Abstract

In the automatic assessment of image quality we obtained a high accuracy in the classification of image degradations in a manner that is widely independent of scene content. Using an all-digital ring–wedge detector system combined with neural-network software, we conducted several experiments in which the end goal is to classify images according to numerical quality scales. Experiments are presented to stress the importance of both local and global image quality assessment. Two databases of degraded images were prepared. One uses five levels of Gaussian blur to simulate depth of field. The other was prepared with lossy compression and recovery with artifacts generated by a JPEG (Joint Photographic Experts Group) compression algorithm. In quantitative terms our best sorting of Gaussian blur without knowledge of the original scene was to an accuracy of 96%. For degradation using JPEG we obtained an accuracy of 95% without knowledge of the original and 98% when the original scene is available as a reference.

© 2000 Optical Society of America

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1999

1998

M. P. Eckert, A. P. Bradley, “Perceptual quality metrics applied to still image compression,” Signal. Process. 70, 177–200 (1998).
[CrossRef]

1996

V. Kayargadde, J.-B. Martens, “Perceptual characterization of images degraded by blur and noise: experiments,” J. Opt. Soc. Am. A 13, 1166–1177 (1996).
[CrossRef]

V. Kayargadde, J.-B. Martens, “Estimation of perceived image blur using edge features,” Int. J. Imaging Syst. Technol. 7, 102–109 (1996).
[CrossRef]

1995

D. R. Fuhrmann, J. A. Baro, J. R. Cox, “Experimental evaluation of psychophysical distortion metrics for JPEG-encoded images,” J. Electron. Imaging 4, 397–406 (1995).
[CrossRef]

C.-H. Chou, Y.-C. Li, “A perceptually tuned subband image coder based on the measure of just-noticeable-distortion profile,” IEEE. Trans. Circuits Syst. V 5, 467–476 (1995).

1994

N. Belaid, J. Cespedes, J. M. Thijssen, J. Ophir, “Lesion detection in simulated elastographic and echographic images: a psychophysical study,” Ultrasound Med. Biol. 20, 877–891 (1994).
[CrossRef] [PubMed]

1993

N. Jayant, J. Johnston, R. Safranek, “Signal compression based on models of human perception,” Proc. IEEE 81, 1385–422 (1993).
[CrossRef]

1992

N. B. Nill, B. H. Bouzas, “Objective image quality measure derived from digital image power spectra,” Opt. Eng. 31, 813–825 (1992).
[CrossRef]

J. A. J. Roufs, “Perceptual image quality: concept and measurement,” Philips J. Res. 47, 35–62 (1992).

1991

S. Ohtsuka, M. Kosugi, “Quality evaluation of locally impaired pictures,” J. Soc. Inf. Disp. 32, 19–24 (1991).

S. D. Coston, N. George, “Recovery of particle size distributions by inversion of the optical transform intensity,” Opt. Lett. 16, 1918–1920 (1991).
[CrossRef] [PubMed]

G. K. Wallace, “The JPEG still picture compression standard,” Commun. ACM 34, 30–44 (1991).
[CrossRef]

S. Ohtsuka, M. Kosugi, “Quality evaluation of locally impaired pictures,” J. Soc. Inf. Disp. 32, 19–24 (1991).

1990

1989

J. H. D. M. Westerink, J. A. J. Roufs, “Subjective image quality as a function of viewing distance, resolution, and picture size,” J. Soc. Motion Pict. Tel. Eng. 98, 113–119 (1989).

J. A. Saghri, P. S. Cheatham, A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. 28, 813–818 (1989).
[CrossRef]

1987

A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision, Graph. Image Process. 39, 311–27 (1987).
[CrossRef]

A. B. Watson, “Efficiency of a model human image code,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
[CrossRef] [PubMed]

1982

H. L. Snyder, M. E. Maddox, D. I. Shedivy, J. A. Turpin, J. J. Burke, R. N. Strickland, “Digital image quality and interpretability: database and hardcopy studies,” Opt. Eng. 21, 14–22 (1982).
[CrossRef]

1978

R. Shaw, “Evaluating the efficient of imaging processes,” Rep. Prog. Phys. 41, 1103–1155 (1978).
[CrossRef]

1976

1974

1973

N. Jensen, “High-speed image analysis techniques,” Photograph. Eng. 39, 1321–1328 (1973).

1969

1964

O. H. Schade, “An evaluation of photographic image quality and resolving power,” J. Soc. Motion Pict. Tel. Eng. 73, 81–119 (1964).

1956

1955

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part IV. Image analysis in photographic and television systems (definition and sharpness),” J. Soc. Motion Pict. Tel. Eng. 64, 593–617 (1955).

1953

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part III. The grain structure of television images,” J. Soc. Motion Pict. Tel. Eng. 61, 97–164 (1953).

1952

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part II. The trainstructure of motion picture images—an analysis of deviations and fluctuations of the sample number,” J. Soc. Motion Pict. Tel. Eng. 58, 181–222 (1952).

1951

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part I. image structure and transfer characteristics,” J. Soc. Motion Pict. Tel. Eng. 56, 137–177 (1951).

Abbey, C. K.

C. K. Abbey, H. H. Barrett, M. P. Eckstein, “Practical issues and methodology in assessment of image quality using model observers,” in Medical Imaging 1997. Physics of Medical Imaging, R. L. Van Metter, J. Beutel, eds., Proc. SPIE3032, 182–194 (1997).
[CrossRef]

Allebach, J. P.

C. C. Taylor, Z. Pizlo, J. P. Allebach, C. A. Bouman, “Image quality assessment with a Gabor pyramid model of the human visual system,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 58–69 (1997).
[CrossRef]

Allen, C.

