Abstract

An innovative way of calculating the von Mises distribution of image entropy is introduced in this paper. The von Mises distribution’s concentration parameter and some fitness parameter that will be defined later have been analyzed in the experimental part for determining their suitability as an image quality assessment measure in some particular distortions such as Gaussian blur or additive Gaussian noise. To achieve such measure, the local Rényi entropy is calculated in four equally spaced orientations and used to determine the parameters of the von Mises distribution of the image entropy. Considering contextual images, experimental results after applying this model show that the best-in-focus noise-free images are associated with the highest values for the von Mises distribution concentration parameter and the highest approximation of image data to the von Mises distribution model. Our defined von Mises fitness parameter experimentally appears also as a suitable no-reference image quality assessment indicator for no-contextual images.

© 2012 Optical Society of America

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  37. A. G. Valdecasas, D. Marshall, J. M. Becerra, and J. J. Terrero, “On the extended depth of focus algorithms for bright field microscopy,” Micron 32, 559–569 (2001).
    [CrossRef]
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    [CrossRef]

2010

J. Redi, R. Zunino, H. Liu, H. Alers, and I. Heynderickx, “Comparing subjective image quality measurement methods for the creation of public databases,” Proc. SPIE 7529, 752903 (2010).
[CrossRef]

X. Zhu and P. Milanfar, “Automatic parameter selection for denoising algorithms using a no-reference measure of image content,” IEEE Trans. Image Process. 19, 3116–3132 (2010).
[CrossRef]

2009

N. Ponomarenko, V. Lukin, A. Zelensky, K. Egiazarian, M. Carli, and F. Battisti, “A database for evaluation of full-reference visual quality assessment metrics,” Adv. Mod. Radioelectron. 10, pp. 30–45 (2009).

G. Ciocca, F. Marini, and R. Schettini, “Image quality assessment in multimedia applications,” Proc. SPIE 7255, 72550A (2009).
[CrossRef]

R. Ferzli and L. J. Karam, “A no-reference objective image sharpness metric based on the notion of just noticeable blur (JNB),” IEEE Trans. Image Process. 18, 717–728 (2009).
[CrossRef]

2007

2004

K. Conrad, “Probability distributions and maximum entropy,” Entropy 6, 1–10 (2004).
[CrossRef]

E. Snelson, C. E. Rasmussen, and Z. Ghahramani, “Warped Gaussian processes,” Adv. Neural Inform. Process. Syst. 16, 337–344 (2004).

2003

K. Zyczkowski, “Rényi extrapolation of Shannon entropy,” Open Syst. Inf. Dyn. 10, 297–310 (2003).
[CrossRef]

2001

L. Stankovic, “A measure of some time-frequency distributions concentration,” Signal Process. 81, 621–631 (2001).
[CrossRef]

A. G. Valdecasas, D. Marshall, J. M. Becerra, and J. J. Terrero, “On the extended depth of focus algorithms for bright field microscopy,” Micron 32, 559–569 (2001).
[CrossRef]

2000

C. R. Stephens and J. Mora Vargas, “Effective fitness as an alternative paradigm for evolutionary computation I: general formalism,” Genet. Program. Evolvable Mach. 1, 363–378(2000).

1991

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Adv. Signal Process. 1566, 144–156 (1991).

1988

L. D. Jacobson and H. Wechsler, “Joint spatial/spatial-frequency representation,” Signal Process. 14, 37–68 (1988).
[CrossRef]

1980

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution—a tool for time frequency analysis, parts I-III.” Philips J. Res., 35, 217–250 (1980).

1966

L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7, 781–786 (1966).
[CrossRef]

1932

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
[CrossRef]

1918

R. von Mises “Uber die ’Ganzzahligkeit’ der Atomgewicht und verwandte Fragen,” Physikalische Z. 19, 490–500 (1918).

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Alers, H.

J. Redi, R. Zunino, H. Liu, H. Alers, and I. Heynderickx, “Comparing subjective image quality measurement methods for the creation of public databases,” Proc. SPIE 7529, 752903 (2010).
[CrossRef]

Atlas, L.

