Abstract

We propose the use of the wavelet transform to characterize the time evolution of dynamic speckle patterns. We describe it by using as an example a method used for the assessment of the drying of paint. Optimal texture features are determined and the time evolution is described in terms of the Mahalanobis distance to the final (dry) state. From the behavior of this distance function, two parameters are defined that characterize the evolution. Because detailed knowledge of the involved dynamics is not required, the methodology could be implemented for other complex or poorly understood dynamic phenomena.

© 2002 Optical Society of America

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References

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  1. J. C. Dainty, Laser Speckle and Related Phenomena, (Springer-Verlag, Berlin, 1975).
  2. R. S. Sirohi, ed., Speckle Metrology, (Marcel Dekker, New York, 1993).
  3. Y. Aizu, T. Asakura, “Biospeckle,” Trends in Optics, A. Consortini, ed. (Academic, San Diego, 1996), Chap. 2.
  4. H. J. Rabal, M. Trivi, R. Arizaga, G. Romero, E. Alanis, “Transient phenomena analysis using dynamic speckle patterns,” Opt. Eng. 35, 57–60 (1996).
    [CrossRef]
  5. R. Arizaga, M. Trivi, H. J. Rabal, “Speckle time evolution characterization by the cooccurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
    [CrossRef]
  6. Y. Aizu, T. Asakura, “Bio-speckle phenomena and their applications to the evaluation of blood flow,” Opt. Laser Technol. 23, 205–219 (1991).
    [CrossRef]
  7. G. J. Tearney, B. E. Bouma, “Atherosclerotic plaque characterization by spatial and temporal speckle pattern analysis,” Opt. Lett. 27, 533–535 (2002).
    [CrossRef]
  8. G. Romero, E. Alanis, H. J. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its applications to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
    [CrossRef]
  9. A. Oulamara, G. Tribillon, J. Doubernoy, “Biological activity measurements on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
    [CrossRef]
  10. R. Haralick, “Statistical and Structural Approaches to Texture,” Proc. IEEE 67, 786–803 (1979).
    [CrossRef]
  11. M. Unser, “Sum and difference histograms for texture classification,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI 8, 118–125 (1986).
    [CrossRef]
  12. M. Tejera, A. Mavilio, M. Fernández, “Dimensiones promediadas como descriptores de textura,” presented at Foro Iberoam. Trat. Dig. Imag. y Visión Industrial, Valencia, Spain, 5–8 Oct. 1996.
  13. T. P. Weldon, W. E. Higgins, “Design of multiple Gabor filters for texture segmentation,” in IEEE Trans. Acoust. Speech, Signal Proc. (ICASSP96)IV, Atlanta, Ga., 2245–2248 (1996).
  14. M. Fernández, A. Mavilio, M. Tejera, “Texture segmentation of a 3D seismic section with wavelet transform and Gabor filters,” in Proceeding of the IEEE of the 15th International Conference on Pattern Recognition, 3, 358–361 (2000).
  15. T. Chang, C. C. J. Kuo, “Texture Analysis and Classification with Tree-Structured Wavelet Transform,” IEEE Trans. Image Process. 2, 429–441 (1993).
    [CrossRef] [PubMed]
  16. See, for example, R. O. Duda http://www.engr.sjsu.edu/~knapp/HCIRODPR/PR_home.htm .
  17. J. Amalvy, C. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Progress in Organic Coatings 42, 89–99 (2001).
    [CrossRef]
  18. V. Manian, R. Vasquez, “Scaled and rotated texture segmentation using a class of basis functions,” in Wavelet Applications IV, H. H. Szu, ed., Proc. SPIE3078, 324–332 (1997).

2002 (1)

2001 (1)

J. Amalvy, C. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Progress in Organic Coatings 42, 89–99 (2001).
[CrossRef]

2000 (2)

G. Romero, E. Alanis, H. J. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its applications to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

M. Fernández, A. Mavilio, M. Tejera, “Texture segmentation of a 3D seismic section with wavelet transform and Gabor filters,” in Proceeding of the IEEE of the 15th International Conference on Pattern Recognition, 3, 358–361 (2000).