C. Allen, R. Schindler, “Determining image quality from electronic or digital signal characteristics,” in Advances in Image Transmission II, A. G. Tescher, ed., Proc. SPIE249, 179–184 (1980).
[CrossRef]

Barnwell, T. P.

T. P. Barnwell, R. M. Mersereau, “A comparison of some subjective and objective measures for image quality,” in Proceedings of the Eleventh Annual Asilomar Conference on Circuits Systems and Computers (Institute of Electrical and Electronics Engineers, New York, 1978), pp. 96–100.

Baro, J. A.

D. R. Fuhrmann, J. A. Baro, J. R. Cox, “Experimental evaluation of psychophysical distortion metrics for JPEG-encoded images,” J. Electron. Imaging 4, 397–406 (1995).
[CrossRef]

Barrett, H. H.

C. K. Abbey, H. H. Barrett, M. P. Eckstein, “Practical issues and methodology in assessment of image quality using model observers,” in Medical Imaging 1997. Physics of Medical Imaging, R. L. Van Metter, J. Beutel, eds., Proc. SPIE3032, 182–194 (1997).
[CrossRef]

Barten, P. G. J.

Beaton, R. J.

C. Y. Wen, R. J. Beaton, “Subjective image quality evaluation of image compression techniques,” in Proceedings of the Human Factors and Ergonomics Society, 40th Annual Meeting 1996 (Human Factors and Ergonomics Society, Santa Monica, Calif., 1996), Vol. 2, pp. 1188–1192.
[CrossRef]

B. P. Chao, R. J. Beaton, H. L. Snyder, “Human performance evaluations of digital image quality,” in Advances in Display Technology III, E. Schlam, ed., Proc. SPIE386, 20–24 (1983).
[CrossRef]

Belaid, N.

N. Belaid, J. Cespedes, J. M. Thijssen, J. Ophir, “Lesion detection in simulated elastographic and echographic images: a psychophysical study,” Ultrasound Med. Biol. 20, 877–891 (1994).
[CrossRef] [PubMed]

Berfanger, D.

Berfanger, D. M.

D. M. Berfanger, N. George, “Automatic image quality assessment,” in Proceedings of ICPS ’94: The Physics and Chemistry of Imaging Systems, IS&T’s 47th Annual Conference (Society for Imaging Science and Technology, Springfield, Va., 1994), Vol 2, pp. 436–438.

Boschman, M. C.

J. A. J. Roufs, M. C. Boschman, “Methods for evaluating the perceptual quality of VDUs,” in Human Vision and Electronic Imaging: Models, Methods, and Applications, B. E. Rogowitz, J. P. Allebached, eds., Proc. SPIE1249, 2–11 (1990).

Bouman, C. A.

C. C. Taylor, Z. Pizlo, J. P. Allebach, C. A. Bouman, “Image quality assessment with a Gabor pyramid model of the human visual system,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 58–69 (1997).
[CrossRef]

Bouzas, B. H.

N. B. Nill, B. H. Bouzas, “Objective image quality measure derived from digital image power spectra,” Opt. Eng. 31, 813–825 (1992).
[CrossRef]

Bradley, A. P.

M. P. Eckert, A. P. Bradley, “Perceptual quality metrics applied to still image compression,” Signal. Process. 70, 177–200 (1998).
[CrossRef]

Briggs, S. J.

G. L. Latshaw, P. L. Zuzelo, S. J. Briggs, “Tactical photointerpreter evaluations of hardcopy and softcopy imagery,” in Airborne Reconnaissance III: Collection and Exploitation of Reconnaissance Data, J. H. Smith, T. C. Freitag, eds., Proc. SPIE137, 179–87 (1978).
[CrossRef]

S. J. Briggs, “The definition and measurement of image quality,” in Advances in Image Transmission II, A. G. Tescher, ed., Proc. SPIE249, 170–174 (1980).
[CrossRef]

Burke, J. J.

H. L. Snyder, M. E. Maddox, D. I. Shedivy, J. A. Turpin, J. J. Burke, R. N. Strickland, “Digital image quality and interpretability: database and hardcopy studies,” Opt. Eng. 21, 14–22 (1982).
[CrossRef]

J. J. Burke, H. L. Snyder, “Quality metrics of digitally derived imagery and their relation to interpreter performance,” in Image Quality, P. S. Cheatham, ed., Proc. SPIE310, 16–23 (1981).
[CrossRef]

Cespedes, J.

N. Belaid, J. Cespedes, J. M. Thijssen, J. Ophir, “Lesion detection in simulated elastographic and echographic images: a psychophysical study,” Ultrasound Med. Biol. 20, 877–891 (1994).
[CrossRef] [PubMed]

Chao, B. P.

B. P. Chao, R. J. Beaton, H. L. Snyder, “Human performance evaluations of digital image quality,” in Advances in Display Technology III, E. Schlam, ed., Proc. SPIE386, 20–24 (1983).
[CrossRef]

Cheatham, P. S.

J. A. Saghri, P. S. Cheatham, A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. 28, 813–818 (1989).
[CrossRef]

Cherifi, H.

T. Eude, H. Cherifi, “Quality metrics for low bitrate coding,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 70–81 (1997).
[CrossRef]

Chou, C.-H.

C.-H. Chou, Y.-C. Li, “A perceptually tuned subband image coder based on the measure of just-noticeable-distortion profile,” IEEE. Trans. Circuits Syst. V 5, 467–476 (1995).

Coluccio, T. L.

Coston, S. D.

Cox, J. R.

D. R. Fuhrmann, J. A. Baro, J. R. Cox, “Experimental evaluation of psychophysical distortion metrics for JPEG-encoded images,” J. Electron. Imaging 4, 397–406 (1995).
[CrossRef]

Daly, S.

S. Daly, “The visible differences predictor: an algorithm for the assessment of image fidelity,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 2–14 (1992).
[CrossRef]

Davies, I. R. L.

