Noisy texture analysis based on higher order spectra
DOI:
https://doi.org/10.14419/ijet.v7i3.14066Keywords:
Texture analysis, Higher order spectra, Phase, Wrapped Cauchy distribution, Texture classificationAbstract
Texture is described in several approaches by 1st and 2nd order statistics which cannot preserve phase information carried by the Fourier spectrum. Besides, these statistics are very sensitive to noise. In this paper, we study features derived from higher order spectra, especially the third order spectrum, namely the bispectrum, known to offer a high noise immunity and to recover Fourier phase information. In this paper, we exploit phase preservation property by using bispectrum phase. We propose wrapped Cauchy distribution to model phase. Wrapped Cauchy parameters are estimated by maximizing the log-likelihood function. Experiments show that the wrapped Cauchy distribution fits our phase information well. Hence, their parameters are used to feed our feature vector in order to classify textures corrupted by Gaussian noise. Classification results using the proposed approach show a good noise immunity compared to a statistical model based on Gabor phase.References
[1] Chandran, V., Carswell, B., Boashash, B., Elgar, S., “Pattern recognition
using invariants defined from higher order spectra: 2-d image
inputsâ€, Image Processing, IEEE Transactions on, Vol.6, No.5, (1997),
pp.703-712.[2] Surya, Arun and Saha, Swapan K., “Computationally efficient method
for retrieval of atmospherically distorted astronomical imagesâ€, Journal
of Optics, Vol.43, No.7, (2014), pp.317-324.[3] Lagdali, Salwa and Rziza, Mohammed, “Novel phase-based descriptor
using bispectrum for texture classificationâ€, Pattern Recognition
Letters, Vol.100, (2017), pp.1-5.[4] Acharya, U Rajendra and Dua, Sumeet and Du, Xian and Chua, Chua
Kuang and others, “Automated diagnosis of glaucoma using texture
and higher order spectra featuresâ€, IEEE Transactions on information
technology in biomedicine, Vol.15, No.3, (2011), pp.449-455.[5] Acharya, U Rajendra and Sudarshan, Vidya K and Koh, Joel EW
and Martis, Roshan Joy and Tan, Jen Hong and Oh, Shu Lih and
Muhammad, Adam and Hagiwara, Yuki and Mookiah, Muthu Rama
Krishanan and Chua, Kok Poo and others, “Application of higherorder
spectra for the characterization of coronary artery disease using
electrocardiogram signalsâ€, Biomedical Signal Processing and Control,
Vol.31, (2017), pp.31-43.[6] Vo, A., Oraintara, S., “A study of relative phase in complex wavelet
domain: Property, statistics and applications in texture image retrieval
and segmentationâ€, Signal Processing: Image Communication, Vol.25,
No.1, (2010), pp.28-46.[7] Chandran, V., Elgar, S., “Bispectral analysis of two-dimensional random
processesâ€, Acoustics, Speech and Signal Processing, IEEE Transactions
on, Vol.38, No.12, (1990), pp.2181-2186.[8] Oppenheim, A.V., Lim, J.S., “The importance of phase in signalsâ€,
Proceedings of the IEEE, Vol.69, No.5, (1981), pp.529-541.[9] Matsuoka, T., Ulrych, T.J., “Phase estimation using the bispectrumâ€,
Proceedings of the IEEE, Vol.72, No.10, (1984), pp.1403-1411.[10] Vo, An Phuoc Nhu., “Complex Directional Wavelet Transforms: Representation,
Statistical Modeling And Applicationsâ€, ProQuest, (2008).[11] Fisher, N.I., “Statistical analysis of circular dataâ€, Cambridge University
Press, (1995).[12] Mardia, Kanti V and Jupp, Peter E., “Directional statisticsâ€, John Wiley
& Sons, Vol.94, (2009).[13] Vo, An and Oraintara, Soontorn, “On the distributions of the relative
phase of complex wavelet coefficientsâ€, Circuits and Systems, 2009. ISCAS 2009. IEEE International Symposium on, (2009), pp.529-532.[14] Nikias, C.L., Petropulu, A.P., “Higher-order spectra analysis: A nonlinear
signal processing frameworkâ€, PTR Prentice Hall, Englewood
Cliffs, NJ, (1993).[15] Tsatsanis, M.K., Giannakis, G.B., “Object and texture classification
using higher order statisticsâ€, IEEE Transactions on Pattern Analysis
& Machine Intelligence, Vol.7, (1992), pp.733-750.[16] Murino, V., Ottonello, C., Pagnan, S., “Noisy texture classification: A
higher-order statistics approachâ€, Pattern Recognition, Vol.31, No.4,
(1998), pp.383-393.[17] Mendel, J.M., “Tutorial on higher-order statistics (spectra) in signal
processing and system theory: theoretical results and some applicationsâ€,
Proceedings of the IEEE, Vol.79, No.3, (1991), pp.278-305.[18] Best, D., Fisher, N., “The bias of the maximum likelihood estimators
of the von Mises-fisher concentration parameters: The bias of the maximum
likelihood estimatorsâ€, Communications in Statistics-Simulation
and Computation, Vol.10, No.5, (1981), pp.493-502.[19] Kent, J.T., Tyler, D.E., “Maximum likelihood estimation for the
wrapped Cauchy distributionâ€, Journal of Applied Statistics, Vol.15,
No.2, (1988), pp.247-254.
Downloads
How to Cite
Received date: June 12, 2018
Accepted date: July 12, 2018
Published date: July 27, 2018