J. Pitton, P. Loughlin, and L. Atlas, “Positive time-frequency distributions via maximum entropy deconvolution of the evolutionary spectrum,” in Proceedings of ICASSP IV (1993), pp. 436–439.

Baraniuk, R. G.

P. Flandrin, R. G. Baraniuk, and O. Michel, “Time-frequency complexity and information,” in Proceedings of the ICASSP (1994), Vol. 3, pp. 329–332.

Battisti, F.

N. Ponomarenko, V. Lukin, A. Zelensky, K. Egiazarian, M. Carli, and F. Battisti, “A database for evaluation of full-reference visual quality assessment metrics,” Adv. Mod. Radioelectron. 10, pp. 30–45 (2009).

Becerra, J. M.

A. G. Valdecasas, D. Marshall, J. M. Becerra, and J. J. Terrero, “On the extended depth of focus algorithms for bright field microscopy,” Micron 32, 559–569 (2001).
[CrossRef]

Bentley, J.

J. Bentley, “Modelling circular data using a mixture of Von Mises and uniform distributions” (Department of Statistics and Actuarial Science, Simon Fraser University, 2006).

Borghesani, D.

C. Grana, D. Borghesani, and R. Cucchiara, “Describing texture directions with von Mises distributions,” in Proceedings of ICPR (2008), pp. 1–4.

Bovik, A.

Z. Wang and A. Bovik, “Modern image quality assessment,” in Synthesis Lectures on Image, Video, and Multimedia Processing (Morgan & Claypool, 2006), Vol. 2, pp. 1–156.

Brenner, K. H.

K. H. Brenner, “A discrete version of the Wigner distribution function,” in Proceedings of EURASIP, Signal Processing II: Theories and Applications (1983), pp. 307–309.

Brown, M. L.

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Adv. Signal Process. 1566, 144–156 (1991).

Carli, M.

N. Ponomarenko, V. Lukin, A. Zelensky, K. Egiazarian, M. Carli, and F. Battisti, “A database for evaluation of full-reference visual quality assessment metrics,” Adv. Mod. Radioelectron. 10, pp. 30–45 (2009).

Ciocca, G.

G. Ciocca, F. Marini, and R. Schettini, “Image quality assessment in multimedia applications,” Proc. SPIE 7255, 72550A (2009).
[CrossRef]

Claasen, T. A. C. M.

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution—a tool for time frequency analysis, parts I-III.” Philips J. Res., 35, 217–250 (1980).

Cohen, L.

L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7, 781–786 (1966).
[CrossRef]

Conrad, K.

K. Conrad, “Probability distributions and maximum entropy,” Entropy 6, 1–10 (2004).
[CrossRef]

Cristóbal, G.

Cucchiara, R.

C. Grana, D. Borghesani, and R. Cucchiara, “Describing texture directions with von Mises distributions,” in Proceedings of ICPR (2008), pp. 1–4.

Dhillon, I. S.

I. S. Dhillon and S. Sra, “Modeling data using directional distributions,” Technical Report # TR-03-06 (Department of Computer Sciences, The University of Texas at Austin, 2003).

Egiazarian, K.

N. Ponomarenko, V. Lukin, A. Zelensky, K. Egiazarian, M. Carli, and F. Battisti, “A database for evaluation of full-reference visual quality assessment metrics,” Adv. Mod. Radioelectron. 10, pp. 30–45 (2009).

Feng, X.

X. Feng, “The analysis and approaches to image local orientation estimation,” Master’s thesis (University of California, 2003).

Ferzli, R.

R. Ferzli and L. J. Karam, “A no-reference objective image sharpness metric based on the notion of just noticeable blur (JNB),” IEEE Trans. Image Process. 18, 717–728 (2009).
[CrossRef]

Flandrin, P.

P. Flandrin, R. G. Baraniuk, and O. Michel, “Time-frequency complexity and information,” in Proceedings of the ICASSP (1994), Vol. 3, pp. 329–332.

Gabarda, S.

Ghahramani, Z.

E. Snelson, C. E. Rasmussen, and Z. Ghahramani, “Warped Gaussian processes,” Adv. Neural Inform. Process. Syst. 16, 337–344 (2004).

Grana, C.