I. R. L. Davies, D. Rose, R. J. Smith, “Automated image quality assessment,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 27–36 (1993).
[CrossRef]

de Ridder, H.

R. Hamberg, H. de Ridder, “Continuous assessment of time-varying image quality,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 248–259 (1997).
[CrossRef]

Eckert, M. P.

M. P. Eckert, A. P. Bradley, “Perceptual quality metrics applied to still image compression,” Signal. Process. 70, 177–200 (1998).
[CrossRef]

Eckstein, M. P.

C. K. Abbey, H. H. Barrett, M. P. Eckstein, “Practical issues and methodology in assessment of image quality using model observers,” in Medical Imaging 1997. Physics of Medical Imaging, R. L. Van Metter, J. Beutel, eds., Proc. SPIE3032, 182–194 (1997).
[CrossRef]

Eude, T.

T. Eude, H. Cherifi, “Quality metrics for low bitrate coding,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 70–81 (1997).
[CrossRef]

Fuhrmann, D. R.

D. R. Fuhrmann, J. A. Baro, J. R. Cox, “Experimental evaluation of psychophysical distortion metrics for JPEG-encoded images,” J. Electron. Imaging 4, 397–406 (1995).
[CrossRef]

George, N.

D. Berfanger, N. George, “All-digital ring-wedge detector applied to fingerprint recognition,” Appl. Opt. 38, 357–369 (1999).
[CrossRef]

S. D. Coston, N. George, “Recovery of particle size distributions by inversion of the optical transform intensity,” Opt. Lett. 16, 1918–1920 (1991).
[CrossRef] [PubMed]

N. George, S.-G. Wang, D. L. Venable, “Pattern recognition using the ring-wedge photodetector and neural-network software,” in Optical Pattern Recognition II, H. J. Caufield, ed., Proc. SPIE1134, 96–106 (1989).
[CrossRef]

N. George, “Image quality rating system,” U.S. patent3,788,749 (29January1974).

N. George, J. T. Thomasson, A. Spindel, “Photodetector light pattern detector,” U.S. patent3,689,772 (5September1972).

D. M. Berfanger, N. George, “Automatic image quality assessment,” in Proceedings of ICPS ’94: The Physics and Chemistry of Imaging Systems, IS&T’s 47th Annual Conference (Society for Imaging Science and Technology, Springfield, Va., 1994), Vol 2, pp. 436–438.

Grogan, T. A.

T. A. Grogan, D. Keene, “Image quality evaluation with a contour-based perceptual model,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 188–197 (1992).
[CrossRef]

Habibi, A.

J. A. Saghri, P. S. Cheatham, A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. 28, 813–818 (1989).
[CrossRef]

Hamberg, R.

R. Hamberg, H. de Ridder, “Continuous assessment of time-varying image quality,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 248–259 (1997).
[CrossRef]

Hirleman, E. D.

E. D. Hirleman, “Optimal scaling of the inverse Fraunhofer diffraction particle sizing problem: the linear system produced by quadrature,” in Optical Particle Sizing Theory and Practice, G. Gouesbet, G. Grehan, eds. (Plenum, New York, 1988).
[CrossRef]

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1989), pp. 244–255.

Jayant, N.

N. Jayant, J. Johnston, R. Safranek, “Signal compression based on models of human perception,” Proc. IEEE 81, 1385–422 (1993).
[CrossRef]

Jensen, N.

N. Jensen, “High-speed image analysis techniques,” Photograph. Eng. 39, 1321–1328 (1973).

N. Jensen, Optical and Photographic Reconnaissance Systems (Wiley, New York, 1968), Chap. 8, pp. 102–115.

Johnston, J.

N. Jayant, J. Johnston, R. Safranek, “Signal compression based on models of human perception,” Proc. IEEE 81, 1385–422 (1993).
[CrossRef]

Jones, C. T.

A. A. Webster, C. T. Jones, M. H. Pinson, S. D. Voran, S. Wolf, “An objective video quality assessment system based on human perception,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 15–26 (1993).
[CrossRef]

Kayargadde, V.

V. Kayargadde, J.-B. Martens, “Estimation of perceived image blur using edge features,” Int. J. Imaging Syst. Technol. 7, 102–109 (1996).
[CrossRef]

V. Kayargadde, J.-B. Martens, “Perceptual characterization of images degraded by blur and noise: experiments,” J. Opt. Soc. Am. A 13, 1166–1177 (1996).
[CrossRef]

Keene, D.

T. A. Grogan, D. Keene, “Image quality evaluation with a contour-based perceptual model,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 188–197 (1992).
[CrossRef]

Kosugi, M.

S. Ohtsuka, M. Kosugi, “Quality evaluation of locally impaired pictures,” J. Soc. Inf. Disp. 32, 19–24 (1991).

S. Ohtsuka, M. Kosugi, “Quality evaluation of locally impaired pictures,” J. Soc. Inf. Disp. 32, 19–24 (1991).

Kusaka, H.

H. Kusaka, “Consideration of vision and picture quality: psychological effects induced by picture sharpness,” in Human Vision, Visual Processing, and Digital Display, B. E. Rogowitz, ed., Proc. SPIE1077, 50–55 (1989).
[CrossRef]

Latshaw, G. L.

G. L. Latshaw, P. L. Zuzelo, S. J. Briggs, “Tactical photointerpreter evaluations of hardcopy and softcopy imagery,” in Airborne Reconnaissance III: Collection and Exploitation of Reconnaissance Data, J. H. Smith, T. C. Freitag, eds., Proc. SPIE137, 179–87 (1978).
[CrossRef]

Li, Y.-C.

C.-H. Chou, Y.-C. Li, “A perceptually tuned subband image coder based on the measure of just-noticeable-distortion profile,” IEEE. Trans. Circuits Syst. V 5, 467–476 (1995).

