Abstract

A radiometric/geometric transform has been developed which generates images with approximately wide-sense stationary first (mean)- and second (autocorrelation)-order statistics [ R. N. Strickland, Appl. Opt. 22, 1462 ( 1983)]. The transform is found to enhance the performance of predictive coding. The radiometric transform reduces radiometric redundancy in the image data and, therefore, aids efficient quantization at low bit rates. A spatial transformation, or warp, is applied to produce nearly uniform autocorrelation length throughout the data. This affords a convenient means of reducing spatial redundancy by varying the spatial resolution in the transformed image. Final bit rates of ~0.6 bits/pixel are realized for high-quality images. We discuss hybrid digital/optical implementation of the stationary transforms for data compression.

© 1983 Optical Society of America

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References

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  1. H. G. Musmann, “Predictive Image Coding,” in Image Transmission Techniques, W. K. Pratt, Ed., Adv. Electron. Electron Phys.12, 73 (1979).
  2. A. G. Tescher, “Transform Image Coding,” in Image Transmission Techniques, W. K. Pratt, Ed., Adv. Electron. Electron Phys.12, 113 (1979).
  3. J. A. Roese, “Hybrid Transform/Predictive Image Coding,” in Image Transmission Techniques, W. K. Pratt, Ed., Adv. Electron. Electron Phys.12, 157 (1979).
  4. A. Habibi, IEEE Trans. Commun. COM-25, 1315 (1977).
  5. R. N. Strickland, Appl. Opt. 22, 1462 (1983).
    [CrossRef] [PubMed]
  6. B. R. Hunt, Appl. Opt. 17, 2944 (1978).
    [CrossRef] [PubMed]
  7. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).
  8. R. Wallis, “An Approach to the Space-Variant Restoration and Enhancement of Images,” in Proceedings, Symposium on Current Mathematical Problems in Image Science (Naval Postgraduate School, Monterey, Calif., Nov.1976).
  9. P. Cummiskey, N. S. Jayant, J. L. Flanagan, Bell Syst. Tech. J. 52, 1105 (1973).
  10. D. J. Goodman, A. Gersho,. IEEE Trans. Commun. COM-22, 1073 (1974).
  11. T. S. Huang, IEEE Spectrum 2, No. 12, 57 (1965).
  12. E. J. Delp, O. R. Mitchell, IEEE Trans. Commun. COM-27, 1335 (1979).
    [CrossRef]
  13. H. N. Ito, B. R. Hunt, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 77 (1981).

1983

1981

H. N. Ito, B. R. Hunt, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 77 (1981).

1979

E. J. Delp, O. R. Mitchell, IEEE Trans. Commun. COM-27, 1335 (1979).
[CrossRef]

1978

1977

A. Habibi, IEEE Trans. Commun. COM-25, 1315 (1977).

1974

D. J. Goodman, A. Gersho,. IEEE Trans. Commun. COM-22, 1073 (1974).

1973

P. Cummiskey, N. S. Jayant, J. L. Flanagan, Bell Syst. Tech. J. 52, 1105 (1973).

1965

T. S. Huang, IEEE Spectrum 2, No. 12, 57 (1965).

Cummiskey, P.

P. Cummiskey, N. S. Jayant, J. L. Flanagan, Bell Syst. Tech. J. 52, 1105 (1973).

Delp, E. J.

E. J. Delp, O. R. Mitchell, IEEE Trans. Commun. COM-27, 1335 (1979).
[CrossRef]

Flanagan, J. L.

P. Cummiskey, N. S. Jayant, J. L. Flanagan, Bell Syst. Tech. J. 52, 1105 (1973).

Gersho, A.

D. J. Goodman, A. Gersho,. IEEE Trans. Commun. COM-22, 1073 (1974).

Goodman, D. J.

D. J. Goodman, A. Gersho,. IEEE Trans. Commun. COM-22, 1073 (1974).

Habibi, A.

A. Habibi, IEEE Trans. Commun. COM-25, 1315 (1977).

Huang, T. S.

T. S. Huang, IEEE Spectrum 2, No. 12, 57 (1965).

Hunt, B. R.

H. N. Ito, B. R. Hunt, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 77 (1981).

B. R. Hunt, Appl. Opt. 17, 2944 (1978).
[CrossRef] [PubMed]

Ito, H. N.

H. N. Ito, B. R. Hunt, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 77 (1981).

Jayant, N. S.

P. Cummiskey, N. S. Jayant, J. L. Flanagan, Bell Syst. Tech. J. 52, 1105 (1973).

Mitchell, O. R.

E. J. Delp, O. R. Mitchell, IEEE Trans. Commun. COM-27, 1335 (1979).
[CrossRef]

Musmann, H. G.

H. G. Musmann, “Predictive Image Coding,” in Image Transmission Techniques, W. K. Pratt, Ed., Adv. Electron. Electron Phys.12, 73 (1979).

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).

Roese, J. A.

J. A. Roese, “Hybrid Transform/Predictive Image Coding,” in Image Transmission Techniques, W. K. Pratt, Ed., Adv. Electron. Electron Phys.12, 157 (1979).

Strickland, R. N.

Tescher, A. G.

A. G. Tescher, “Transform Image Coding,” in Image Transmission Techniques, W. K. Pratt, Ed., Adv. Electron. Electron Phys.12, 113 (1979).

