Image Enhancement of Medical Images using Gabor Filter Bank on Hexagonal Sampled Grids
For about two decades scientists have been
developing techniques for enhancing the quality of medical images
using Fourier transform, DWT (Discrete wavelet transform),PDE
model etc., Gabor wavelet on hexagonal sampled grid of the images
is proposed in this work. This method has optimal approximation
theoretic performances, for a good quality image. The computational
cost is considerably low when compared to similar processing in the
rectangular domain. As X-ray images contain light scattered pixels,
instead of unique sigma, the parameter sigma of 0.5 to 3 is found to
satisfy most of the image interpolation requirements in terms of high
Peak Signal-to-Noise Ratio (PSNR) , lower Mean Squared Error
(MSE) and better image quality by adopting windowing technique.
[1] R. S, L. S. Rotolo, C. M. Park, T. J. Golab," X-RAY Image
Enhancement" , IEEE,1980.
[2] Hakan O¨ ktem, Karen Egiazarian, Jarkko Niittylahti Juha Lemmetti,"
An approach to adaptive Enhancement of Diagnostic X-Ray Images ,"
EURASIP Journal on Applied Signal Processing 2003:5, 430-436.
[3] Du-Yih TSAI and Katsuyuki KOJIMA,"Wavelet coefficient mapping
for enhancement of chest x-ray images, " Proceedings, XVII IMEKO
World Congress, June 22 - 27, 2003, Dubrovnik, Croatia.
[4] Tomoko Tateyama, Zensho Nakao, Xianhua Han and Yen-Wei Chen,"
Contrast enhancement of MR brain images by Canonical correlations
based Kernel independent component analysis," International Journal of
Innovative Computing, Information and Control, Vol.5, No.7, July 2009.
[5] Yan-Fei Zhao, Qing- Wei Gao, De-Xiang Zhang, and Yi-Xiang Lu,"
Medical X-Ray Image Enhancement Based on Kramer-s PDE Model,"
Journal of Electronic Science and Technology of China, Vol. 5, No. 2,
June 2007.
[6] M. Dirk Robinson , Sina Farsiu, Joseph Y. Lo and Cynthia A. Toth ,"
Efficient Restoration and Enhancement of Super-resolved X-ray
Images," ICIP , IEEE , 2008.
[7] M.Golay, "Hexagonal parallel pattern transformation", IEEE
Transactions on computers, Vol. 18, No.8, pp.733- 740, 1969.
[8] R.M.Mersereau., "The process of hexagonally sampled Two -
dimensional signals", Proceedings of the IEEE, Vol 67, pp.930-949,
1979.
[9] B.Kamgar-Parsi and W.A. Sander, III, "Quantization error in spatial
sampling: comparison between square and hexagonal pixels", Computer
Vision and Pattern Recognition, Proceedings CVPR ÔÇÿ89- pp. 604 - 611,
1989.
[10] B.Kamgar-Parsi, "Quantization error in hexagonal sensory
configurations", IEEE Transactions on Pattern Analysis and Machine
Intelligence, Vol.14, No.6, pp. 665-671, 1992.
[11] J.P.Mylopoulos and T.Pavlidis, "On the topological properties of
quantized spaces, I. the notion of dimension", Journal of the ACM
(JACM), Vol.18, No.2, pp. 239-246, 1971.
[12] J.P.Mylopoulos and T.Pavlidis, "On the topological properties of
quantized spaces, II. connectivity and order of connectivity", Journal of
the ACM (JACM), Vol 18,No 2, pp.247- 254,1971.
[13] R.Vitulli, et al., "Aliasing effects mitigation by optimized sampling grids
and impact on image acquisition chains", Geoscience and Remote
Sensing Symposium, IGARSS '02, pp. 979-981, 2002.
[14] Eric Anterrieu, Philippe Waldteufel and André Lannes, "Apodization
Functions for 2-D Hexagonally Sampled Synthetic Aperture Imaging
Radiometers", IEEE Transactions On Geoscience And Remote
Sensing, Vol. 40, No. 12, pp. 2531-2542, December 2002.
[15] Lee Middleton and Jayanthi Sivaswamy , "Hexagonal Image Processing
- A Practical approach", Springer-Verlag London Limited, 2005.
[16] Senthil Periaswamy, "Detection of Micro calcifications in Mammograms
Using Hexagonal Wavelets", Thesis work, University of South Carolina,
1996.
[17] L. Condat, D. Van De Ville, and T. Blu, "Hexagonal versus orthogonal
lattices: A new comparison using approximation theory," in Proceedings
of IEEE, ICIP,Vol. 3, Sept. 2005.