Linfoot, E. H.

E. H. Linfoot, “Transmission factors and optical design,” J. Opt. Soc. Am. 46, 740–752 (1956).
[CrossRef]

E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal Press, London, 1964).

MacLeod, S.

Maddox, M. E.

H. L. Snyder, M. E. Maddox, D. I. Shedivy, J. A. Turpin, J. J. Burke, R. N. Strickland, “Digital image quality and interpretability: database and hardcopy studies,” Opt. Eng. 21, 14–22 (1982).
[CrossRef]

Maier, J. J.

Martens, J.-B.

V. Kayargadde, J.-B. Martens, “Perceptual characterization of images degraded by blur and noise: experiments,” J. Opt. Soc. Am. A 13, 1166–1177 (1996).
[CrossRef]

V. Kayargadde, J.-B. Martens, “Estimation of perceived image blur using edge features,” Int. J. Imaging Syst. Technol. 7, 102–109 (1996).
[CrossRef]

Mersereau, R. M.

T. P. Barnwell, R. M. Mersereau, “A comparison of some subjective and objective measures for image quality,” in Proceedings of the Eleventh Annual Asilomar Conference on Circuits Systems and Computers (Institute of Electrical and Electronics Engineers, New York, 1978), pp. 96–100.

Nill, N. B.

N. B. Nill, B. H. Bouzas, “Objective image quality measure derived from digital image power spectra,” Opt. Eng. 31, 813–825 (1992).
[CrossRef]

N. B. Nill, “Scene power spectra: the moment as an image quality merit factor,” Appl. Opt. 15, 2846–2854 (1976).
[CrossRef] [PubMed]

Ohtsuka, S.

S. Ohtsuka, M. Kosugi, “Quality evaluation of locally impaired pictures,” J. Soc. Inf. Disp. 32, 19–24 (1991).

S. Ohtsuka, M. Kosugi, “Quality evaluation of locally impaired pictures,” J. Soc. Inf. Disp. 32, 19–24 (1991).

Ophir, J.

N. Belaid, J. Cespedes, J. M. Thijssen, J. Ophir, “Lesion detection in simulated elastographic and echographic images: a psychophysical study,” Ultrasound Med. Biol. 20, 877–891 (1994).
[CrossRef] [PubMed]

Overington, I.

I. Overington, “Image quality and observer performance,” in Image Quality, P. S. Cheatham, ed., Proc. SPIE310, 2–9 (1981).
[CrossRef]

Parsons, J. R.

Pinson, M. H.

A. A. Webster, C. T. Jones, M. H. Pinson, S. D. Voran, S. Wolf, “An objective video quality assessment system based on human perception,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 15–26 (1993).
[CrossRef]

Pizlo, Z.

C. C. Taylor, Z. Pizlo, J. P. Allebach, C. A. Bouman, “Image quality assessment with a Gabor pyramid model of the human visual system,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 58–69 (1997).
[CrossRef]

Rose, D.

I. R. L. Davies, D. Rose, R. J. Smith, “Automated image quality assessment,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 27–36 (1993).
[CrossRef]

Roufs, J. A. J.

J. A. J. Roufs, “Perceptual image quality: concept and measurement,” Philips J. Res. 47, 35–62 (1992).

J. H. D. M. Westerink, J. A. J. Roufs, “Subjective image quality as a function of viewing distance, resolution, and picture size,” J. Soc. Motion Pict. Tel. Eng. 98, 113–119 (1989).

J. A. J. Roufs, M. C. Boschman, “Methods for evaluating the perceptual quality of VDUs,” in Human Vision and Electronic Imaging: Models, Methods, and Applications, B. E. Rogowitz, J. P. Allebached, eds., Proc. SPIE1249, 2–11 (1990).

Safranek, R.

N. Jayant, J. Johnston, R. Safranek, “Signal compression based on models of human perception,” Proc. IEEE 81, 1385–422 (1993).
[CrossRef]

Saghri, J. A.

J. A. Saghri, P. S. Cheatham, A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. 28, 813–818 (1989).
[CrossRef]

Schade, O. H.

O. H. Schade, “An evaluation of photographic image quality and resolving power,” J. Soc. Motion Pict. Tel. Eng. 73, 81–119 (1964).

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part IV. Image analysis in photographic and television systems (definition and sharpness),” J. Soc. Motion Pict. Tel. Eng. 64, 593–617 (1955).

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part III. The grain structure of television images,” J. Soc. Motion Pict. Tel. Eng. 61, 97–164 (1953).

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part II. The trainstructure of motion picture images—an analysis of deviations and fluctuations of the sample number,” J. Soc. Motion Pict. Tel. Eng. 58, 181–222 (1952).

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part I. image structure and transfer characteristics,” J. Soc. Motion Pict. Tel. Eng. 56, 137–177 (1951).

Schindler, R.

C. Allen, R. Schindler, “Determining image quality from electronic or digital signal characteristics,” in Advances in Image Transmission II, A. G. Tescher, ed., Proc. SPIE249, 179–184 (1980).
[CrossRef]

Schindler, R. A.

R. A. Schindler, “Physical measures of image quality and their relationship to performance,” in Advances in Display Technology, J. R. Parsons, ed., Proc. SPIE199, 117–125 (1979).
[CrossRef]

Shaw, R.

R. Shaw, “Evaluating the efficient of imaging processes,” Rep. Prog. Phys. 41, 1103–1155 (1978).
[CrossRef]

Shedivy, D. I.

H. L. Snyder, M. E. Maddox, D. I. Shedivy, J. A. Turpin, J. J. Burke, R. N. Strickland, “Digital image quality and interpretability: database and hardcopy studies,” Opt. Eng. 21, 14–22 (1982).
[CrossRef]

Smith, R. J.