Wallis, R.

R. Wallis, “An Approach to the Space-Variant Restoration and Enhancement of Images,” in Proceedings, Symposium on Current Mathematical Problems in Image Science (Naval Postgraduate School, Monterey, Calif., Nov.1976).

Appl. Opt.

Bell Syst. Tech. J.

P. Cummiskey, N. S. Jayant, J. L. Flanagan, Bell Syst. Tech. J. 52, 1105 (1973).

IEEE Spectrum

T. S. Huang, IEEE Spectrum 2, No. 12, 57 (1965).

IEEE Trans. Commun.

E. J. Delp, O. R. Mitchell, IEEE Trans. Commun. COM-27, 1335 (1979).
[CrossRef]

A. Habibi, IEEE Trans. Commun. COM-25, 1315 (1977).

D. J. Goodman, A. Gersho,. IEEE Trans. Commun. COM-22, 1073 (1974).

Proc. Soc. Photo-Opt. Instrum. Eng.

H. N. Ito, B. R. Hunt, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 77 (1981).

Other

H. G. Musmann, “Predictive Image Coding,” in Image Transmission Techniques, W. K. Pratt, Ed., Adv. Electron. Electron Phys.12, 73 (1979).

A. G. Tescher, “Transform Image Coding,” in Image Transmission Techniques, W. K. Pratt, Ed., Adv. Electron. Electron Phys.12, 113 (1979).

J. A. Roese, “Hybrid Transform/Predictive Image Coding,” in Image Transmission Techniques, W. K. Pratt, Ed., Adv. Electron. Electron Phys.12, 157 (1979).

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).

R. Wallis, “An Approach to the Space-Variant Restoration and Enhancement of Images,” in Proceedings, Symposium on Current Mathematical Problems in Image Science (Naval Postgraduate School, Monterey, Calif., Nov.1976).

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Figures (6)

Fig. 1
Fig. 1

Data compression by radiometric transform.

Fig. 2
Fig. 2

Example of data compression using the radiometric transform: (a) original; (b) 3-bit PCM; (radiometric transform; (d) radiometric transform after 8-level quantization; (e) inverse radiometric transform (3.25 bits/pixel); (f) repeat of (d); (e) using 8 levels (2.25 bits/pixel).

Fig. 3
Fig. 3

Data compression by geometric transform.

Fig. 4
Fig. 4

Example of data compression by radiometric/geometric transforms: (a) geometric transform of Fig. 2(e). (b) Result of compression using radiometric/geometric transforms (1.2 bits/pixel).

Fig. 5
Fig. 5

(a) Enhanced IDPCM. Architecture—generation of low- and high-frequency channels; (b) reconstruction.

Fig. 6
Fig. 6

Enhanced IDPCM results: (a) MR = 8, MG = 16,0.75 bits/pixel; (b) MR = 16, MG = 16, 0.56 bits/pixel.

Tables (1)

Tables Icon

Table I Quantization Performance of Radiometric Transform (8-Level Quantizer: 16, 48, 80, 112, 144, 176, 208, 240)

Equations (24)

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mean             μ N             = μ s constant ;
autocorrelation             R N ( r , s )             = R s ( r , s ) .
μ N = 1 M 2 j - 0 M - 1 k = 0 M - 1 f ( j , k ) ;
R N = 1 M 2 j = 0 m - r - 1 k = 0 M - s - 1 f ( j , k ) f ( j + r , k + s ) ,
σ N 2 = R N ( 0 , 0 ) - μ N 2 .
R NS = R N ( r , 0 ) = σ N 2 exp ( - ρ NS r ) + μ N 2 ,
R EW = R N ( 0 , s ) = σ N 2 exp ) - ρ EW s ) + μ N 2 ,
C NS = C N ( r , 0 ) = R NS - μ N 2 ;
C EN = C N ( 0 , s ) = R EW - μ N 2 .
g ( j , k ) = K f ( j , k ) - μ N + μ s ; K = σ s / σ N ,
E NS = ρ NS ρ s ( NS )             and             E EW = ρ EW ρ s ( EW ) ,
f ^ A = ( g A q - 128 ) / K + μ A , K = σ B / σ A .
g N = [ d · ( f N - f min ) ( f max - f min ) ] ,
B total = N 2 n + 16 ( N / M ) 2 ,
B / pixel = n + ( 16 / M 2 ) .
σ N 2 = [ f ( j , k ) - μ N 2 ] 2 ¯
F NS = ρ NS ρ s ( NS )             ( 0 < F NS 1 )
B / subblock = M 2 F NS F EW .
B total = M 2 all N F NS F EW .
B control points = 16 [ ( N / M ) + 1 ] 2 .
B / pixel = n M 2 N 2 all N ( F NS F EW ) image data + 32 M 2 overhead .
B / pixel = n M G 2 N 2 all N F NS F Ew + 16 ( 1 M G 2 + 1 M R 2 ) ,
B / pixel ( IDPCM ) = ¼ LF + ¾ HF ,
B / pixel ( enhanced IDPCM ) = ( LF 4 + 3 4 HF ) ( M G 2 N 2 ) ( all N F NS F EW ) + 16 ( 1 M R 2 + 1 M G 2 ) .

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