1999 (1)

R. Arizaga, M. Trivi, H. J. Rabal, “Speckle time evolution characterization by the cooccurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

1996 (1)

H. J. Rabal, M. Trivi, R. Arizaga, G. Romero, E. Alanis, “Transient phenomena analysis using dynamic speckle patterns,” Opt. Eng. 35, 57–60 (1996).
[CrossRef]

1993 (1)

T. Chang, C. C. J. Kuo, “Texture Analysis and Classification with Tree-Structured Wavelet Transform,” IEEE Trans. Image Process. 2, 429–441 (1993).
[CrossRef] [PubMed]

1991 (1)

Y. Aizu, T. Asakura, “Bio-speckle phenomena and their applications to the evaluation of blood flow,” Opt. Laser Technol. 23, 205–219 (1991).
[CrossRef]

1989 (1)

A. Oulamara, G. Tribillon, J. Doubernoy, “Biological activity measurements on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

1986 (1)

M. Unser, “Sum and difference histograms for texture classification,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI 8, 118–125 (1986).
[CrossRef]

1979 (1)

R. Haralick, “Statistical and Structural Approaches to Texture,” Proc. IEEE 67, 786–803 (1979).
[CrossRef]

Aizu, Y.

Y. Aizu, T. Asakura, “Bio-speckle phenomena and their applications to the evaluation of blood flow,” Opt. Laser Technol. 23, 205–219 (1991).
[CrossRef]

Y. Aizu, T. Asakura, “Biospeckle,” Trends in Optics, A. Consortini, ed. (Academic, San Diego, 1996), Chap. 2.

Alanis, E.

G. Romero, E. Alanis, H. J. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its applications to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

H. J. Rabal, M. Trivi, R. Arizaga, G. Romero, E. Alanis, “Transient phenomena analysis using dynamic speckle patterns,” Opt. Eng. 35, 57–60 (1996).
[CrossRef]

Amalvy, J.

J. Amalvy, C. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Progress in Organic Coatings 42, 89–99 (2001).
[CrossRef]

Arizaga, R.

J. Amalvy, C. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Progress in Organic Coatings 42, 89–99 (2001).
[CrossRef]

R. Arizaga, M. Trivi, H. J. Rabal, “Speckle time evolution characterization by the cooccurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

H. J. Rabal, M. Trivi, R. Arizaga, G. Romero, E. Alanis, “Transient phenomena analysis using dynamic speckle patterns,” Opt. Eng. 35, 57–60 (1996).
[CrossRef]

Asakura, T.

Y. Aizu, T. Asakura, “Bio-speckle phenomena and their applications to the evaluation of blood flow,” Opt. Laser Technol. 23, 205–219 (1991).
[CrossRef]

Y. Aizu, T. Asakura, “Biospeckle,” Trends in Optics, A. Consortini, ed. (Academic, San Diego, 1996), Chap. 2.

Bouma, B. E.

Chang, T.

T. Chang, C. C. J. Kuo, “Texture Analysis and Classification with Tree-Structured Wavelet Transform,” IEEE Trans. Image Process. 2, 429–441 (1993).
[CrossRef] [PubMed]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena, (Springer-Verlag, Berlin, 1975).

Doubernoy, J.

A. Oulamara, G. Tribillon, J. Doubernoy, “Biological activity measurements on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Fernández, M.

M. Fernández, A. Mavilio, M. Tejera, “Texture segmentation of a 3D seismic section with wavelet transform and Gabor filters,” in Proceeding of the IEEE of the 15th International Conference on Pattern Recognition, 3, 358–361 (2000).

M. Tejera, A. Mavilio, M. Fernández, “Dimensiones promediadas como descriptores de textura,” presented at Foro Iberoam. Trat. Dig. Imag. y Visión Industrial, Valencia, Spain, 5–8 Oct. 1996.

Haralick, R.

R. Haralick, “Statistical and Structural Approaches to Texture,” Proc. IEEE 67, 786–803 (1979).
[CrossRef]

Higgins, W. E.