[18] M. Unser, "Splines: A perfect fit for signal and image processing," IEEE
Signal Processing Magazine., Vol. 16, No. 6, pp. 22-38, Nov. 1999.
[19] D. Van De Ville, W. Philips, and I. Lemahieu, "Least-squares spline
resampling to a hexagonal lattice," Signal Processing: Image
Communication, Vol. 17, No. 5, pp. 393-408, May 2002.
[20] L. Condat and D. Van De Ville , "Quasi-interpolating spline models for
hexagonally sampled data," IEEE Transactions on Image Processing,
Vol. 16, No. 5, May 2007, pp.1195-1206.
[21] P. Th'evenaz, T. Blu, and M. Unser, "Interpolation revisited," IEEE
Transactions on Medical Imaging , Vol. 19, No.7, pp. 739-758, July
2000.
[22] D. E. Dudgeon and M. E. Mersereau, Multidimensional Signal
Processing. Englewood Cliffs, NJ: Prentice-Hall, 1984.
[23] D. Van De Ville, T. Blu,M. Unser,W. Philips and I. Lemahieu, "Hexspline:
A novel family for hexagonal lattices," IEEE Transactions on
Image Processing, Vol. 13, No. 6, June 2004, pp.758-772.
[24] Laurent Condat and Dimitri Van De Ville,"Three-directional boxsplines:
Characterization and efficient evaluation," IEEE Signal
Processing Letters., Vol. 13, No. 7, July 2006 , pp. 417-420.
[25] C. de Boor, K. Hollig, and S. Riemenschneider, "Box Splines":
Springer-Verlag, 1993, Applied Mathematical Sciences,Vol. 98.
[26] H. Prautzsch and W. Boehm, "Box splines," in Handbook of Computer
Aided Geometric Design. Berlin: Springer, 2001.
[27] Lee, T.S, "Image Representation Using 2D Gabor Wavelets, IEEE
Transactions on Pattern Analysis and Machine Intelligence, " Vol. 18,
Issue 10, 1996, pp. 951-979.
[28] D. J. Gabor, "Theory of communication," IEE, Vol. 93, No. 26, pp. 429-
457, 1946.
[29] Xu, Y., Zhang, X ," Gabor Filter bank and its Application in the
Fingerprint Texture Analysis," PDCAT 2005, pp. 829-831.
[30] Huang, L., Shimizu, A., Kobatake, H , "Classification-Based Face
Detection Using Gabor Filter Features," Proceedings of the IEEE
International Conference on Automatic Face and Gesture Recognition,
2004, pp. 397-402.
[31] Jain, A.K., Prabhakar, S., Hong, L., Pankanti, S,"Filter bank-Based
Fingerprint Matching," IEEE Transactions on Image Processing, Vol. 9,
Issue 5, 2000, pp. 846-859.
[32] Jones, J.P., Palmer, L.A, "An Evaluation of the Two-Dimensional Gabor
Filter Model of Simple Receptive Fields in Cat Striate Cortex, " Journal
of Neurophysiology, Vol. 58, Issue 6, 1987, pp. 1233-1258.
[33] D.Hubel and T.Weisel ," Receptive fields and functional architecture of
monkey striate cortex," Journal of Physiology ,Vol..195, pp.215-
243,1968.
[34] B. S. Manjunath and W. Y. Ma, "Texture features for browsing and
retrieval of image data," IEEE Transactions on Pattern Analysis and
Machine Intelligence., Vol. 18, No 8, August 1996, pp. 837-842.
[35] Mohamed Najim ,"Digital Filters Design for Signal and Image
Processing," ISTE Ltd, USA.
[36] Veni. S, K.A. Narayanankutty, Satyapal Reddy.L, Vidya.P ," Wavelet
based Edge detection and Multiresolution analysis on Hexagonal
Sampled Grid Using Interpolation," proceedings ICSIP - 2009 , August
12-14 2009 , Excel publications, ISBN:978-93-80043-26-5,pp.186-200.
[37] Veni.S, K.A.Narayanankutty , Vidya.P ," Performance analysis of Edge
Detection methods on hexagonal sampling Grid," International Journal
of Electronics Engineering and Research (IJEER), Research India
publications Vol.1, No. 4 (2009) ,pp. 313-328.
[1] R. S, L. S. Rotolo, C. M. Park, T. J. Golab," X-RAY Image
Enhancement" , IEEE,1980.
