Local quaternion Fourier transform and color image texture analysis

Signal Processing

Volumn 90, Issue 6, 2010, Pages 1825-1835

  Assefa, Dawit ^a   Mansinha, Lalu ^b   Tiampo, Kristy F ^b   Rasmussen, Henning ^b   Abdella, Kenzu ^c  

^a PRINCESS MARGARET HOSPITAL   (Canada)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

^c TRENT UNIVERSITY   (Canada)

Author keywords

Color image analysis; Fourier; Hartley; Quaternion; S transform

Indexed keywords

COLOR IMAGE ANALYSIS; COLOR IMAGES; COMPUTATIONAL ASPECTS; FOURIER; GAUSSIANS; HARTLEY; INVERTIBILITY; JOINT SPACE; LOCAL COLOR; PATTERN ANALYSIS; ROTATION INVARIANCE; S TRANSFORMS; SIMULTANEOUS DETERMINATIONS; WAVE NUMBERS;

COLOR; COLOR IMAGE PROCESSING; IMAGE ANALYSIS; TEXTURES; TWO DIMENSIONAL;

FOURIER TRANSFORMS;

EID: 76749104248     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2009.11.031     Document Type: Article

References (64)

1. R.N. Bracewell, The Fourier Transform and its Applications, McGraw-Hill Series in Electrical Engineering, Circuits and Systems, New York, 1986.
2. Gabor D. Theory of communication. J. Inst. Elect. Eng. 93 26 (1946) 429-457
3. Bovik A.C., Clark M., and Geisler W.S. Multichannel texture analysis using localized spatial filters. IEEE Trans. Pattern Anal. Mach. Intell. 12 1 (January 1990) 55-73
4. Kingsbury N. Image processing with complex wavelets. Philos. Trans. R. Soc. London Ser. A 357 1760 (1999) 2543-2560
5. Lina J. Image processing with complex daubechies wavelets. J. Math. Imag. Vision 7 3 (June 1997) 211-223
6. R. Polikar, The Wavelet tutorial, Rowan University [Online], 1996. Available: 〈http://engineering.rowan.edu/∼polikar/Wavelets〉.
7. Eramian M., Schincariol R.A., Stockwell R.G., Lowe R.P., and Mansinha L. Review of applications of 1- and 2-D S transforms. SPIE Proc. Ser. 3078 (April 1997) 558-568
8. Mansinha L., Stockwell R.G., and Lowe R.P. Pattern analysis with two-dimensional spectral localization: applications of two-dimensional S transforms. Physica A 239 1 (May 1997) 286-295
9. Mansinha L., Stockwell R.G., Lowe R.P., Eramian M., and Schincariol R.A. Local S-spectrum analysis of 1-D and 2-D data. Phys. Earth Planet. Interi. 103 3 (November 1997) 329-336
10. R.G. Stockwell, S-transform analysis of gravity wave activity, Ph.D. Dissertation, Department of Physics and Astronomy, The University of Western Ontario, London, Ont., Canada, 1999.
11. Y. Zhou, Boundary detection in petrographic images and applications of S-transform space-wavenumber analysis to image processing for texture definition, Ph.D. Dissertation, Department of Earth Sciences, The University of Western Ontario, London, Ont., Canada, 2002.
12. Pascale D. A Review of RGB Color Spaces ... from xyY to R'G'B' (2003), The BabelColor Company, Montreal (Quebec), Canada
13. A.K. Douglas, P.E. Color and color spaces [Online], November 2005. Available: 〈http://doug.kerr.home.att.net/pumpkin/Color_Models.pdf〉.
14. Ell T.A., and Sangwine S.J. Hypercomplex Fourier transforms of color images. IEEE Trans. Image Proc. 16 1 (January 2007) 22-35
15. S.J. Sangwine, T.A. Ell, Hypercomplex Fourier transforms of color images, in: IEEE International Conference on Image Processing (ICIP 2001), vol. 1, Thessaloniki, Greece, October 2001, pp. 137-140.
16. S.J. Sangwine, The problem of defining the Fourier transform of a color image, in: IEEE Proceedings of the International Conference on Image Processing (ICIP 98), vol. 1, Chicago, IL, USA, October 1998, pp. 171-175.
17. S.J. Sangwine, T.A. Ell, Hypercomplex auto and cross-correlation of color images, in: IEEE Proceedings of the International Conference on Image Processing (ICIP 99), vol. 4, Kobe, Japan, October 1999, pp. 319-322.
18. S.J. Sangwine, T.A. Ell, B.N. Gatsheni, Color-dependent linear vector image filtering, in: Proceedings of the EUSIPCO 2004, 12th European Signal Processing Conference, Vienna, Austria, September 6-10, 2004, pp. 585-588.
19. Denis P., Carre P., and Fernandez-Maloigne C. Spatial and spectral quaternionic approaches for colour images. Comput. Vision Image Understanding 107 1-2 (July 2007) 74-87
