Abstract

We apply two novel nonuniform quantization techniques to digital holograms of three-dimensional real-world objects. Our companding approach, combines the efficiency of uniform quantization with the improved performance of nonuniform quantization. We show that the performance of companding techniques can be comparable with k-means clustering and a competitive neural network, while only requiring a single-pass processing step. The quantized holographic pixels are coded using lossless techniques for the calculation of compression ratio.

© 2006 Optical Society of America

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  1. J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
    [CrossRef]
  2. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, "Digital wavefront measuring interferometer for testing optical surfaces and lenses," Appl. Opt. 13(11), 2693-2703 (1974).
    [CrossRef]
  3. L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26(11), 1124-1132 (1987).
  4. U. Schnars and W. P. O. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33(2), 179-181 (1994).
    [CrossRef]
  5. I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22(16), 1268-1270 (1997).
    [CrossRef]
  6. E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital holography for quantitative phase-contrast imaging," Opt. Lett. 24(5), 291-293 (1999).
    [CrossRef]
  7. T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, Berlin, 2004).
    [CrossRef]
  8. B. Javidi and F. Okano, eds., Three-Dimensional Television, Video, and Display Technologies (Springer, Berlin, 2002).
  9. B. Javidi and E. Tajahuerce, "Three-dimensional object recognition by use of digital holography," Opt. Lett. 25(9), 610-612 (2000).
    [CrossRef]
  10. H. J. Caulfield, ed., Handbook of Optical Holography (Academic Press, New York, 1979).
  11. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  12. T. J. Naughton, J. B. Mc Donald, and B. Javidi, "Efficient compression of Fresnel fields for Internet transmission of three-dimensional images," Appl. Opt. 42(23), 4758-4764 (2003).
    [CrossRef]
  13. T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three-dimensional object reconstruction and recognition," Appl. Opt. 41(20), 4124-4132 (2002).
    [CrossRef]
  14. W. J. Dallas and A. W. Lohmann, "Phase quantization in holograms - depth effects," Appl. Opt. 11(1), 192-194 (1972).
    [CrossRef]
  15. T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, and B. Javidi, "Image reconstruction from compressed encrypted digital hologram," Opt. Eng. 44(7), 075,801-1-075,801-7 (2005).
  16. O. Matoba, T. J. Naughton, Y. Frauel, N. Bertaux, and B. Javidi, "Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram," Appl. Opt. 41(29), 6187-6192 (2002).
    [CrossRef]
  17. T. J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43(10), 2233-2238 (2004).
    [CrossRef]
  18. D. Kayser, T. Kreis, and W. Jüptner, "Compression of digital holographic data using its electromagnetic field properties," Proc. SPIE 5908, 97-105 (2005).
  19. I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, "Image reconstruction only by phase in phase-shifting digital holography," Appl. Opt. 45(5), 975-983 (2006).
    [CrossRef]
  20. E. Darakis and J. J. Soraghan, "Compression of interference patterns with application to phase-shifting digital holography," Appl. Opt. 45 2437-2443 (2006).
    [CrossRef] [PubMed]
  21. A. E. Shortt, T. J. Naughton, and B. Javidi, "Compression of digital holograms of three-dimensional objects using wavelets," Opt. Express 14(7), 2625-2630 (2006).
    [CrossRef]
  22. J. MacQueen, "Some methods for classification and analysis of multivariate observations." Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1, 281-297 (1967).
  23. T. Kohonen, Self-Organizing Maps (Springer-Verlag, Berlin, 1994).
  24. D. A. Huffman, "A method for the construction of minimum redundancy codes," Proc. IRE 40, 1098-1101 (1952).
    [CrossRef]
  25. J. Ziv and A. Lempel, "A universal algorithm for sequential data compression," IEEE Trans. Inf. Theory IT-23(3), 337-343 (1977).
    [CrossRef]
  26. T. A. Welch, "A technique for high performance data compression," IEEE Computer 17(6), 8-19 (1984).
    [CrossRef]
  27. M. Burrows and D. J. Wheeler, "A block-sorting lossless data compression algorithm," Tech. Rep. 124, Digital Systems Research Center, Palo Alto, California (1994).

2006 (3)

2004 (1)

T. J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43(10), 2233-2238 (2004).
[CrossRef]

2003 (1)

2002 (2)

2000 (1)

1999 (1)

1997 (1)

1987 (1)

L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26(11), 1124-1132 (1987).

1984 (1)

T. A. Welch, "A technique for high performance data compression," IEEE Computer 17(6), 8-19 (1984).
[CrossRef]

1977 (1)

J. Ziv and A. Lempel, "A universal algorithm for sequential data compression," IEEE Trans. Inf. Theory IT-23(3), 337-343 (1977).
[CrossRef]

1974 (1)

1972 (1)

1967 (2)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. MacQueen, "Some methods for classification and analysis of multivariate observations." Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1, 281-297 (1967).

1952 (1)

D. A. Huffman, "A method for the construction of minimum redundancy codes," Proc. IRE 40, 1098-1101 (1952).
[CrossRef]

Bertaux, N.

Bevilacqua, F.

