Abstract

We present a method for the analysis of dynamic speckle signals based on morphological granulometry. We obtain selected information differentiating the morphological patterns of the temporal history of each pixel through the granulometric size distribution. The method is exemplified by detecting bruised regions on apples and studying the germination of corn seeds. Different levels of activity are observed in the bruised and healthy areas of the apple, within a certain range of the morphological spectrum. Likewise, the activity of the corn seed embryo can also be distinguished from the endosperm area.

© 2009 Optical Society of America

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  1. M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, Opt. Lasers Eng. 40, 13 (2003).
    [CrossRef]
  2. R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
    [CrossRef]
  3. J. D. Briers and S. Webster, J. Biomed. Opt. 1, 174 (1996).
    [CrossRef]
  4. R. Arizaga, N. Cap, H. J. Rabal, and M. Trivi, Opt. Eng. (Bellingham) 41, 287 (2002).
    [CrossRef]
  5. G. H. Sendra, R. Arizaga, H. Rabal, and M. Trivi, Opt. Lett. 30, 1641 (2005).
    [CrossRef] [PubMed]
  6. A. Federico and G. Kaufmann, Evaluation of Dynamic Speckle Activity Using the Empirical Mode Decomposition Method (Elsevier Science, 2006).
  7. G. Matheron, Random Sets and Integral Geometry, Wiley Series in Probability and Mathematical Statistics (Wiley, 1975).
  8. J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982), Vol I.
  9. J. G. Hampton, L. Kahre, and A. J. G. Van Gastel, Seed Sci. Technol. 24, 393 (1996).
  10. E. R. Dougherty and J. T. Astola, in Tutorial Texts in Optical Engineering (SPIE, 1994).

2005

2003

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, Opt. Lasers Eng. 40, 13 (2003).
[CrossRef]

R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
[CrossRef]

2002

R. Arizaga, N. Cap, H. J. Rabal, and M. Trivi, Opt. Eng. (Bellingham) 41, 287 (2002).
[CrossRef]

1996

J. G. Hampton, L. Kahre, and A. J. G. Van Gastel, Seed Sci. Technol. 24, 393 (1996).

J. D. Briers and S. Webster, J. Biomed. Opt. 1, 174 (1996).
[CrossRef]

Arizaga, R.

G. H. Sendra, R. Arizaga, H. Rabal, and M. Trivi, Opt. Lett. 30, 1641 (2005).
[CrossRef] [PubMed]

R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
[CrossRef]

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, Opt. Lasers Eng. 40, 13 (2003).
[CrossRef]

R. Arizaga, N. Cap, H. J. Rabal, and M. Trivi, Opt. Eng. (Bellingham) 41, 287 (2002).
[CrossRef]

Astola, J. T.

E. R. Dougherty and J. T. Astola, in Tutorial Texts in Optical Engineering (SPIE, 1994).

Baldwin, G.

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, Opt. Lasers Eng. 40, 13 (2003).
[CrossRef]

Borem, F.

R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
[CrossRef]

Braga, R.

R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
[CrossRef]

Briers, J. D.

J. D. Briers and S. Webster, J. Biomed. Opt. 1, 174 (1996).
[CrossRef]

Cap, N.

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, Opt. Lasers Eng. 40, 13 (2003).
[CrossRef]

R. Arizaga, N. Cap, H. J. Rabal, and M. Trivi, Opt. Eng. (Bellingham) 41, 287 (2002).
[CrossRef]

Dal Fabbro, I.

R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
[CrossRef]

Dougherty, E. R.

E. R. Dougherty and J. T. Astola, in Tutorial Texts in Optical Engineering (SPIE, 1994).

Federico, A.

A. Federico and G. Kaufmann, Evaluation of Dynamic Speckle Activity Using the Empirical Mode Decomposition Method (Elsevier Science, 2006).

Hampton, J. G.

J. G. Hampton, L. Kahre, and A. J. G. Van Gastel, Seed Sci. Technol. 24, 393 (1996).

Kahre, L.

J. G. Hampton, L. Kahre, and A. J. G. Van Gastel, Seed Sci. Technol. 24, 393 (1996).

Kaufmann, G.

