Abstract

A psychophysical experiment is described that quantifies human sensitivities to suprathreshold distortions caused by wavelet coefficient quantization in natural images, and the resulting analysis is explained. The quantizer step sizes that cause the first three visible degradations relative to the original image are well predicted by exponential functions of subband standard deviation. The resulting root-mean-square (RMS) error in the image is constant for a spatial frequency and is independent of orientation. Contrast sensitivity calculations suggest a higher sensitivity to bands with higher energy, and threshold elevations for the second and third visible degradations are predicted well by the constant-RMS model. A quantization strategy based on the results is proposed for low-bit-rate applications.

© 2001 Optical Society of America

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References

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  1. J. M. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process. 41, 3445–3462 (1993).
    [CrossRef]
  2. A. Said, W. Pearlman, “A new fast and efficient image coded based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Syst. Video Technol. 6, 243–250 (1996).
    [CrossRef]
  3. S. Daly, JPEG-2000 proposal (Joint Photographic Experts Group) Sharp Labs of America, daly@sharplabs.com (personal communication, November1998).
  4. R. A. Devore, B. Jawerth, B. J. Lucier, “Image compression through wavelet coding,” IEEE Trans. Infor. Theory 38, 719–746 (1992).
    [CrossRef]
  5. M. K. Mandal, S. Panchanathan, T. Aboulnasr, “Wavelet-based image coding using HVS characteristics,” in Wavelet Applications in Signal and Image Processing III, A. F. Laine, M. A. Unser, eds., Proc. SPIE2569, 345–352 (1995).
    [CrossRef]
  6. P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
    [CrossRef]
  7. 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. Video Technol. 5, 467–476 (1995).
    [CrossRef]
  8. A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
    [CrossRef] [PubMed]
  9. R. J. Safranek, J. D. Johnston, “A perceptually tuned subband image coder with image dependent quantization and post-quantization data compression,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N. J., 1989), Vol. 3, pp. 1945–1948.
  10. I. Hontsch, L. J. Karam, R. J. Safranek, “A perceptually tuned embedded zerotree image coder,” in Proceedings of the IEEE International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1997), Vol. 1, pp. 41–44.
  11. A. Mazzarri, R. Leonardi, “Perceptual embedded image coding using wavelet transforms,” in Proceedings of the IEEE International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1995), Vol. 1, pp. 586–589.
  12. W. C. Fong, S. C. Chan, K. L. Ho, “Determination of the visibility thresholds for subband image coding,” in Proceedings of the IEEE International Symposium on Circuits and Systems (IEEE Press, Piscataway, N.J., 1997), pp. 1121–1124.
  13. L. Gaudart, T. Grebassa, J. P. Petrakian, “Wavelet transforms in human visual channels,” Appl. Opt. 32, 4119–4127 (1993).
    [CrossRef] [PubMed]
  14. B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3125 (1997).
    [CrossRef]
  15. R. Sekuler, R. Blake, Perception (McGraw-Hill, New York, 1994).
  16. S. Daly, “Application of a noise-adaptive contrast sensitivity function to image data compression,” Opt. Eng. (Bellingham) 29, 977–987 (1990).
    [CrossRef]
  17. D. Taubman, “High performance scalable image compression with EBCOT,” IEEE Trans. Image Process. 9, 1158–1170 (1999).
    [CrossRef]
  18. J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for efficient image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
    [CrossRef]
  19. M. G. Ramos, S. S. Hemami, “Perceptually-based scalable image coding for packet networks,” J. Electron. Imaging 7, 453–463 (1998).
    [CrossRef]
  20. A. Gersho, R. M. Gray, Vector Quantization and Signal Compression (Kluwer Academic, Dordrecht, The Netherlands, 1992).
  21. E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
    [CrossRef] [PubMed]
  22. A. B. Watson, “DCT quantization matrices visually optimized for individual images,” in Human Vision, Visual Processing, and Digital Display, J. P. Alleback, B. E. Rogowitz, eds., Proc. SPIE1913, 202–216 (1993).
    [CrossRef]