20. N. Le Bihan, S.J. Sangwine, Quaternion principal component analysis of color images, in: IEEE International Conference on Image Processing, vol. 1, September 2003, pp. 809-812.
21. S.C. Pei, J.H. Chang, J.J. Ding, Quaternion matrix singular value decomposition and its applications for color image processing, in: IEEE International Conference on Image Processing, vol. 1, September 2003, pp. 805-808.
22. T. Bülow, G. Sommer, Quaternionic Gabor filters for local structure classification, in: Proceedings of the 14th Annual Conference on Pattern Recognition, vol. 11, 1998, pp. 808-810.
23. Bayro-Corrochano E. The theory and use of the quaternion wavelet transform. J. Math. Imaging Vision 24 1 (2006) 19-35
24. Chan W.L., Choi H., and Baraniuk R.G. Coherent multiscale image processing using dual-tree quaternion wavelets. IEEE Trans. Image Process. 17 7 (July 2008) 1069-1082
25. Tüceryan M., and Jain A.K. Texture analysis. In: Chen C.H., Pau L.F., and Wang P.S.P. (Eds). The Handbook of Pattern Recognition and Computer Vision. second ed. (1998), World Scientific Publishing Co., Singapore 207-248
26. Sonka M., Hlavac V., and Boyle R. Image Processing Analysis and Machine Vision. second ed. (2001), Thomson Asia Pte Ltd and PPTPH, Berlin
27. Grigorescu S.E., Petkov N., and Kruizinga P. Comparison of texture features based on Gabor filters. IEEE Trans. Image Process. 11 10 (October 2002) 1160-1167
28. X.-F. Song, Z.-G. Chen, C.-L.Wen, Q.-B. Ge, Wavelet transform-based texture segmentation using feature smoothing, in: IEEE International Conference on Machine Learning and Cybernetics, vol. 2003, November 2003, pp. 2370-2373.
29. Palm C., and Lehmann T.M. Classification of color textures by Gabor filtering. J. Mach. Graph. Vis. 11 2/3 (2002) 195-219
30. Hoang M.A., Geusebroek J.M., and Smeulders A.W.M. Color texture measurement and segmentation. Signal Process. 85 (2005) 265-275
31. H. Wang, X.-H. Wang, Y. Zhou, J. Yang, Color texture segmentation using quaternion-Gabor filters, in: IEEE International Conference on Image Processing (ICIP 2006), Atlanta, GA, USA, October 2006, pp. 745-748.
32. Shi L., and Funt B. Quaternion color texture segmentation. Comput. Vision Image Understanding 107 1-2 (July 2007) 88-96
33. L. Shi, Exploration in quaternion colour, M.S. Thesis, School of Computing Science, Simon Fraser University, Burnaby, BC, Canada, 2005.
34. W.R. Hamilton, Lectures on Quaternions, Hodges and Smith, Dublin, 1853. [Online]. Available: 〈http://historical.library.cornell.edu/math/〉.
35. T.A. Ell, Quaternion-Fourier transforms for analysis of two-dimensional linear time-invariant partial differential systems, in: IEEE Proceedings of the 32nd Conference on Decision and Control, San Antonio, TX, USA, December 1993, pp. 1830-1841.
36. T. Bülow, G. Sommer, Multi-dimensional signal processing using an algebraically extended signal representation, in: G. Sommer, J.J. Koenderink (Eds.), AFPAC'97 Kiel, Lecture Notes in Computer Science, vol. 15, Springer, Berlin, 1997, pp. 148-163.
37. S.J. Sangwine, The discrete quaternion Fourier transform, in: IEEE 6th International Conference on Image Processing and its Applications (IPA97), vol. 2, Dublin, Ireland, July 1997, pp. 790-793.
38. Hitzer E.M.S. Quaternion Fourier transform on quaternion fields and generalizations. J. Adv. Appl. Clifford Alg. 17 3 (August 2007) 497-517
39. Pei S.-C., Ding J.-J., and Chang J.-H. Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT. IEEE Trans. Signal Process. 49 11 (November 2001) 2783-2797
40. Felsberg M., Bülow T., and Sommer G. Commutative hypercomplex Fourier transforms of multidimensional signals. Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and Robotics (2001), Springer, London 209-229
41. Bülow T., and Sommer G. Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case. IEEE Trans. Signal Process. 49 11 (November 2001) 2844-2852
42. T.A. Ell, S.J. Sangwine, Decomposition of 2D hypercomplex Fourier transforms into pairs of complex Fourier transforms, in: 10th Signal Processing Conference on Theory and Applications, Proceedings of the EUSIPCO, vol. 2, Tampere, Finland, September 2000, pp. 1061-1064.