[2] Hakan O¨ ktem, Karen Egiazarian, Jarkko Niittylahti Juha Lemmetti,"
An approach to adaptive Enhancement of Diagnostic X-Ray Images ,"
EURASIP Journal on Applied Signal Processing 2003:5, 430-436.
[3] Du-Yih TSAI and Katsuyuki KOJIMA,"Wavelet coefficient mapping
for enhancement of chest x-ray images, " Proceedings, XVII IMEKO
World Congress, June 22 - 27, 2003, Dubrovnik, Croatia.
[4] Tomoko Tateyama, Zensho Nakao, Xianhua Han and Yen-Wei Chen,"
Contrast enhancement of MR brain images by Canonical correlations
based Kernel independent component analysis," International Journal of
Innovative Computing, Information and Control, Vol.5, No.7, July 2009.
[5] Yan-Fei Zhao, Qing- Wei Gao, De-Xiang Zhang, and Yi-Xiang Lu,"
Medical X-Ray Image Enhancement Based on Kramer-s PDE Model,"
Journal of Electronic Science and Technology of China, Vol. 5, No. 2,
June 2007.
[6] M. Dirk Robinson , Sina Farsiu, Joseph Y. Lo and Cynthia A. Toth ,"
Efficient Restoration and Enhancement of Super-resolved X-ray
Images," ICIP , IEEE , 2008.
[7] M.Golay, "Hexagonal parallel pattern transformation", IEEE
Transactions on computers, Vol. 18, No.8, pp.733- 740, 1969.
[8] R.M.Mersereau., "The process of hexagonally sampled Two -
dimensional signals", Proceedings of the IEEE, Vol 67, pp.930-949,
1979.
[9] B.Kamgar-Parsi and W.A. Sander, III, "Quantization error in spatial
sampling: comparison between square and hexagonal pixels", Computer
Vision and Pattern Recognition, Proceedings CVPR ÔÇÿ89- pp. 604 - 611,
1989.
[10] B.Kamgar-Parsi, "Quantization error in hexagonal sensory
configurations", IEEE Transactions on Pattern Analysis and Machine
Intelligence, Vol.14, No.6, pp. 665-671, 1992.
[11] J.P.Mylopoulos and T.Pavlidis, "On the topological properties of
quantized spaces, I. the notion of dimension", Journal of the ACM
(JACM), Vol.18, No.2, pp. 239-246, 1971.
[12] J.P.Mylopoulos and T.Pavlidis, "On the topological properties of
quantized spaces, II. connectivity and order of connectivity", Journal of
the ACM (JACM), Vol 18,No 2, pp.247- 254,1971.
[13] R.Vitulli, et al., "Aliasing effects mitigation by optimized sampling grids
and impact on image acquisition chains", Geoscience and Remote
Sensing Symposium, IGARSS '02, pp. 979-981, 2002.
[14] Eric Anterrieu, Philippe Waldteufel and André Lannes, "Apodization
Functions for 2-D Hexagonally Sampled Synthetic Aperture Imaging
Radiometers", IEEE Transactions On Geoscience And Remote
Sensing, Vol. 40, No. 12, pp. 2531-2542, December 2002.
[15] Lee Middleton and Jayanthi Sivaswamy , "Hexagonal Image Processing
- A Practical approach", Springer-Verlag London Limited, 2005.
[16] Senthil Periaswamy, "Detection of Micro calcifications in Mammograms
Using Hexagonal Wavelets", Thesis work, University of South Carolina,
1996.
[17] L. Condat, D. Van De Ville, and T. Blu, "Hexagonal versus orthogonal
lattices: A new comparison using approximation theory," in Proceedings
of IEEE, ICIP,Vol. 3, Sept. 2005.
[18] M. Unser, "Splines: A perfect fit for signal and image processing," IEEE
Signal Processing Magazine., Vol. 16, No. 6, pp. 22-38, Nov. 1999.
[19] D. Van De Ville, W. Philips, and I. Lemahieu, "Least-squares spline
resampling to a hexagonal lattice," Signal Processing: Image
Communication, Vol. 17, No. 5, pp. 393-408, May 2002.
[20] L. Condat and D. Van De Ville , "Quasi-interpolating spline models for
hexagonally sampled data," IEEE Transactions on Image Processing,
Vol. 16, No. 5, May 2007, pp.1195-1206.
[21] P. Th'evenaz, T. Blu, and M. Unser, "Interpolation revisited," IEEE
Transactions on Medical Imaging , Vol. 19, No.7, pp. 739-758, July
2000.