1999

D. Taubman, “High performance scalable image compression with EBCOT,” IEEE Trans. Image Process. 9, 1158–1170 (1999).
[CrossRef]

1998

M. G. Ramos, S. S. Hemami, “Perceptually-based scalable image coding for packet networks,” J. Electron. Imaging 7, 453–463 (1998).
[CrossRef]

1997

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3125 (1997).
[CrossRef]

1996

A. Said, W. Pearlman, “A new fast and efficient image coded based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Syst. Video Technol. 6, 243–250 (1996).
[CrossRef]

1995

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. Video Technol. 5, 467–476 (1995).
[CrossRef]

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for efficient image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef]

1993

J. M. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process. 41, 3445–3462 (1993).
[CrossRef]

L. Gaudart, T. Grebassa, J. P. Petrakian, “Wavelet transforms in human visual channels,” Appl. Opt. 32, 4119–4127 (1993).
[CrossRef] [PubMed]

1992

R. A. Devore, B. Jawerth, B. J. Lucier, “Image compression through wavelet coding,” IEEE Trans. Infor. Theory 38, 719–746 (1992).
[CrossRef]

1990

S. Daly, “Application of a noise-adaptive contrast sensitivity function to image data compression,” Opt. Eng. (Bellingham) 29, 977–987 (1990).
[CrossRef]

E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
[CrossRef] [PubMed]

Aboulnasr, T.

M. K. Mandal, S. Panchanathan, T. Aboulnasr, “Wavelet-based image coding using HVS characteristics,” in Wavelet Applications in Signal and Image Processing III, A. F. Laine, M. A. Unser, eds., Proc. SPIE2569, 345–352 (1995).
[CrossRef]

Belzer, B.

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for efficient image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef]

Blake, R.

R. Sekuler, R. Blake, Perception (McGraw-Hill, New York, 1994).

Chan, S. C.

W. C. Fong, S. C. Chan, K. L. Ho, “Determination of the visibility thresholds for subband image coding,” in Proceedings of the IEEE International Symposium on Circuits and Systems (IEEE Press, Piscataway, N.J., 1997), pp. 1121–1124.

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. Video Technol. 5, 467–476 (1995).
[CrossRef]

Daly, S.

S. Daly, “Application of a noise-adaptive contrast sensitivity function to image data compression,” Opt. Eng. (Bellingham) 29, 977–987 (1990).
[CrossRef]

S. Daly, JPEG-2000 proposal (Joint Photographic Experts Group) Sharp Labs of America, daly@sharplabs.com (personal communication, November1998).

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

Devore, R. A.

R. A. Devore, B. Jawerth, B. J. Lucier, “Image compression through wavelet coding,” IEEE Trans. Infor. Theory 38, 719–746 (1992).
[CrossRef]

Field, D. J.

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3125 (1997).
[CrossRef]

Fong, W. C.

W. C. Fong, S. C. Chan, K. L. Ho, “Determination of the visibility thresholds for subband image coding,” in Proceedings of the IEEE International Symposium on Circuits and Systems (IEEE Press, Piscataway, N.J., 1997), pp. 1121–1124.

Gaborsky, R. S.

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

Gaudart, L.

Gersho, A.

A. Gersho, R. M. Gray, Vector Quantization and Signal Compression (Kluwer Academic, Dordrecht, The Netherlands, 1992).

Gray, R. M.

A. Gersho, R. M. Gray, Vector Quantization and Signal Compression (Kluwer Academic, Dordrecht, The Netherlands, 1992).

Grebassa, T.

Hemami, S. S.

M. G. Ramos, S. S. Hemami, “Perceptually-based scalable image coding for packet networks,” J. Electron. Imaging 7, 453–463 (1998).
[CrossRef]

Ho, K. L.