43. Chernov V.M. Arithmetic method in the theory of discrete orthogonal transforms. Proc. SPIE 2363 (1995) 134-141
44. Felsberg M., Bülow T., Sommer G., and Chernov V.M. Fast algorithms for the hypercomplex Fourier transforms. Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and Robotics (2001), Springer, Berlin 231-254
45. V.M. Chernov, Discrete orthogonal transforms with data representation in composition algebras, in: Proceedings of the 9th Scandinavian Conference on Image Analysis (SCIA'95), vol. 1, Uppsala, Sweden, 1995, pp. 357-364.
46. V.M. Chernov, Hurwitzion algebra and its application to the FFT synthesis, in: G. Sommer, Y.Y. Zeevi (Eds.), Algebraic Frames for the Perception-Action Cycle (AFPAC 2000), Springer-Verlag Lecture Notes in Comput Science, vol. 1888, 2000, pp. 154-163.
47. V.M. Chernov, Clifford algebras as projections of group algebras, in: E. Bayro-Corrochano, G. Sobczyk, (Eds.), Advances in Geometric Algebra with Applications in Science and Engineering, Birkhauser, Boston, 2001, pp. 467-482.
48. Chernov V.M. Some FFT-like algorithms for RGB-spectra calculation. Mach. Graph. Vision Int. J. 11 2/3 (2002) 139-151
49. Davenport C.M. A commutative hypercomplex algebra with associated function theory. In: Ablamowicz R., Lounesto P., and Parra J.M. (Eds). Clifford Algebras with Numeric and Symbolic Computations (1996), Birkhauser, Boston, MA 213-227
50. Pei S.-C., Chang J.H., and Ding J.J. Commutative reduced biquaternions and their Fourier transform for signal and image processing applications. IEEE Trans. Signal Process. 52 7 (July 2004) 2012-2031
51. Said S., Bihan N.L., and Sangwine S.J. Fast complexified quaternion Fourier transform. IEEE Trans. Signal Process. 56 4 (April 2008) 1522-1531
52. M. Felsberg, G. Sommer, Optimized fast algorithms for the quaternionic Fourier transform, in: Proceedings of the 8th International Conference on Comput Analysis of Images and Patterns, vol. 1689, Ljubljana, Slovenia, September 1999, pp. 209-216.
53. A.N. Belbachir, T. Chilton, M. Dunn, M. Nunkesser, S. Sidhom, G. Szajnowski, Image compression using Hartley transform, Pattern Recognition and Image Processing Group, Institute of Computer Aided Automation, Vienna, Austria, Technical Report PRIP-TR-087, December 2003.
54. Bracewell R.N. Assessing the Hartley transform. IEEE Trans. Acoust. Speech Signal Process. 38 12 (December 1990) 2174-2176
55. A.M. Grigoryan, S.S. Agaian, Three algorithms for computing the 2-D discrete Hartley transform, in: IEEE Proceedings of the International Conference on Image Processing, vol. 2, Vancouver, BC, Canada, September 2000, pp. 359-362.
56. Paik C.H., and Fox M.D. Fast Hartley transforms for image processing. IEEE Trans. Med. Imag. 7 2 (June 1988) 149-153
57. Sun H. The Hartley transform applied to particle image velocimetry. Meas. Sci. Technol. 13 12 (December 2002) 1996-2000
58. T. Theußl, R.F. Tobler, E. Gröller, The multi-dimensional Hartley transform as a basis for volume rendering, in: WSCG 2000 Conference Proceedings, February 2000. [Online]. Available: 〈http://citeseer.ist.psu.edu/262068.html〉.
59. R.F. Ullmann, An algorithm for the fast Hartley transform, Stanford Exploration Project (SEP), Technical Report 38, May 1984. [Online]. Available: 〈http://sepwww.stanford.edu/oldreports/sep38/38_29_abs.html〉.
60. Bracewell R.N. The Hartley transform (March 1986), Oxford University Press, Inc., New York, NY
61. Sundararajan N. 2-D Hartley transforms. Geophysics 60 1 (January-February 1995) 262-267
62. Haralick R.M., Shanmugam K., and Dinstein I. Textural features for image classification. IEEE Trans. Systems Man Cybern. SMC-3 6 (November 1973) 610-621
63. R. Muñiz, J.A. Corrales, Novel techniques for color texture classification, in: Proceedings of the IPCV'06, 2006, pp. 114-120.
64. Benèo M., and Hudec R. Novel method for color textures features extraction based on GLCM. Radioengineering-Prague 16 4 (2007) 64-67