C. Grana, D. Borghesani, and R. Cucchiara, “Describing texture directions with von Mises distributions,” in Proceedings of ICPR (2008), pp. 1–4.

Hero, A. O.

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Adv. Signal Process. 1566, 144–156 (1991).

Heynderickx, I.

J. Redi, R. Zunino, H. Liu, H. Alers, and I. Heynderickx, “Comparing subjective image quality measurement methods for the creation of public databases,” Proc. SPIE 7529, 752903 (2010).
[CrossRef]

Jacobson, L. D.

L. D. Jacobson and H. Wechsler, “Joint spatial/spatial-frequency representation,” Signal Process. 14, 37–68 (1988).
[CrossRef]

Jammalamadaka, S. R.

S. R. Jammalamadaka and A. SenGupta, Topics in Circular Statistics (World Scientific, 2001).

Karam, L. J.

R. Ferzli and L. J. Karam, “A no-reference objective image sharpness metric based on the notion of just noticeable blur (JNB),” IEEE Trans. Image Process. 18, 717–728 (2009).
[CrossRef]

N. D. Narvekar and L. J. Karam, “An improved no-reference sharpness metric based on the probability of blur detection,” in Proceedings of International Workshop on Video Processing and Quality Metrics for Consumer Electronics (VPQM), http://www.vpqm.org [pdf] [Software] (2010).

Liu, H.

J. Redi, R. Zunino, H. Liu, H. Alers, and I. Heynderickx, “Comparing subjective image quality measurement methods for the creation of public databases,” Proc. SPIE 7529, 752903 (2010).
[CrossRef]

Loughlin, P.

J. Pitton, P. Loughlin, and L. Atlas, “Positive time-frequency distributions via maximum entropy deconvolution of the evolutionary spectrum,” in Proceedings of ICASSP IV (1993), pp. 436–439.

Lukin, V.

N. Ponomarenko, V. Lukin, A. Zelensky, K. Egiazarian, M. Carli, and F. Battisti, “A database for evaluation of full-reference visual quality assessment metrics,” Adv. Mod. Radioelectron. 10, pp. 30–45 (2009).

Marini, F.

G. Ciocca, F. Marini, and R. Schettini, “Image quality assessment in multimedia applications,” Proc. SPIE 7255, 72550A (2009).
[CrossRef]

Marshall, D.

A. G. Valdecasas, D. Marshall, J. M. Becerra, and J. J. Terrero, “On the extended depth of focus algorithms for bright field microscopy,” Micron 32, 559–569 (2001).
[CrossRef]

Mecklenbräuker, W. F. G.

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution—a tool for time frequency analysis, parts I-III.” Philips J. Res., 35, 217–250 (1980).

Michel, O.

P. Flandrin, R. G. Baraniuk, and O. Michel, “Time-frequency complexity and information,” in Proceedings of the ICASSP (1994), Vol. 3, pp. 329–332.

Milanfar, P.

X. Zhu and P. Milanfar, “Automatic parameter selection for denoising algorithms using a no-reference measure of image content,” IEEE Trans. Image Process. 19, 3116–3132 (2010).
[CrossRef]

Mora Vargas, J.

C. R. Stephens and J. Mora Vargas, “Effective fitness as an alternative paradigm for evolutionary computation I: general formalism,” Genet. Program. Evolvable Mach. 1, 363–378(2000).

Narvekar, N. D.

N. D. Narvekar and L. J. Karam, “An improved no-reference sharpness metric based on the probability of blur detection,” in Proceedings of International Workshop on Video Processing and Quality Metrics for Consumer Electronics (VPQM), http://www.vpqm.org [pdf] [Software] (2010).

Oraintara, S.

A. P. N. Vo and S. Oraintara, “Statistical image modeling using von Mises distribution in the complex directional wavelet domain,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2008), pp. 2885–2888..

Palacios, A. R.

A. R. Palacios, C. Rodríguez, and C. Vejarano, “Circular processing of the hue variable a particular trait of colour image processing,” in 2nd International Conference on Computer Vision Theory and Applications (VISAPP 2007) (2007), pp. 69–78.

Pitton, J.