W. C. Fong, S. C. Chan, K. L. Ho, “Determination of the visibility thresholds for subband image coding,” in Proceedings of the IEEE International Symposium on Circuits and Systems (IEEE Press, Piscataway, N.J., 1997), pp. 1121–1124.

Hontsch, I.

I. Hontsch, L. J. Karam, R. J. Safranek, “A perceptually tuned embedded zerotree image coder,” in Proceedings of the IEEE International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1997), Vol. 1, pp. 41–44.

Jawerth, B.

R. A. Devore, B. Jawerth, B. J. Lucier, “Image compression through wavelet coding,” IEEE Trans. Infor. Theory 38, 719–746 (1992).
[CrossRef]

Johnston, J. D.

R. J. Safranek, J. D. Johnston, “A perceptually tuned subband image coder with image dependent quantization and post-quantization data compression,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N. J., 1989), Vol. 3, pp. 1945–1948.

Jones, P. W.

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

Karam, L. J.

I. Hontsch, L. J. Karam, R. J. Safranek, “A perceptually tuned embedded zerotree image coder,” in Proceedings of the IEEE International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1997), Vol. 1, pp. 41–44.

Leonardi, R.

A. Mazzarri, R. Leonardi, “Perceptual embedded image coding using wavelet transforms,” in Proceedings of the IEEE International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1995), Vol. 1, pp. 586–589.

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. Video Technol. 5, 467–476 (1995).
[CrossRef]

Liao, J.

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for efficient image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef]

Lucier, B. J.

R. A. Devore, B. Jawerth, B. J. Lucier, “Image compression through wavelet coding,” IEEE Trans. Infor. Theory 38, 719–746 (1992).
[CrossRef]

Mandal, M. K.

M. K. Mandal, S. Panchanathan, T. Aboulnasr, “Wavelet-based image coding using HVS characteristics,” in Wavelet Applications in Signal and Image Processing III, A. F. Laine, M. A. Unser, eds., Proc. SPIE2569, 345–352 (1995).
[CrossRef]

Mazzarri, A.

A. Mazzarri, R. Leonardi, “Perceptual embedded image coding using wavelet transforms,” in Proceedings of the IEEE International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1995), Vol. 1, pp. 586–589.

Olshausen, B. A.

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3125 (1997).
[CrossRef]

Panchanathan, S.

M. K. Mandal, S. Panchanathan, T. Aboulnasr, “Wavelet-based image coding using HVS characteristics,” in Wavelet Applications in Signal and Image Processing III, A. F. Laine, M. A. Unser, eds., Proc. SPIE2569, 345–352 (1995).
[CrossRef]

Pearlman, W.

A. Said, W. Pearlman, “A new fast and efficient image coded based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Syst. Video Technol. 6, 243–250 (1996).
[CrossRef]

Peli, E.

Petrakian, J. P.

Rabbani, M.

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

Ramos, M. G.

M. G. Ramos, S. S. Hemami, “Perceptually-based scalable image coding for packet networks,” J. Electron. Imaging 7, 453–463 (1998).
[CrossRef]

Safranek, R. J.

I. Hontsch, L. J. Karam, R. J. Safranek, “A perceptually tuned embedded zerotree image coder,” in Proceedings of the IEEE International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1997), Vol. 1, pp. 41–44.

R. J. Safranek, J. D. Johnston, “A perceptually tuned subband image coder with image dependent quantization and post-quantization data compression,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N. J., 1989), Vol. 3, pp. 1945–1948.

Said, A.

A. Said, W. Pearlman, “A new fast and efficient image coded based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Syst. Video Technol. 6, 243–250 (1996).
[CrossRef]

Sekuler, R.

R. Sekuler, R. Blake, Perception (McGraw-Hill, New York, 1994).

Shapiro, J. M.

J. M. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process. 41, 3445–3462 (1993).
[CrossRef]

Solomon, J. A.

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

Taubman, D.