T. P. Weldon, W. E. Higgins, “Design of multiple Gabor filters for texture segmentation,” in IEEE Trans. Acoust. Speech, Signal Proc. (ICASSP96)IV, Atlanta, Ga., 2245–2248 (1996).

Kuo, C. C. J.

T. Chang, C. C. J. Kuo, “Texture Analysis and Classification with Tree-Structured Wavelet Transform,” IEEE Trans. Image Process. 2, 429–441 (1993).
[CrossRef] [PubMed]

Lasquibar, C.

J. Amalvy, C. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Progress in Organic Coatings 42, 89–99 (2001).
[CrossRef]

Manian, V.

V. Manian, R. Vasquez, “Scaled and rotated texture segmentation using a class of basis functions,” in Wavelet Applications IV, H. H. Szu, ed., Proc. SPIE3078, 324–332 (1997).

Mavilio, A.

M. Fernández, A. Mavilio, M. Tejera, “Texture segmentation of a 3D seismic section with wavelet transform and Gabor filters,” in Proceeding of the IEEE of the 15th International Conference on Pattern Recognition, 3, 358–361 (2000).

M. Tejera, A. Mavilio, M. Fernández, “Dimensiones promediadas como descriptores de textura,” presented at Foro Iberoam. Trat. Dig. Imag. y Visión Industrial, Valencia, Spain, 5–8 Oct. 1996.

Oulamara, A.

A. Oulamara, G. Tribillon, J. Doubernoy, “Biological activity measurements on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Rabal, H.

J. Amalvy, C. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Progress in Organic Coatings 42, 89–99 (2001).
[CrossRef]

Rabal, H. J.

G. Romero, E. Alanis, H. J. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its applications to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

R. Arizaga, M. Trivi, H. J. Rabal, “Speckle time evolution characterization by the cooccurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

H. J. Rabal, M. Trivi, R. Arizaga, G. Romero, E. Alanis, “Transient phenomena analysis using dynamic speckle patterns,” Opt. Eng. 35, 57–60 (1996).
[CrossRef]

Romero, G.

G. Romero, E. Alanis, H. J. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its applications to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

H. J. Rabal, M. Trivi, R. Arizaga, G. Romero, E. Alanis, “Transient phenomena analysis using dynamic speckle patterns,” Opt. Eng. 35, 57–60 (1996).
[CrossRef]

Tearney, G. J.

Tejera, M.

M. Fernández, A. Mavilio, M. Tejera, “Texture segmentation of a 3D seismic section with wavelet transform and Gabor filters,” in Proceeding of the IEEE of the 15th International Conference on Pattern Recognition, 3, 358–361 (2000).

M. Tejera, A. Mavilio, M. Fernández, “Dimensiones promediadas como descriptores de textura,” presented at Foro Iberoam. Trat. Dig. Imag. y Visión Industrial, Valencia, Spain, 5–8 Oct. 1996.

Tribillon, G.

A. Oulamara, G. Tribillon, J. Doubernoy, “Biological activity measurements on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Trivi, M.

J. Amalvy, C. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Progress in Organic Coatings 42, 89–99 (2001).
[CrossRef]

R. Arizaga, M. Trivi, H. J. Rabal, “Speckle time evolution characterization by the cooccurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

H. J. Rabal, M. Trivi, R. Arizaga, G. Romero, E. Alanis, “Transient phenomena analysis using dynamic speckle patterns,” Opt. Eng. 35, 57–60 (1996).
[CrossRef]

Unser, M.

M. Unser, “Sum and difference histograms for texture classification,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI 8, 118–125 (1986).
[CrossRef]

Vasquez, R.

V. Manian, R. Vasquez, “Scaled and rotated texture segmentation using a class of basis functions,” in Wavelet Applications IV, H. H. Szu, ed., Proc. SPIE3078, 324–332 (1997).

Weldon, T. P.

T. P. Weldon, W. E. Higgins, “Design of multiple Gabor filters for texture segmentation,” in IEEE Trans. Acoust. Speech, Signal Proc. (ICASSP96)IV, Atlanta, Ga., 2245–2248 (1996).

