Kaiser-Hamming pencere yapısı ve Huang dönüşümü kullanılarak iki boyutlu sayısal süzgeç tasarımı ve imge iyileştirme uygulaması

Yıl 2018, Cilt: 33 Sayı: 4, 1459 - 1474, 19.12.2018

Kemal Avcı

https://doi.org/10.17341/gazimmfd.416442

Öz

İmge iyileştirme işlemleri için uzamsal alanda veya frekans alanda süzme işlemleri yapan iki boyutlu sayısal süzgeçler kullanılmaktadır. Yüksek çözünürlüklü imge iyileştirme işlemleri için hesaplama avantajından dolayı frekans alanda süzme yapan iki boyutlu sayısal süzgeçler tercih edilmektedir. Fakat frekans alan tabanlı iki boyutlu sayısal süzgeç tasarım yöntemlerinde hesap karmaşıklığı fazlalığı, optimum olmayan kötü süzgeç performansı ve elastikiyetsizlik gibi çeşitli sorunlar bulunmaktadır. Ayrıca literatürde önerilen birçok tasarım yönteminde imge üzerinde uygulamanın hiç yapılmadığı görülmektedir. Bu çalışmada önerilen yöntem az hesap karmaşıklığında iyileştirilmiş süzgeç performansı ve elastikiyete sahip bir çözüm sunmaktadır. İmge iyileştirme üzerindeki etkisinin de çalışıldığı önerilen yöntem,  Huang yöntemi kullanarak elde edilen iki boyutlu Kaiser-Hamming pencere ailesinin türetilmesine dayanmaktadır. Önerilen yöntem sabit bir uzunlukta farklı süzgeç karakteristiğine sahip birçok iki boyutlu sayısal süzgeç tasarlanmasını sağlamaktadır. İki imge için farklı süzme örneklerinden elde edilen benzeşim sonuçları, önerilen yöntemle tasarlanan iki boyutlu sayısal süzgeçlerin imge yumuşatma ve imge keskinleştirme gibi imge iyileştirme uygulamaları için istenilen seviyeye göre geniş ölçekte farklı yumuşatma ve keskinleştirme sağlayabileceğini ve ayrıca önerilen pencerenin uzunluk ile bağımsız biçim parametrelerinin imge üzerinde zıt etkiler yarattığını göstermiştir.

Anahtar Kelimeler

İmge işleme, İmge iyileştirme; İki boyutlu sayısal süzgeçler; İki boyutlu Kaiser-Hamming penceresi; Huang yöntemi

Two dimensional digital filter design using Kaiser-Hamming window structure and Huang transform and image enhancement application

Öz

Two dimensional digital filters which perform spatial filtering or frequency domain filtering are used for image enhancement operations. For high resolution image enhancement operations, two-dimensional digital filters which perform filtering in the frequency domain are preferred due to the computational advantage. However, in frequency domain based two dimensional digital filter design methods, there are various issues such as excess of computational complexity, suboptimal bad filter performance, and lack of elasticity. Moreover, in many design methods proposed in the literature, it is seen that there is no application on the image. The proposed method in this study presents a solution with improved filter performance and elasticity in less computational complexity. The proposed method, in which the effect on image enhancement is also studied, is based on the derivation of a two-dimensional Kaiser-Hamming window family obtained using the Huang’s method. The proposed method provides the design of many two-dimensional digital filters with various filter characteristics at a fixed length. Simulation results obtained from various filtering examples for two images show that two dimensional digital filters designed by the proposed method can provide different smoothing and sharpening on a wide scale according to the desired level for image enhancement applications such as image smoothing and image sharpening, and also the length and independent shape parameters of the proposed window have opposite effects on the image.

Anahtar Kelimeler

Image processing, Image enhancement; Two dimensional digital filter; Two dimensional Kaiser-Hamming window; Huang’s method