D. Taubman, “High performance scalable image compression with EBCOT,” IEEE Trans. Image Process. 9, 1158–1170 (1999).
[CrossRef]

Villasenor, J.

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for efficient image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef]

Watson, A. B.

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

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

Yang, G. Y.

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

Appl. Opt.

IEEE Trans. Circuits Syst. Video Technol.

A. Said, W. Pearlman, “A new fast and efficient image coded based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Syst. Video Technol. 6, 243–250 (1996).
[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. Video Technol. 5, 467–476 (1995).
[CrossRef]

IEEE Trans. Image Process

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for efficient image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef]

IEEE Trans. Image Process.

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

D. Taubman, “High performance scalable image compression with EBCOT,” IEEE Trans. Image Process. 9, 1158–1170 (1999).
[CrossRef]

IEEE Trans. Infor. Theory

R. A. Devore, B. Jawerth, B. J. Lucier, “Image compression through wavelet coding,” IEEE Trans. Infor. Theory 38, 719–746 (1992).
[CrossRef]

IEEE Trans. Signal Process.

J. M. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process. 41, 3445–3462 (1993).
[CrossRef]

J. Electron. Imaging

M. G. Ramos, S. S. Hemami, “Perceptually-based scalable image coding for packet networks,” J. Electron. Imaging 7, 453–463 (1998).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng. (Bellingham)

S. Daly, “Application of a noise-adaptive contrast sensitivity function to image data compression,” Opt. Eng. (Bellingham) 29, 977–987 (1990).
[CrossRef]

Vision Res.

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3125 (1997).
[CrossRef]

Other

R. Sekuler, R. Blake, Perception (McGraw-Hill, New York, 1994).

A. Gersho, R. M. Gray, Vector Quantization and Signal Compression (Kluwer Academic, Dordrecht, The Netherlands, 1992).

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

M. K. Mandal, S. Panchanathan, T. Aboulnasr, “Wavelet-based image coding using HVS characteristics,” in Wavelet Applications in Signal and Image Processing III, A. F. Laine, M. A. Unser, eds., Proc. SPIE2569, 345–352 (1995).
[CrossRef]

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

S. Daly, JPEG-2000 proposal (Joint Photographic Experts Group) Sharp Labs of America, daly@sharplabs.com (personal communication, November1998).

R. J. Safranek, J. D. Johnston, “A perceptually tuned subband image coder with image dependent quantization and post-quantization data compression,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N. J., 1989), Vol. 3, pp. 1945–1948.

I. Hontsch, L. J. Karam, R. J. Safranek, “A perceptually tuned embedded zerotree image coder,” in Proceedings of the IEEE International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1997), Vol. 1, pp. 41–44.

A. Mazzarri, R. Leonardi, “Perceptual embedded image coding using wavelet transforms,” in Proceedings of the IEEE International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1995), Vol. 1, pp. 586–589.

W. C. Fong, S. C. Chan, K. L. Ho, “Determination of the visibility thresholds for subband image coding,” in Proceedings of the IEEE International Symposium on Circuits and Systems (IEEE Press, Piscataway, N.J., 1997), pp. 1121–1124.

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Figures (13)

Fig. 1
Fig. 1

Frequency response of a five-level hierarchical 9/7 biorthogonal synthesis filter bank.

Fig. 2
Fig. 2

Tiling of the two-dimensional frequency plane by five-level hierarchical wavelet decomposition. Only the upper right quadrant is shown, and the fifth-level bands are not labeled. The labels refer to the subbands described in Subsection 2.B.

Fig. 3
Fig. 3

ln[MNDSS(1)] versus ln(σsub) for the first VDU. The line is fitted with y=0.3477x+3.4265 and R2=0.5196.

Fig. 4
Fig. 4

RMS error induced in the image by quantization versus spatial frequency: (a) for LH and HL bands; the curve is the average of the six points at each frequency. (b) For HH bands; the curve is the average of the three points at each frequency pair.