[22] D. E. Dudgeon and M. E. Mersereau, Multidimensional Signal
Processing. Englewood Cliffs, NJ: Prentice-Hall, 1984.
[23] D. Van De Ville, T. Blu,M. Unser,W. Philips and I. Lemahieu, "Hexspline:
A novel family for hexagonal lattices," IEEE Transactions on
Image Processing, Vol. 13, No. 6, June 2004, pp.758-772.
[24] Laurent Condat and Dimitri Van De Ville,"Three-directional boxsplines:
Characterization and efficient evaluation," IEEE Signal
Processing Letters., Vol. 13, No. 7, July 2006 , pp. 417-420.
[25] C. de Boor, K. Hollig, and S. Riemenschneider, "Box Splines":
Springer-Verlag, 1993, Applied Mathematical Sciences,Vol. 98.
[26] H. Prautzsch and W. Boehm, "Box splines," in Handbook of Computer
Aided Geometric Design. Berlin: Springer, 2001.
[27] Lee, T.S, "Image Representation Using 2D Gabor Wavelets, IEEE
Transactions on Pattern Analysis and Machine Intelligence, " Vol. 18,
Issue 10, 1996, pp. 951-979.
[28] D. J. Gabor, "Theory of communication," IEE, Vol. 93, No. 26, pp. 429-
457, 1946.
[29] Xu, Y., Zhang, X ," Gabor Filter bank and its Application in the
Fingerprint Texture Analysis," PDCAT 2005, pp. 829-831.
[30] Huang, L., Shimizu, A., Kobatake, H , "Classification-Based Face
Detection Using Gabor Filter Features," Proceedings of the IEEE
International Conference on Automatic Face and Gesture Recognition,
2004, pp. 397-402.
[31] Jain, A.K., Prabhakar, S., Hong, L., Pankanti, S,"Filter bank-Based
Fingerprint Matching," IEEE Transactions on Image Processing, Vol. 9,
Issue 5, 2000, pp. 846-859.
[32] Jones, J.P., Palmer, L.A, "An Evaluation of the Two-Dimensional Gabor
Filter Model of Simple Receptive Fields in Cat Striate Cortex, " Journal
of Neurophysiology, Vol. 58, Issue 6, 1987, pp. 1233-1258.
[33] D.Hubel and T.Weisel ," Receptive fields and functional architecture of
monkey striate cortex," Journal of Physiology ,Vol..195, pp.215-
243,1968.
[34] B. S. Manjunath and W. Y. Ma, "Texture features for browsing and
retrieval of image data," IEEE Transactions on Pattern Analysis and
Machine Intelligence., Vol. 18, No 8, August 1996, pp. 837-842.
[35] Mohamed Najim ,"Digital Filters Design for Signal and Image
Processing," ISTE Ltd, USA.
[36] Veni. S, K.A. Narayanankutty, Satyapal Reddy.L, Vidya.P ," Wavelet
based Edge detection and Multiresolution analysis on Hexagonal
Sampled Grid Using Interpolation," proceedings ICSIP - 2009 , August
12-14 2009 , Excel publications, ISBN:978-93-80043-26-5,pp.186-200.
[37] Veni.S, K.A.Narayanankutty , Vidya.P ," Performance analysis of Edge
Detection methods on hexagonal sampling Grid," International Journal
of Electronics Engineering and Research (IJEER), Research India
publications Vol.1, No. 4 (2009) ,pp. 313-328.
@article{"International Journal of Electrical, Electronic and Communication Sciences:62178", author = "Veni.S and K.A.Narayanankutty", title = "Image Enhancement of Medical Images using Gabor Filter Bank on Hexagonal Sampled Grids", abstract = "For about two decades scientists have been
developing techniques for enhancing the quality of medical images
using Fourier transform, DWT (Discrete wavelet transform),PDE
model etc., Gabor wavelet on hexagonal sampled grid of the images
is proposed in this work. This method has optimal approximation
theoretic performances, for a good quality image. The computational
cost is considerably low when compared to similar processing in the
rectangular domain. As X-ray images contain light scattered pixels,
instead of unique sigma, the parameter sigma of 0.5 to 3 is found to
satisfy most of the image interpolation requirements in terms of high
Peak Signal-to-Noise Ratio (PSNR) , lower Mean Squared Error
(MSE) and better image quality by adopting windowing technique.", keywords = "Hexagonal lattices, Gabor filter, Interpolation, imageprocessing.", volume = "4", number = "5", pages = "861-6", }
