. Soc. Lond. B 207, 187-217 (1980).
12. A. Grossmann, "Wavelet transform and edge detection," in Stochastic Processes in Physics and Engineering. Ph. Blanchard, L. Streit, and M. Hazenwinkel (eds.), Reidel, Dordrecht, 1986.
13. M. Holschneider, Wavelets, an Analysis Tool (Oxford University Press, Oxford), 1955.
14. S. Mallat and S. Zhong, "Wavelet maxima representation," in Wavelets and Applications. Y. Meyer (ed.), Springer-Verlag, Berlin, 1991, pp. 207-284.
15. J.-P. Antoine, P. Carrette, R. Murenzi, and B. Piette, "Image analysis with two-dimensional continuous wavelet transform," Signal Proc. 31, 241-272 (1993).
16. J.-P. Antoine and R. Murenzi, "The continuous wavelet transform, from 1 to 3 dimensions," in Subband and Wavelet Transforms: Design and Applications. A. N. Akansu and M. J. T. Smith (eds.), Kluwer, Dordrecht, 1995, pp. 149-187.
17. M. Holschneider and Ph. Tchamitchian, "Pointwise analysis of Riemann's 'nondifferentiable' function," Invent. Math. 105, 157-175 (1991).
18. A. Grossmann and J. Morlet, "Decomposition of functions into wavelets of constant shape, and related transforms," in Mathematics + Physics, Lectures on Recent Results. L. Streit (ed.), World Scientific, Singapore, 1985.
19. S. T. Ali, J.-P. Antoine, J.-P. Gazeau, and U. A. Mueller, "Coherent states and their generalizations: A mathematical overview," Reviews Math. Phys. (in press).
20. I. Daubechies, A. Grossmann, and Y. Meyer, "Painless nonorthogonal expansions," J. Math. Phys. 27, 1271-1283 (1986).
21. I. Daubechies, "The wavelet transform, time-frequency localization and signal analysis," IEEE Trans. Inform. Theory 36, 961-1005 (1990).
22. J. G. Daugman, "Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression," IEEE Trans. Acoust. Speech, Signal Process. 36, 1169-1179 (1988).
23. A. B. Watson and A. J. Ahumada, Jr., "A hexagonal orthogonal-oriented pyramid as a model of image representation in visual cortex," IEEE Trans. Biomed. Eng. 37, 97-105 (1989).
24. J.-P. Antoine and R. Murenzi, "Two-dimensional directional wavelets and the scale-angle representation," preprint UCL-IPT-95-03.
25. E. Slezak, A. Bijaoui, and G. Mars, "Identification of structures from galaxy counts. Use of the wavelet transform," Astron. Astrophys. 227, 301-316 (1990).
26. M. Farge and Th. Philipovitch, "Coherent structure analysis and extraction using wavelets," in Progress in Wavelet Analysis and Applications (Proceedings of Toulouse 1992). Y. Meyer and S. Roques (eds.), Frontières, Gif-sur-Yvette, 1993, pp. 477-481.
27. M. Farge, "Wavelet transforms and their applications to turbulence," Anna. Rev. Fluid Mech. 24, 395-457 (1992).
28. D. Marr, Vision (Freeman, San Francisco), 1982.
29. C. K. Chui, An Introduction to Wavelets (Academic Press, San Diego), 1992.
30. A. Arnédo, F. Argoul, E. Bacry, J. Elezgaray, E. Freysz, G. Grasseau, J. Grasseau, J. F. Muzy and B. Pouligny, "Wavelet transform of fractals," in Wavelets and Applications. Y. Meyer (eds.), Springer-Verlag, Berlin, 1991, pp. 286-352.
31. J.-P. Antoine, M. Duval-Destin, R. Murenzi and B. Piette, "Image analysis with 2D wavelet transform: detection of position, orientation and visual contrast of simple objects," in Wavelets and Applications. Y. Meyer (ed.), Springer-Verlag, Berlin, 1991, pp. 144-159.
32. M. Duval-Destin, Analyse spatiale et spatio-temporelle de la stimulation visuelle à l'aide de la transformée en ondelettes, Thèse de Doctorat, Université d'Aix-Marseille II, 1991.
33. J.-R Antoine, P. Vandergheynst, K. Bouyoucef, and R. Murenzi, "Alternative representations of an image via the 2D wavelet transform. Application to character recognition," in Proceedings of the Conference on "Visual Information Processing IV," SPIE's Symposium on Optical Engineering/Aerospace Sensing and Dual Use Photonics. Orlando, Florida, April 1995.
34. W. Wisnoe, P. Gajan, A. Strzelecki, C. Lempereur, and J.-M. Mathé, "The use of the two-dimensional wavelet transform in flow visualization processing," in Progress in Wavelet Analysis and Applications. Y. Meyer and S. Roques (ed.), Frontières, Gif-sur-Yvette, 1993, pp. 455-458.
35. W. Wisnoe, Utilisation de la méthode de transformée en ondelettes 2-D pour r analyse de visualisation d'écoulements, Thése de Doctorat ENSAE, Toulouse, 1993.
36. G. Saracco, A. Grossmann, and Ph. Tchamitchian, "Use of wavelet transforms in the study of propagation of transient acoustic signals across a plane interface between two homogeneous media," in Wavelets, Time-Frequency Methods and Phase Space, J.-M. Combes, A. Grossmann, and Ph. Tchamitchian (eds.), Springer-Verlag, Berlin, 1989, pp. 139-146.
37. J.-P Antoine, P. Vandergheynst, K. Bouyoucef, and R. Murenzi, "Target detection and recognition using two-dimensional continuous isotropic and anisotropic wavelets," in Proceedings of the Conference on "Automatic Object Recognition V", SPIE's 1995 Symposium on Optical Engineering/Aerospace Sensing and Dual Use Photonics, Orlando, Florida, April 1995, pp. 20-31.
38. D. Astruc, L. Plantié, R. Murenzi, Y. Lebret, and D. Vandromme, "On the use of the 3-D wavelet transform for the analysis of computational fluid dynamics results," in Progress in Wavelets Analysis and Applications. Y. Meyer and S. Roques (eds.), Frontières, Gif-sur-Yvette, 1993, pp. 463-470.
39. J.-P. Antoine and R. Murenzi, "Isotropic and anisotropic 3-D wavelets: Detection of position and orientation of 3-D objects," in Tempsfréquence, Ondelettes et Multirésolution: Théorie, Modèles et Applications (Proceedings of Lyon 1994). R. Goutte (ed.), CNRS-INSA, Lyon, 1994, pp. 44.1-44.5.