IEEE Trans. Image Process (1)

T. Chang, C. C. J. Kuo, “Texture Analysis and Classification with Tree-Structured Wavelet Transform,” IEEE Trans. Image Process. 2, 429–441 (1993).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. PAMI (1)

M. Unser, “Sum and difference histograms for texture classification,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI 8, 118–125 (1986).
[CrossRef]

J. Mod. Opt. (1)

A. Oulamara, G. Tribillon, J. Doubernoy, “Biological activity measurements on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Opt. Eng. (2)

G. Romero, E. Alanis, H. J. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its applications to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

H. J. Rabal, M. Trivi, R. Arizaga, G. Romero, E. Alanis, “Transient phenomena analysis using dynamic speckle patterns,” Opt. Eng. 35, 57–60 (1996).
[CrossRef]

Opt. Laser Technol. (2)

R. Arizaga, M. Trivi, H. J. Rabal, “Speckle time evolution characterization by the cooccurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

Y. Aizu, T. Asakura, “Bio-speckle phenomena and their applications to the evaluation of blood flow,” Opt. Laser Technol. 23, 205–219 (1991).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

R. Haralick, “Statistical and Structural Approaches to Texture,” Proc. IEEE 67, 786–803 (1979).
[CrossRef]

Proceeding of the IEEE of the 15th International Conference on Pattern Recognition (1)

M. Fernández, A. Mavilio, M. Tejera, “Texture segmentation of a 3D seismic section with wavelet transform and Gabor filters,” in Proceeding of the IEEE of the 15th International Conference on Pattern Recognition, 3, 358–361 (2000).

Progress in Organic Coatings (1)

J. Amalvy, C. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Progress in Organic Coatings 42, 89–99 (2001).
[CrossRef]

Other (7)

V. Manian, R. Vasquez, “Scaled and rotated texture segmentation using a class of basis functions,” in Wavelet Applications IV, H. H. Szu, ed., Proc. SPIE3078, 324–332 (1997).

J. C. Dainty, Laser Speckle and Related Phenomena, (Springer-Verlag, Berlin, 1975).

R. S. Sirohi, ed., Speckle Metrology, (Marcel Dekker, New York, 1993).

Y. Aizu, T. Asakura, “Biospeckle,” Trends in Optics, A. Consortini, ed. (Academic, San Diego, 1996), Chap. 2.

See, for example, R. O. Duda http://www.engr.sjsu.edu/~knapp/HCIRODPR/PR_home.htm .

M. Tejera, A. Mavilio, M. Fernández, “Dimensiones promediadas como descriptores de textura,” presented at Foro Iberoam. Trat. Dig. Imag. y Visión Industrial, Valencia, Spain, 5–8 Oct. 1996.

T. P. Weldon, W. E. Higgins, “Design of multiple Gabor filters for texture segmentation,” in IEEE Trans. Acoust. Speech, Signal Proc. (ICASSP96)IV, Atlanta, Ga., 2245–2248 (1996).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

THSP corresponding to three different drying stages: (a) wet paint, (b) intermediate state of drying, (c) dry paint.

Fig. 3
Fig. 3

(a) Hierarchical decomposition of an image, (b) pyramidal wavelet decomposition.

Fig. 4
Fig. 4

Behavior of the distance function to Lat 14 calculated for the average residual feature by using the orthogonal bases Daubechie-8 (asterisks), Daubechies-2 (open circles), and Haar (crosses). The percentages represent the third-degree polynomial fit quality.

Fig. 5
Fig. 5

Behavior of the distance function to Lat 14 calculated for the modulus feature by using the Daubechies-2 basis. The solid curve represents a third-degree polynomial fit. The straight line (dashed), corresponds to the linear fit of the first experimental points.

Tables (2)

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Table 1 Results of the classification (in percent)a

Tables Icon

Table 2 Drying Parameters

Equations (5)

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mdi=1Mj=1M|ci,j|,
Ei=1Mj=1M|ci,j|2,
sdi=j=1Mci,j-vmi2M-11/2,
rmsi=1Mj=1M|ci,j-vmi|,
Dtf=uf-utfTcovtf-1uf-utf

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