A. Federico and G. Kaufmann, Evaluation of Dynamic Speckle Activity Using the Empirical Mode Decomposition Method (Elsevier Science, 2006).

Matheron, G.

G. Matheron, Random Sets and Integral Geometry, Wiley Series in Probability and Mathematical Statistics (Wiley, 1975).

Pajuelo, M.

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, Opt. Lasers Eng. 40, 13 (2003).
[CrossRef]

Rabal, H.

G. H. Sendra, R. Arizaga, H. Rabal, and M. Trivi, Opt. Lett. 30, 1641 (2005).
[CrossRef] [PubMed]

R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
[CrossRef]

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, Opt. Lasers Eng. 40, 13 (2003).
[CrossRef]

Rabal, H. J.

R. Arizaga, N. Cap, H. J. Rabal, and M. Trivi, Opt. Eng. (Bellingham) 41, 287 (2002).
[CrossRef]

Rabelo, G.

R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
[CrossRef]

Sendra, G. H.

Serra, J.

J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982), Vol I.

Trivi, M.

G. H. Sendra, R. Arizaga, H. Rabal, and M. Trivi, Opt. Lett. 30, 1641 (2005).
[CrossRef] [PubMed]

R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
[CrossRef]

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, Opt. Lasers Eng. 40, 13 (2003).
[CrossRef]

R. Arizaga, N. Cap, H. J. Rabal, and M. Trivi, Opt. Eng. (Bellingham) 41, 287 (2002).
[CrossRef]

Van Gastel, A. J. G.

J. G. Hampton, L. Kahre, and A. J. G. Van Gastel, Seed Sci. Technol. 24, 393 (1996).

Webster, S.

J. D. Briers and S. Webster, J. Biomed. Opt. 1, 174 (1996).
[CrossRef]

Biosyst. Eng.

R. Braga, Jr., I. Dal Fabbro, F. Borem, G. Rabelo, R. Arizaga, H. Rabal, and M. Trivi, Biosyst. Eng. 86, 287 (2003).
[CrossRef]

J. Biomed. Opt.

J. D. Briers and S. Webster, J. Biomed. Opt. 1, 174 (1996).
[CrossRef]

Opt. Eng. (Bellingham)

R. Arizaga, N. Cap, H. J. Rabal, and M. Trivi, Opt. Eng. (Bellingham) 41, 287 (2002).
[CrossRef]

Opt. Lasers Eng.

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, Opt. Lasers Eng. 40, 13 (2003).
[CrossRef]

Opt. Lett.

Seed Sci. Technol.

J. G. Hampton, L. Kahre, and A. J. G. Van Gastel, Seed Sci. Technol. 24, 393 (1996).

Other

E. R. Dougherty and J. T. Astola, in Tutorial Texts in Optical Engineering (SPIE, 1994).

A. Federico and G. Kaufmann, Evaluation of Dynamic Speckle Activity Using the Empirical Mode Decomposition Method (Elsevier Science, 2006).

G. Matheron, Random Sets and Integral Geometry, Wiley Series in Probability and Mathematical Statistics (Wiley, 1975).

J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982), Vol I.

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Figures (4)

Fig. 1
Fig. 1

Morphological opening applied on a biospeckle signal.

Fig. 2
Fig. 2

Aspect of GSD applied to a biospeckle signal.

Fig. 3
Fig. 3

Images obtained with GSD using structuring elements of sizes (a) 2, (b) 10, and (c) 30.

Fig. 4
Fig. 4

Images obtained with GSD using structuring elements of sizes (a) 2, (b) 10, and (c) 30.

Equations (4)

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

ε ( f , b ) ( s , t ) = min ( s + x , f + y ) D f ( x , y ) D b { f ( s + x , t + y ) b ( x , y ) } ,
δ ( f , b ) ( s , t ) = max ( s x , f y ) D f ( x , y ) D b { f ( s x , t y ) + b ( x , y ) } .
γ ( f , b ) = δ ( ε ( f , b ) , b ) .
ϕ ( n ) = 1 Ω ( f n ) Ω ( f 0 ) , n = 0 , , N .

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