I. R. L. Davies, D. Rose, R. J. Smith, “Automated image quality assessment,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 27–36 (1993).
[CrossRef]

Snyder, H. L.

H. L. Snyder, M. E. Maddox, D. I. Shedivy, J. A. Turpin, J. J. Burke, R. N. Strickland, “Digital image quality and interpretability: database and hardcopy studies,” Opt. Eng. 21, 14–22 (1982).
[CrossRef]

H. L. Snyder, “Image quality: measures and visual performance,” in Flat Panel Displays and CRT’s, L. E. Tannas, ed. (Van Nostrand Reinhold, New York, 1980), pp 70–90.

J. J. Burke, H. L. Snyder, “Quality metrics of digitally derived imagery and their relation to interpreter performance,” in Image Quality, P. S. Cheatham, ed., Proc. SPIE310, 16–23 (1981).
[CrossRef]

B. P. Chao, R. J. Beaton, H. L. Snyder, “Human performance evaluations of digital image quality,” in Advances in Display Technology III, E. Schlam, ed., Proc. SPIE386, 20–24 (1983).
[CrossRef]

Spindel, A.

N. George, J. T. Thomasson, A. Spindel, “Photodetector light pattern detector,” U.S. patent3,689,772 (5September1972).

Strickland, R. N.

H. L. Snyder, M. E. Maddox, D. I. Shedivy, J. A. Turpin, J. J. Burke, R. N. Strickland, “Digital image quality and interpretability: database and hardcopy studies,” Opt. Eng. 21, 14–22 (1982).
[CrossRef]

Taylor, C. C.

C. C. Taylor, Z. Pizlo, J. P. Allebach, C. A. Bouman, “Image quality assessment with a Gabor pyramid model of the human visual system,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 58–69 (1997).
[CrossRef]

Tescher, A. G.

Thijssen, J. M.

N. Belaid, J. Cespedes, J. M. Thijssen, J. Ophir, “Lesion detection in simulated elastographic and echographic images: a psychophysical study,” Ultrasound Med. Biol. 20, 877–891 (1994).
[CrossRef] [PubMed]

Thomasson, J. T.

N. George, J. T. Thomasson, A. Spindel, “Photodetector light pattern detector,” U.S. patent3,689,772 (5September1972).

Turpin, J. A.

H. L. Snyder, M. E. Maddox, D. I. Shedivy, J. A. Turpin, J. J. Burke, R. N. Strickland, “Digital image quality and interpretability: database and hardcopy studies,” Opt. Eng. 21, 14–22 (1982).
[CrossRef]

Venable, D. L.

D. L. Venable, “Pattern classification using diffraction pattern sampling and the limitations due to film grain noise,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1989).

N. George, S.-G. Wang, D. L. Venable, “Pattern recognition using the ring-wedge photodetector and neural-network software,” in Optical Pattern Recognition II, H. J. Caufield, ed., Proc. SPIE1134, 96–106 (1989).
[CrossRef]

Voran, S. D.

A. A. Webster, C. T. Jones, M. H. Pinson, S. D. Voran, S. Wolf, “An objective video quality assessment system based on human perception,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 15–26 (1993).
[CrossRef]

Wallace, G. K.

G. K. Wallace, “The JPEG still picture compression standard,” Commun. ACM 34, 30–44 (1991).
[CrossRef]

Wang, S.-G.

N. George, S.-G. Wang, D. L. Venable, “Pattern recognition using the ring-wedge photodetector and neural-network software,” in Optical Pattern Recognition II, H. J. Caufield, ed., Proc. SPIE1134, 96–106 (1989).
[CrossRef]

Watson, A. B.

A. B. Watson, “Efficiency of a model human image code,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
[CrossRef] [PubMed]

A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision, Graph. Image Process. 39, 311–27 (1987).
[CrossRef]

A. B. Watson, “DCT quantization matrices visually optimized for individual images,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 202–216 (1993).
[CrossRef]

Webster, A. A.

A. A. Webster, C. T. Jones, M. H. Pinson, S. D. Voran, S. Wolf, “An objective video quality assessment system based on human perception,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 15–26 (1993).
[CrossRef]

Wen, C. Y.

C. Y. Wen, R. J. Beaton, “Subjective image quality evaluation of image compression techniques,” in Proceedings of the Human Factors and Ergonomics Society, 40th Annual Meeting 1996 (Human Factors and Ergonomics Society, Santa Monica, Calif., 1996), Vol. 2, pp. 1188–1192.
[CrossRef]

Westerink, J. H. D. M.

J. H. D. M. Westerink, J. A. J. Roufs, “Subjective image quality as a function of viewing distance, resolution, and picture size,” J. Soc. Motion Pict. Tel. Eng. 98, 113–119 (1989).

Wetherell, W. B.

W. B. Wetherell, “The calculation of image quality,” in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1980), Vol. VIII, pp. 171–312.
[CrossRef]

Wolf, S.

A. A. Webster, C. T. Jones, M. H. Pinson, S. D. Voran, S. Wolf, “An objective video quality assessment system based on human perception,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 15–26 (1993).
[CrossRef]

Zuzelo, P. L.

G. L. Latshaw, P. L. Zuzelo, S. J. Briggs, “Tactical photointerpreter evaluations of hardcopy and softcopy imagery,” in Airborne Reconnaissance III: Collection and Exploitation of Reconnaissance Data, J. H. Smith, T. C. Freitag, eds., Proc. SPIE137, 179–87 (1978).
[CrossRef]

Appl. Opt.

Commun. ACM

G. K. Wallace, “The JPEG still picture compression standard,” Commun. ACM 34, 30–44 (1991).
[CrossRef]

Comput. Vision, Graph. Image Process.