Brangaccio, D. J.

Bruning, J. H.

Cuche, E.

Dallas, W. J.

Darakis, E.

Depeursinge, C.

Frauel, Y.

Gallagher, J. E.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Herriott, D. R.

Huffman, D. A.

D. A. Huffman, "A method for the construction of minimum redundancy codes," Proc. IRE 40, 1098-1101 (1952).
[CrossRef]

Javidi, B.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Lempel, A.

J. Ziv and A. Lempel, "A universal algorithm for sequential data compression," IEEE Trans. Inf. Theory IT-23(3), 337-343 (1977).
[CrossRef]

Lohmann, A. W.

MacQueen, J.

J. MacQueen, "Some methods for classification and analysis of multivariate observations." Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1, 281-297 (1967).

Matoba, O.

Mc Donald, J. B.

Mills, G. A.

Naughton, T. J.

Onural, L.

L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26(11), 1124-1132 (1987).

Rosenfeld, D. P.

Scott, P. D.

L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26(11), 1124-1132 (1987).

Shortt, A. E.

Soraghan, J. J.

Tajahuerce, E.

Welch, T. A.

T. A. Welch, "A technique for high performance data compression," IEEE Computer 17(6), 8-19 (1984).
[CrossRef]

White, A. D.

Yamaguchi, I.

Yamamoto, K.

Yokota, M.

Zhang, T.

Ziv, J.

J. Ziv and A. Lempel, "A universal algorithm for sequential data compression," IEEE Trans. Inf. Theory IT-23(3), 337-343 (1977).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

IEEE Computer (1)

T. A. Welch, "A technique for high performance data compression," IEEE Computer 17(6), 8-19 (1984).
[CrossRef]

IEEE Trans. Inf. Theory (1)

J. Ziv and A. Lempel, "A universal algorithm for sequential data compression," IEEE Trans. Inf. Theory IT-23(3), 337-343 (1977).
[CrossRef]

Opt. Eng. (2)

L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26(11), 1124-1132 (1987).

T. J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43(10), 2233-2238 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Proc. IRE (1)

D. A. Huffman, "A method for the construction of minimum redundancy codes," Proc. IRE 40, 1098-1101 (1952).
[CrossRef]

Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (1)

J. MacQueen, "Some methods for classification and analysis of multivariate observations." Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1, 281-297 (1967).

Other (9)

T. Kohonen, Self-Organizing Maps (Springer-Verlag, Berlin, 1994).

D. Kayser, T. Kreis, and W. Jüptner, "Compression of digital holographic data using its electromagnetic field properties," Proc. SPIE 5908, 97-105 (2005).

U. Schnars and W. P. O. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33(2), 179-181 (1994).
[CrossRef]

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, Berlin, 2004).
[CrossRef]

B. Javidi and F. Okano, eds., Three-Dimensional Television, Video, and Display Technologies (Springer, Berlin, 2002).

H. J. Caulfield, ed., Handbook of Optical Holography (Academic Press, New York, 1979).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

M. Burrows and D. J. Wheeler, "A block-sorting lossless data compression algorithm," Tech. Rep. 124, Digital Systems Research Center, Palo Alto, California (1994).

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, and B. Javidi, "Image reconstruction from compressed encrypted digital hologram," Opt. Eng. 44(7), 075,801-1-075,801-7 (2005).

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Figures (7)

Fig. 1.
Fig. 1.

NRMS error of the reconstructed die object plotted against number of clusters with uniform quantization and (a) k-means quantization and (b) Kohonen competitive. Non-optimized means using the clusters from the bolt to quantize the die.

Fig. 2.
Fig. 2.

Scatter plots of the diamond companding grid with (a) 9, (b) 25, and (c) 49 clusters.

Fig. 3.
Fig. 3.

NRMS error of the reconstructed object plotted against number of clusters with uniform, companding diamond, k-means, and Kohonen competitive for (a) die and (b) bolt.

Fig. 4.
Fig. 4.

Scatter plots of the spiral companding grid with (a) 25, (b) 49, and (c) 81 clusters.

Fig. 5.
Fig. 5.

NRMS error of the reconstructed object plotted against number of clusters with companding diamond and spiral grids for (a) die and (b) bolt.

Fig. 6.
Fig. 6.

Reconstructions with 5×5 mean filtering using the spiral companding grid for die with (a) 9 clusters, and (b) 49 clusters, and for bolt with (c) 9 clusters, and (d) 49 clusters.

Fig. 7.
Fig. 7.

NRMS error of the reconstructed object plotted against compression ratio with companding spiral grid for (a) die and (b) bolt.

Equations (4)

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H ( x , y ) = round { H ( x , y ) × σ 1 × [ 2 ( b 1 ) 1 ] }
σ = max { min [ Im ( H ) ] , max [ Im ( H ) ] , min [ Re ( H ) ] , max [ Re ( H ) ] } .
D = [ m = 0 N x 1 n = 0 N y 1 { U ( m , n ) U ( m , n ) } 2 × ( m = 0 N x 1 n = 0 N y 1 U ( m , n ) 2 ) 1 ] 1 2 ,
r = uncompressed size compressed size .

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