J. Pitton, P. Loughlin, and L. Atlas, “Positive time-frequency distributions via maximum entropy deconvolution of the evolutionary spectrum,” in Proceedings of ICASSP IV (1993), pp. 436–439.

Ponomarenko, N.

N. Ponomarenko, V. Lukin, A. Zelensky, K. Egiazarian, M. Carli, and F. Battisti, “A database for evaluation of full-reference visual quality assessment metrics,” Adv. Mod. Radioelectron. 10, pp. 30–45 (2009).

Rasmussen, C. E.

E. Snelson, C. E. Rasmussen, and Z. Ghahramani, “Warped Gaussian processes,” Adv. Neural Inform. Process. Syst. 16, 337–344 (2004).

Redi, J.

J. Redi, R. Zunino, H. Liu, H. Alers, and I. Heynderickx, “Comparing subjective image quality measurement methods for the creation of public databases,” Proc. SPIE 7529, 752903 (2010).
[CrossRef]

Rényi, A.

A. Rényi, “Some fundamental questions of information theory,” in Selected Papers of Alfred Rényi (Akadémiai Kiadó, Budapest), Vol. 3, pp. 526–552. (Originally: MTA III. Oszt. Közl., 10, 1960, pp. 251-282) (1976).

Rodríguez, C.

A. R. Palacios, C. Rodríguez, and C. Vejarano, “Circular processing of the hue variable a particular trait of colour image processing,” in 2nd International Conference on Computer Vision Theory and Applications (VISAPP 2007) (2007), pp. 69–78.

Sang, T. H.

T. H. Sang and W. J. Williams, “Rényi information and signal dependent optimal kernel design,” in Proceedings of the ICASSP (1995), Vol. 2, pp. 997–1000.

Schettini, R.

G. Ciocca, F. Marini, and R. Schettini, “Image quality assessment in multimedia applications,” Proc. SPIE 7255, 72550A (2009).
[CrossRef]

SenGupta, A.

S. R. Jammalamadaka and A. SenGupta, Topics in Circular Statistics (World Scientific, 2001).

Shannon, C. E.

C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois, 1949).

Snelson, E.

E. Snelson, C. E. Rasmussen, and Z. Ghahramani, “Warped Gaussian processes,” Adv. Neural Inform. Process. Syst. 16, 337–344 (2004).

Sra, S.

I. S. Dhillon and S. Sra, “Modeling data using directional distributions,” Technical Report # TR-03-06 (Department of Computer Sciences, The University of Texas at Austin, 2003).

Stankovic, L.

L. Stankovic, “A measure of some time-frequency distributions concentration,” Signal Process. 81, 621–631 (2001).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Stephens, C. R.

C. R. Stephens and J. Mora Vargas, “Effective fitness as an alternative paradigm for evolutionary computation I: general formalism,” Genet. Program. Evolvable Mach. 1, 363–378(2000).

Stephens, M. A.

M. A. Stephens, “Techniques for directional data,” Technical report no. 150 (Department of Statistics, Stanford University, 1969).

Terrero, J. J.

A. G. Valdecasas, D. Marshall, J. M. Becerra, and J. J. Terrero, “On the extended depth of focus algorithms for bright field microscopy,” Micron 32, 559–569 (2001).
[CrossRef]

Valdecasas, A. G.

A. G. Valdecasas, D. Marshall, J. M. Becerra, and J. J. Terrero, “On the extended depth of focus algorithms for bright field microscopy,” Micron 32, 559–569 (2001).
[CrossRef]

Vejarano, C.

A. R. Palacios, C. Rodríguez, and C. Vejarano, “Circular processing of the hue variable a particular trait of colour image processing,” in 2nd International Conference on Computer Vision Theory and Applications (VISAPP 2007) (2007), pp. 69–78.

Vo, A. P. N.

A. P. N. Vo and S. Oraintara, “Statistical image modeling using von Mises distribution in the complex directional wavelet domain,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2008), pp. 2885–2888..

von Mises, R.

R. von Mises “Uber die ’Ganzzahligkeit’ der Atomgewicht und verwandte Fragen,” Physikalische Z. 19, 490–500 (1918).

Wang, Z.