A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision, Graph. Image Process. 39, 311–27 (1987).
[CrossRef]

IEEE. Trans. Circuits Syst. V

C.-H. Chou, Y.-C. Li, “A perceptually tuned subband image coder based on the measure of just-noticeable-distortion profile,” IEEE. Trans. Circuits Syst. V 5, 467–476 (1995).

Int. J. Imaging Syst. Technol.

V. Kayargadde, J.-B. Martens, “Estimation of perceived image blur using edge features,” Int. J. Imaging Syst. Technol. 7, 102–109 (1996).
[CrossRef]

J. Electron. Imaging

D. R. Fuhrmann, J. A. Baro, J. R. Cox, “Experimental evaluation of psychophysical distortion metrics for JPEG-encoded images,” J. Electron. Imaging 4, 397–406 (1995).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Soc. Inf. Disp.

S. Ohtsuka, M. Kosugi, “Quality evaluation of locally impaired pictures,” J. Soc. Inf. Disp. 32, 19–24 (1991).

S. Ohtsuka, M. Kosugi, “Quality evaluation of locally impaired pictures,” J. Soc. Inf. Disp. 32, 19–24 (1991).

J. Soc. Motion Pict. Tel. Eng.

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part I. image structure and transfer characteristics,” J. Soc. Motion Pict. Tel. Eng. 56, 137–177 (1951).

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part II. The trainstructure of motion picture images—an analysis of deviations and fluctuations of the sample number,” J. Soc. Motion Pict. Tel. Eng. 58, 181–222 (1952).

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part III. The grain structure of television images,” J. Soc. Motion Pict. Tel. Eng. 61, 97–164 (1953).

O. H. Schade, “Image gradiation, graininess and sharpness in television and motion-picture systems. Part IV. Image analysis in photographic and television systems (definition and sharpness),” J. Soc. Motion Pict. Tel. Eng. 64, 593–617 (1955).

O. H. Schade, “An evaluation of photographic image quality and resolving power,” J. Soc. Motion Pict. Tel. Eng. 73, 81–119 (1964).

J. H. D. M. Westerink, J. A. J. Roufs, “Subjective image quality as a function of viewing distance, resolution, and picture size,” J. Soc. Motion Pict. Tel. Eng. 98, 113–119 (1989).

Opt. Eng.

H. L. Snyder, M. E. Maddox, D. I. Shedivy, J. A. Turpin, J. J. Burke, R. N. Strickland, “Digital image quality and interpretability: database and hardcopy studies,” Opt. Eng. 21, 14–22 (1982).
[CrossRef]

N. B. Nill, B. H. Bouzas, “Objective image quality measure derived from digital image power spectra,” Opt. Eng. 31, 813–825 (1992).
[CrossRef]

J. A. Saghri, P. S. Cheatham, A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. 28, 813–818 (1989).
[CrossRef]

Opt. Lett.

Philips J. Res.

J. A. J. Roufs, “Perceptual image quality: concept and measurement,” Philips J. Res. 47, 35–62 (1992).

Photograph. Eng.

N. Jensen, “High-speed image analysis techniques,” Photograph. Eng. 39, 1321–1328 (1973).

Proc. IEEE

N. Jayant, J. Johnston, R. Safranek, “Signal compression based on models of human perception,” Proc. IEEE 81, 1385–422 (1993).
[CrossRef]

Rep. Prog. Phys.

R. Shaw, “Evaluating the efficient of imaging processes,” Rep. Prog. Phys. 41, 1103–1155 (1978).
[CrossRef]

Signal. Process.

M. P. Eckert, A. P. Bradley, “Perceptual quality metrics applied to still image compression,” Signal. Process. 70, 177–200 (1998).
[CrossRef]

Ultrasound Med. Biol.

N. Belaid, J. Cespedes, J. M. Thijssen, J. Ophir, “Lesion detection in simulated elastographic and echographic images: a psychophysical study,” Ultrasound Med. Biol. 20, 877–891 (1994).
[CrossRef] [PubMed]

Other

C. Y. Wen, R. J. Beaton, “Subjective image quality evaluation of image compression techniques,” in Proceedings of the Human Factors and Ergonomics Society, 40th Annual Meeting 1996 (Human Factors and Ergonomics Society, Santa Monica, Calif., 1996), Vol. 2, pp. 1188–1192.
[CrossRef]

S. J. Briggs, “The definition and measurement of image quality,” in Advances in Image Transmission II, A. G. Tescher, ed., Proc. SPIE249, 170–174 (1980).
[CrossRef]

J. J. Burke, H. L. Snyder, “Quality metrics of digitally derived imagery and their relation to interpreter performance,” in Image Quality, P. S. Cheatham, ed., Proc. SPIE310, 16–23 (1981).
[CrossRef]

B. P. Chao, R. J. Beaton, H. L. Snyder, “Human performance evaluations of digital image quality,” in Advances in Display Technology III, E. Schlam, ed., Proc. SPIE386, 20–24 (1983).
[CrossRef]

G. L. Latshaw, P. L. Zuzelo, S. J. Briggs, “Tactical photointerpreter evaluations of hardcopy and softcopy imagery,” in Airborne Reconnaissance III: Collection and Exploitation of Reconnaissance Data, J. H. Smith, T. C. Freitag, eds., Proc. SPIE137, 179–87 (1978).
[CrossRef]

W. B. Wetherell, “The calculation of image quality,” in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1980), Vol. VIII, pp. 171–312.
[CrossRef]

N. George, “Image quality rating system,” U.S. patent3,788,749 (29January1974).

N. George, J. T. Thomasson, A. Spindel, “Photodetector light pattern detector,” U.S. patent3,689,772 (5September1972).

N. Jensen, Optical and Photographic Reconnaissance Systems (Wiley, New York, 1968), Chap. 8, pp. 102–115.

E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal Press, London, 1964).