Kaynakça

• Gonzalez, R.C. ve Woods, R.E., Sayısal Görüntü İşleme, 3. Baskıdan Çeviri, Çeviri Editörü: Telatar, Z., Palme Yayıncılık, Ankara, 2014.
• Makandar, A., Halalli, B., Image enhancement techniques using highpass and lowpass filters, International Journal of Computer Applications, 14:12-15, 2015.
• Lim, J.S., Two-Dimensional Signal And Image Processing, Englewood Cliffs, NJ, Prentice Hall, 1989.
• Lu, W.S., Antoniou, A., Two-Dimensional Digital Filters, Marcel Dekker, New York, 1992.
• Kockanat, S., Karaboga, N., The design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms: a review of the literature, Artif Intell Rev, 44:265–287, 2015.
• Saramaki, T., Computationally efficient circularly symmetric two-dimensional FIR filters, IEE Proceedings-Electronic Circuits and Systems, 131 (2):46-50,1984.
• Dumitrescu, B., Trigonometric polynomials positive on frequency domains and applications to 2-D FIR filter design, IEEE Trans. Signal Process, 54:4282-4292, 2006.
• Lai, X., Cheng, Y., A sequential constrained least-square approach to minimax design of 2-D FIR filters, IEEE Trans. Circuits and Systems II: Express Briefs, 54: 994-998, 2007.
• Zhou, Q., Zha, S., Zhang, J., Li, X., A unified approach for optimal design of 2-D FIR filters using second-order cone programming, Proc. IC WCOM'2010, 1-3, Eylül, 2010.
• Zhao, R., Lai, X., A fast matrix iterative technique for the WLS design of 2-D quadrantally symmetic FIR filters, Multidimens. Syst. Signal Process., 22 (4):303–317, 2011.
• Zhao, R., Lai, X., Fast two-dimensional weighted least squares techniques for the design of two-dimensional finite impulse response filters, J. Control Theory Appl., 11(2):141–146, 2013.
• Zhao, R., Lai, X., Efficient 2-D based algorithms for WLS design of 2-D FIR filters with arbitrary weighting functions, Multidimens. Syst. Signal Process., 24 (3):417–434, 2013.
• Wang, H., A new separable two-dimensional finite impulse response filter design with sparse coefficients, IEEE Transactions on Circuits and Systems I: Regular Papers, 62: 2864 – 2873, 2015.
• Zhao, R., Lai, X., Lin, Z., Weighted squares design of 2-D FIR filters using a matrix-based generalized conjugate gradient method, Journal of Franklin Institute, 353 (8): 1759-1780, 2016.
• McClellan, J.H., The design of two-dimensional digital filters by transformations, in Proc. 7th Ann. Princeton Conf. Inf. Sci., 247–251, 1973.
• Mersereau, R.M., Mecklenbrauker, W.F.G., Quatieri, T.F., McClellan transformations for two-dimensional digital filtering: I-Design, IEEE Trans. Circuits Syst., 23(7): 405-414, 1976.
• Karam, L.J., Two-dimensional FIR filter design by transformation, IEEE Transactions on Signal Processing, 47(5):1474-1478, 1999.
• Shyu, J.J., Pei, S.C., Huang, Y.D., Design of variable two-dimensional FIR digital filters by McClellan transformation, IEEE Trans. Circuits Syst. I Reg. Papers, 56(3):574-582, 2009.
• Liu, J.C., Tai, Y.L., Design of 2-D wideband circularly symmetric FIR filters by multiplierless high-order transformation, IEEE Transactions on Circuits and Systems I: Regular Papers, 58(4):746-754, 2011.
• Bindima, T., Manuel, M., Elias, E., An efficient transformation for two dimensional circularly symmetric wideband FIR filters, Proceedings of the 2016 IEEE Region 10 Conference (TENCON), 22-25 Kasım, 2838-2841, Singapore, 2016
• Hu, J.V., Rabiner, L.R., Design techniques for two-dimensional digital filters, IEEE Trans. Audio Electroacoust., 20:249-257, 1972.
• Hu, J., Frequency sampling design of two-dimensional finite impulse response digital filters, Mass. Inst. Tech., MS Thesis, June 1972.
• Ansari, R., Cetin, A.E., Two-dimensional FIR filters, Chapter 22 in The Circuits and Filters Handbook, Ed. by W.K. Chen, pp. 22.1-22.29, CRC Press, 2009.
• Huang, T., Two-dimensional windows, IEEE Trans. Audio and Electroacoustics, 20: 80-90, 1972.
• Speake, T., Mersereau, R., A note on the use of windows for two dimensional FIR filter design, IEEE Trans. Acoust., Speech, Signal Process., 29:125–127, 1981.
• Kato, H., Furukawa, T., Two-dimensional type-preserving circular windows, IEEE Trans. Acoust., Speech, Signal Process., 29:926-928, 1981.
• Yu, T.H., Mitra, S.K. A new two-dimensional window, IEEE Trans. Acowt., Speech, Signal Process., 33:1058-1061, 1985.
• Antoniou, A., Lu, W.S., Design of 2-D nonrecursive filters using window method, IEE Proc, 137: 247–250,1990.
• Avci, K., Kaiser-Hamming window and its performance analysis for nonrecursıve digital fılter design, Journal of the Faculty of Engineering and Architecture of Gazi University, 29(4): 823-833, 2014.
• Antoniou, A., Digital Signal Processing: Signal, Systems, And Filters, McGraw-Hill, New York, NY, USA, 2005.
• Prabhu, K.M.M., Window Functions and Their Applications in Signal Processing, CRC Press, 2014.
• Dumitrescu, B., 2D FIR filter design: What shape is the best?, Proc. IEEE Eur. Conf. Signal Process., 1024–1027, Eylül, 2007.
• MATLAB ® 2016. The MathWorks, Inc. http://www.mathworks.com/Products/Matlab/, 2016