Z. Wang and A. Bovik, “Modern image quality assessment,” in Synthesis Lectures on Image, Video, and Multimedia Processing (Morgan & Claypool, 2006), Vol. 2, pp. 1–156.

Weaver, W.

C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois, 1949).

Wechsler, H.

L. D. Jacobson and H. Wechsler, “Joint spatial/spatial-frequency representation,” Signal Process. 14, 37–68 (1988).
[CrossRef]

Wigner, E.

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
[CrossRef]

Williams, W. J.

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Adv. Signal Process. 1566, 144–156 (1991).

T. H. Sang and W. J. Williams, “Rényi information and signal dependent optimal kernel design,” in Proceedings of the ICASSP (1995), Vol. 2, pp. 997–1000.

Yendrikhovskij, S.

S. Yendrikhovskij, “Image quality and colour categorisation,” in W. Lindsay, M. MacDonald, and L. Ronnier, eds., Colour Image Science: Exploiting Digital Media (Wiley, 2002), pp. 393–420.

Zelensky, A.

N. Ponomarenko, V. Lukin, A. Zelensky, K. Egiazarian, M. Carli, and F. Battisti, “A database for evaluation of full-reference visual quality assessment metrics,” Adv. Mod. Radioelectron. 10, pp. 30–45 (2009).

Zhu, X.

X. Zhu and P. Milanfar, “Automatic parameter selection for denoising algorithms using a no-reference measure of image content,” IEEE Trans. Image Process. 19, 3116–3132 (2010).
[CrossRef]

Zunino, R.

J. Redi, R. Zunino, H. Liu, H. Alers, and I. Heynderickx, “Comparing subjective image quality measurement methods for the creation of public databases,” Proc. SPIE 7529, 752903 (2010).
[CrossRef]

Zyczkowski, K.

K. Zyczkowski, “Rényi extrapolation of Shannon entropy,” Open Syst. Inf. Dyn. 10, 297–310 (2003).
[CrossRef]

Adv. Mod. Radioelectron.

N. Ponomarenko, V. Lukin, A. Zelensky, K. Egiazarian, M. Carli, and F. Battisti, “A database for evaluation of full-reference visual quality assessment metrics,” Adv. Mod. Radioelectron. 10, pp. 30–45 (2009).

Adv. Neural Inform. Process. Syst.

E. Snelson, C. E. Rasmussen, and Z. Ghahramani, “Warped Gaussian processes,” Adv. Neural Inform. Process. Syst. 16, 337–344 (2004).

Adv. Signal Process.

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Adv. Signal Process. 1566, 144–156 (1991).

Entropy

K. Conrad, “Probability distributions and maximum entropy,” Entropy 6, 1–10 (2004).
[CrossRef]

Genet. Program. Evolvable Mach.

C. R. Stephens and J. Mora Vargas, “Effective fitness as an alternative paradigm for evolutionary computation I: general formalism,” Genet. Program. Evolvable Mach. 1, 363–378(2000).

IEEE Trans. Image Process.

R. Ferzli and L. J. Karam, “A no-reference objective image sharpness metric based on the notion of just noticeable blur (JNB),” IEEE Trans. Image Process. 18, 717–728 (2009).
[CrossRef]

X. Zhu and P. Milanfar, “Automatic parameter selection for denoising algorithms using a no-reference measure of image content,” IEEE Trans. Image Process. 19, 3116–3132 (2010).
[CrossRef]

J. Math. Phys.

L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7, 781–786 (1966).
[CrossRef]

J. Opt. Soc. Am. A

Micron

A. G. Valdecasas, D. Marshall, J. M. Becerra, and J. J. Terrero, “On the extended depth of focus algorithms for bright field microscopy,” Micron 32, 559–569 (2001).
[CrossRef]

Open Syst. Inf. Dyn.

K. Zyczkowski, “Rényi extrapolation of Shannon entropy,” Open Syst. Inf. Dyn. 10, 297–310 (2003).
[CrossRef]

Philips J. Res.

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution—a tool for time frequency analysis, parts I-III.” Philips J. Res., 35, 217–250 (1980).

Phys. Rev.

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
[CrossRef]

Physikalische Z.

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