J. A. J. Roufs, M. C. Boschman, “Methods for evaluating the perceptual quality of VDUs,” in Human Vision and Electronic Imaging: Models, Methods, and Applications, B. E. Rogowitz, J. P. Allebached, eds., Proc. SPIE1249, 2–11 (1990).

R. Hamberg, H. de Ridder, “Continuous assessment of time-varying image quality,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 248–259 (1997).
[CrossRef]

T. A. Grogan, D. Keene, “Image quality evaluation with a contour-based perceptual model,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 188–197 (1992).
[CrossRef]

I. R. L. Davies, D. Rose, R. J. Smith, “Automated image quality assessment,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 27–36 (1993).
[CrossRef]

S. Daly, “The visible differences predictor: an algorithm for the assessment of image fidelity,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 2–14 (1992).
[CrossRef]

H. L. Snyder, “Image quality: measures and visual performance,” in Flat Panel Displays and CRT’s, L. E. Tannas, ed. (Van Nostrand Reinhold, New York, 1980), pp 70–90.

I. Overington, “Image quality and observer performance,” in Image Quality, P. S. Cheatham, ed., Proc. SPIE310, 2–9 (1981).
[CrossRef]

C. K. Abbey, H. H. Barrett, M. P. Eckstein, “Practical issues and methodology in assessment of image quality using model observers,” in Medical Imaging 1997. Physics of Medical Imaging, R. L. Van Metter, J. Beutel, eds., Proc. SPIE3032, 182–194 (1997).
[CrossRef]

C. C. Taylor, Z. Pizlo, J. P. Allebach, C. A. Bouman, “Image quality assessment with a Gabor pyramid model of the human visual system,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 58–69 (1997).
[CrossRef]

T. P. Barnwell, R. M. Mersereau, “A comparison of some subjective and objective measures for image quality,” in Proceedings of the Eleventh Annual Asilomar Conference on Circuits Systems and Computers (Institute of Electrical and Electronics Engineers, New York, 1978), pp. 96–100.

R. A. Schindler, “Physical measures of image quality and their relationship to performance,” in Advances in Display Technology, J. R. Parsons, ed., Proc. SPIE199, 117–125 (1979).
[CrossRef]

D. L. Venable, “Pattern classification using diffraction pattern sampling and the limitations due to film grain noise,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1989).

D. M. Berfanger, N. George, “Automatic image quality assessment,” in Proceedings of ICPS ’94: The Physics and Chemistry of Imaging Systems, IS&T’s 47th Annual Conference (Society for Imaging Science and Technology, Springfield, Va., 1994), Vol 2, pp. 436–438.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1989), pp. 244–255.

A. A. Webster, C. T. Jones, M. H. Pinson, S. D. Voran, S. Wolf, “An objective video quality assessment system based on human perception,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 15–26 (1993).
[CrossRef]

A. B. Watson, “DCT quantization matrices visually optimized for individual images,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 202–216 (1993).
[CrossRef]

T. Eude, H. Cherifi, “Quality metrics for low bitrate coding,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 70–81 (1997).
[CrossRef]

N. George, S.-G. Wang, D. L. Venable, “Pattern recognition using the ring-wedge photodetector and neural-network software,” in Optical Pattern Recognition II, H. J. Caufield, ed., Proc. SPIE1134, 96–106 (1989).
[CrossRef]

H. Kusaka, “Consideration of vision and picture quality: psychological effects induced by picture sharpness,” in Human Vision, Visual Processing, and Digital Display, B. E. Rogowitz, ed., Proc. SPIE1077, 50–55 (1989).
[CrossRef]

Joint Photographic Experts Group Compact Disc, “Information technology—digital compression and coding of continuous-tone still images,” International Organization for Standardization/International Electrotechnical Commission Standard (available through American National Standards Institute web site, http://www.ansi.org ). ISO/IEC 10918–1:1994.

C. Allen, R. Schindler, “Determining image quality from electronic or digital signal characteristics,” in Advances in Image Transmission II, A. G. Tescher, ed., Proc. SPIE249, 179–184 (1980).
[CrossRef]

E. D. Hirleman, “Optimal scaling of the inverse Fraunhofer diffraction particle sizing problem: the linear system produced by quadrature,” in Optical Particle Sizing Theory and Practice, G. Gouesbet, G. Grehan, eds. (Plenum, New York, 1988).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

(a) Coherent optoelectronic hybrid processor incorporating the analog ring–wedge detector array and neural-network software. (b) All-digital Fourier domain recognition system incorporating ring–wedge data format and neural-network software. O, input object; L, (a) optical transform lens, (b) imaging lens; S, sampling system; FFT, fast Fourier transform; R/W, digital ring–wedge detector; NS, neural-network software; C, digital computer; A, amplifier and interface.

Fig. 2
Fig. 2

Example gray-scale images used in blur-level and JPEG compression studies. Types of pictures include (a) animals, (b) human faces, (c) natural landscapes, (d) architecture, and (e) other.

Fig. 3
Fig. 3

Spatial masks used in the blurring of images in the blur-level study. No mask is shown for the original image (o). Quality descriptors for blurred images are (1) good, (2) fair, (3) poor, and (4) very poor.

Fig. 4
Fig. 4

Representative degradation levels for images used in the blur-level study. Quality descriptors for the images are (o) very good, (1) good, (2) fair, (3) poor, and (4) very poor.

Fig. 5
Fig. 5

Spatial masks for calculating the weighted average of luminance changes in four directions.

Fig. 6
Fig. 6

Edge profiles of a representative image at the five degradation levels used in the blur-level study. Quality descriptors for the images are (o) very good, (1) good, (2) fair, (3) poor, and (4) very poor.