Fig. 5
Fig. 5

Contrast sensitivity functions for the first VDU for (a) LH and HL bands in the horizontal SEDC, (b) LH and HL bands in the vertical SEDC, (c) LH and HL bands in the nonoriented SEDC, and (d) HH bands in all three SEDCs. Note the higher sensitivity to the LH bands in (a) and the higher sensitivity to the HL bands in (b) and that neither orientation is favored in (c). Sensitivities to the HH bands are approximately equal and are independent of SEDC.

Fig. 6
Fig. 6

Results for the first three VDUs. (a) Regression line fits for ln[MNDSS(VDU)] versus ln(σsub). For the second VDU, y=0.3346x+3.897 and R2=0.5215. For the third VDU, y=0.3478x+4.113 and R2=0.5783. (b) RMS error induced in the synthesized image by quantization versus spatial frequency for LH and HL bands in the three SEDCs. The curves are the averages of the six points for each VDU at each frequency. (c) RMS error induced in the synthesized image by quantization versus spatial frequency for HH bands in the three SEDCs.

Fig. 7
Fig. 7

Contrast sensitivity functions for the second VDU for (a) LH and HL bands in the horizontal SEDC, (b) LH and HL bands in the vertical SEDC, (c) LH and HL bands in the nonoriented SEDC, (d) HH bands in the three SEDCs. Although the sensitivities are lower than for the first VDU, the general trends are the same.

Fig. 8
Fig. 8

Contrast sensitivity functions for the third VDU for (a) LH and HL bands in the horizontal SEDC, (b) LH and HL bands in the vertical SEDC, (c) LH and HL bands in the nonoriented SEDC, and (d) HH bands in the three SEDCs. As with the CSFs for the second VDU, the sensitivities are again lower and the general trends are the same.

Fig. 9
Fig. 9

Relative threshold elevations for the LH and HL bands in the second and third VDUs relative to thresholds for the first VDU. The solid curves were obtained from the actual contrast for each SEDC separately; the dashed curves are the elevation predictions from the mean RMS values from Fig. 6(b) [and are the same in (a)–(c)]. (a) Horizontal SEDC, (b) vertical SEDC, (c) nonoriented SEDC.

Fig. 10
Fig. 10

Relative threshold elevations for the HH bands for the second and third VDUs relative to thresholds for the first VDU. The solid curves were obtained from the actual contrast for each SEDC separately; the dashed curves are the elevation predictions from the mean RMS values from Fig. 6(c) [and are the same in (a)–(c)]. (a) Horizontal SEDC, (b) vertical SEDC, (c) nonoriented SEDC.

Fig. 11
Fig. 11

Sail compressed to 0.2 bits/pixel. (a) Scaled quantization step sizes from Ref. 8. (b) Proposed quantization strategy.

Fig. 12
Fig. 12

Balloon compressed to 0.1 bits/pixel. (a) Scaled quantization step sizes from Ref. 8. (b) Proposed quantization strategy.

Fig. 13
Fig. 13

Segment of balloon compressed to 0.1 bits/pixel, showing reduced ringing artifacts from the finer scales. (a) Scaled quantization step sizes from Ref. 8. (b) Proposed quantization strategy.

Tables (2)

Tables Icon

Table 1 Energy Distribution across Subband Orientations for Three SEDCs Averaged over All Scales

Tables Icon

Table 2 Percent Relative Error in Computed MNDSS(1)–MNDSS(3) for Seven Image/Subband Series

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

=MNDSSinc(i)-MNDSSave(i)MNDSSave(i)×100.
MNDSS(1)=aσb,
MSE(q2/12)(-0.134(q/σ)+1.05).
C(freq, orient)=RMSQ(freq,orient)RMS(freq, orient),
RTE(2:1)=CT(2ndVDU)CT(1stVDU),RTE(3:1)=CT(3rdVDU)CT(1stVDU).
Q(s)=Kσ(s) MNDSS(1)=Kaσ(s)b-1,
s Kσ(s)=1.

Metrics