Fig. 7
Fig. 7

All-digital Fourier domain image quality rating system incorporating ring–wedge data format and neural-network software: O, input object; L, imaging lens; S, sampling system; FFT, fast Fourier transform; EDGE, edge profile calculation; R/W, digital ring–wedge detector; NS, neural-network software.

Fig. 8
Fig. 8

Representative degradation levels for images used in the JPEG compression study. The original image is shown (o), and the q factors for each image are as shown.

Fig. 9
Fig. 9

Edge profiles for the representative images shown in Fig. 9 with q factors as labeled.

Fig. 10
Fig. 10

Error images for a representative image at the five degradation levels used in the JPEG compression study with q factors as labeled.

Fig. 11
Fig. 11

Correlation diagram showing the neural network estimate (without knowledge of the original) versus the signal-to-perceptible-noise ratio (decibels). A single-stage system based on the localized ring–wedge transform is shown to yield a correlation coefficient of 0.68.

Fig. 12
Fig. 12

Correlation diagram showing the neural-network estimate (without knowledge of the original) versus the signal-to-perceptible-noise ratio (decibels). A two-stage system incorporating both a global image quality assessment and subsequent localized assessments is shown to yield a correlation coefficient of 0.95.

Fig. 13
Fig. 13

Representative example of local image fidelity estimation showing a 0.93 correlation between estimates and calculated perceptual fidelity: (a) original image, (b) JPEG compressed image, (c) calculated local perceptual fidelity, and (d) estimated local fidelity.

Fig. 14
Fig. 14

Sampling geometry used by the all-digital ring–wedge detector incorporating 32 ring and 32 wedge sampling regions chosen to simulate the analog multielement array (figure reproduced from Ref. 26 with permission).

Fig. 15
Fig. 15

Low-pass operator for calculating the average background luminance.

Tables (14)

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Table 1 Learning–Testing Strategy for a Preliminary Experiment Based on Blur-Level Classification Including a Single Representative Scene for Each of Five Types in Both the Learning and the Testing Sets

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Table 2 Classification Results Detailing Error Occurrences for Each Degradation Level

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Table 3 Learning–Testing Strategy for a Preliminary Experiment Based on Blur-Level Recognition Including a Single Representative Scene for Only Three of the Five Types in the Learning Set and All Five Types in the Testing Set

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Table 4 Recognition Results

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Table 5 Error Rate Fraction for Blur-Level Classification Showing the Number of Cycles in the Training

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Table 6 Blur-Level Classification Accuracy for Only Ring Data from Both Gray-Scale Imagery and Corresponding Edge Profiles for a Data Set of 250 Separate Images in the Testing Set with Ten Errors

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Table 7 Blur-Level Classification Accuracy for Only Wedge Data from Both Gray-Scale Imagery and Corresponding Edge Profiles for a Data Set of 250 Separate Images in the Testing Set with 59 Errors

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Table 8 Blur-Level Classification Accuracy for Both Ring and Wedge Data from Gray-Scale Imagery and Corresponding Edge Profiles for a Data Set of 250 Separate Images in the Testing Set with 18 Errors

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Table 9 Blur-Level Classification Accuracy Using Four Common Image Objective Image Quality Measures from Gray-Scale Imagery for a Data Set of 250 Separate Images in the Testing Set with an Overall Accuracy of 53%

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Table 10 JPEG Quality Classification Accuracy for Only Ring Data from Both Gray-Scale Imagery and Corresponding Edge Profiles for a Data Set of 250 Separate Images in the Testing Set with 20 Errors

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Table 11 JPEG Quality Classification Accuracy for Only Wedge Data from Both Gray-Scale Imagery and Corresponding Edge Profiles for a Data Set of 250 Separate Images in the Testing Set with 66 Errors

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Table 12 JPEG Quality Classification Accuracy for Both Ring and Wedge Data from Gray-Scale Imagery and Corresponding Edge Profiles for a Data Set of 250 Separate Images in the Testing Set with 13 Errors

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Table 13 JPEG Fidelity Classification Accuracy for Both Ring and Wedge Data from Error Images between Degraded Images and Corresponding High-Quality Originals for a Data Set of 250 Separate Images in the Testing Set with Five Errors

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Table 14 Summary of Results for Automatic Image Quality Assessment Using the All-Digital Ring–Wedge Detector

Equations (18)

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hx, y=12πσ2exp-x2+y22σ2,
Q=uv F˜u, vF˜o*u, vuv |F˜ou, v|2,
T=uv |F˜u, v|2uv |F˜ou, v|2,
Ne=uvF˜u, vF˜ou, v2.
M=uvu2+v23/2|F˜u, v|2uvu2+v21/2|F˜ou, v|2.
mj=Rjdfxdfy|Ffx, fy|,
Rj=fx, fy: ρjfx2+fy21/2<ρj+Δρj,ϕmintan-1fy/fx<ϕmin+π,
Rj=fx, fy: ρminfx2+fy21/2<ρmax,ϕjtan-1fy/fx<ϕj+Δϕj,
mju=0N-1v=0M-1 |F˜u, v|M˜ju, v,
M˜ju, v=1uΔfx, vΔfyRj0otherwise,
M˜ju, v=RjdfxdfyIfx-uΔfx, fy-vΔfy,
PSPNR=20 log10255|fn, m-fon, m|-JNDn, m2δn, m1/2,
δn, m=1if |fn, m-fon, m|>JNDn, m0otherwise,
JNDn, m=maxf1bn, m, gn, m,×f2bn, m,
f1bn, m, gn, m=gn, mαbn, m+βbn, m,
f2bn, m=T01-bn, m/1271/2+3γbn, m-127+3bn, m127otherwise,
αbn, m=0.0001×bn, m+0.115,
βbn, m=λ-0.01×bn, m.

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