Abstract

We present a system for shape tolerant three-dimensional (3D) recognition of biological microorganisms using holographic microscopy. The system recognizes 3D microorganisms by analyzing complex images of the 3D microorganism restored from single-exposure on-line (SEOL) digital hologram. In this technique the SEOL hologram is recorded by a Mach-Zehnder interferometer, and then the original complex images are reconstructed numerically at different depths by inverse Fresnel transformation. For recognition, a number of sampling segment features are arbitrarily extracted from the restored 3D image. These samples are processed using a number of cost functions and the sampling distributions for the difference of the parameters (location, dispersion) between the sample segment features of the reference and input 3D image are calculated using a statistical sampling method. Then, a hypothesis testing for the equality of the parameters between reference and input 3D image is performed for a statistical decision about populations on the basis of sampling distribution information. Student’s t distribution and Fisher’s F distribution are used to statistically analyze the difference of means and the ratio of variances of two populations, respectively. The proposed system is designed to be tolerant to recognizing various, plain microorganisms with analogous shape such as bacteria and algae. Preliminary experimental results are presented to illustrate the robustness of the proposed recognition system using statistical inference.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, "Design and application of quadratic correlation filters for target detection," IEEE Trans. on AES. Vol. 40, 837-850 (2004).
  2. F. Sadjadi, ed., "Selected Papers on Automatic Target Recognition," (SPIE-CDROM, 1999).
  3. P. Refregier, "Noise Theory and Application to physics," (Springer, 2003).
  4. H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. on Geosci. Remote Sens. 43, 388-397 (2005).
    [CrossRef]
  5. J. Alvarez-Borrego, R. R. Mourino-Perez, G. Cristobal-Perez, and J. L. Pech-Pacheco, "Invariant recognition of polychromatic images of Vibrio cholerae 01," Opt. Eng. 41, 872-833 (2002).
    [CrossRef]
  6. A. L. Amaral, M. da Motta, M. N. Pons, H. Vivier, N. Roche, M. Moda, and E. C. Ferreira, "Survey of protozoa and metazoan populations in wastewater treatment plants by image anlaysis and discriminant analysis," Environmentrics 15, 381-390 (2004).
    [CrossRef]
  7. J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phy. Lett. Vol. 11, 77-79 (1967).
    [CrossRef]
  8. B. Javidi, ed., Image Recognition and Classification: Algorithms, Systems, and Applications, (Marcel Dekker, New York, 2002).
  9. B. Javidi and F. Okano, eds., Three-dimensional television, video, and display technologies, (Springer, New York, 2002).
  10. G. Pedrini and H. J. Tiziani, "Short-coherence digital microscopy by use of a lensless holographic imaging system," Appl. Opt. Vol. 41, 4489-4496 (2002).
    [CrossRef]
  11. I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. Vol. 22, 1268-1270 (1997).
    [CrossRef]
  12. T. Kreis, ed., Handbook of Holographic Interferometry, (Wiley, VCH, 2005).
  13. B. Javidi, and E. Tajahuerce, "Three dimensional object recognition using digital holography," Opt. Lett. Vol. 25, 610-612 (2000).
    [CrossRef]
  14. Y. Frauel, and B. Javidi, "Neural network for three-dimensional object recognition based on digital holography," Opt. Lett. Vol. 26, 1478-1480 (2001).
    [CrossRef]
  15. E. Tajahuerce, O. Matoba, and B. Javidi, "Shift-Invariant Three-Dimensional Object Recognition by Means of Digital Holography," Appl. Opt. Vol. 40, 3877-3886 (2001).
    [CrossRef]
  16. S. Yeom and B. Javidi, "Three-dimensional object feature extraction and classification with computational holographic imaging," Appl. Opt. Vol. 43, 442-451 (2004).
    [CrossRef]
  17. B. Javidi and D. Kim, "Three-dimensional-object recognition by use of single-exposure on-axis digital holography," Opt. Lett. Vol. 30, 236-238 (2005).
    [CrossRef]
  18. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, "Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography," Opt. Express. Vol. 13, 4492�??4506 (2005).
    [CrossRef]
  19. N. Mukhopadhyay, ed., Probability and Statistical Inference, (Marcel Dekker, New York, 2000).

Appl. Opt. (3)

Appl. Phy. Lett. (1)

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

Environmentrics (1)

A. L. Amaral, M. da Motta, M. N. Pons, H. Vivier, N. Roche, M. Moda, and E. C. Ferreira, "Survey of protozoa and metazoan populations in wastewater treatment plants by image anlaysis and discriminant analysis," Environmentrics 15, 381-390 (2004).
[CrossRef]

IEEE Trans. on AES. (1)

A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, "Design and application of quadratic correlation filters for target detection," IEEE Trans. on AES. Vol. 40, 837-850 (2004).

IEEE Trans. on Geosci. Remote Sens. (1)

H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. on Geosci. Remote Sens. 43, 388-397 (2005).
[CrossRef]

Opt. Eng. (1)

J. Alvarez-Borrego, R. R. Mourino-Perez, G. Cristobal-Perez, and J. L. Pech-Pacheco, "Invariant recognition of polychromatic images of Vibrio cholerae 01," Opt. Eng. 41, 872-833 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Other (6)

F. Sadjadi, ed., "Selected Papers on Automatic Target Recognition," (SPIE-CDROM, 1999).

P. Refregier, "Noise Theory and Application to physics," (Springer, 2003).

B. Javidi, ed., Image Recognition and Classification: Algorithms, Systems, and Applications, (Marcel Dekker, New York, 2002).

B. Javidi and F. Okano, eds., Three-dimensional television, video, and display technologies, (Springer, New York, 2002).

T. Kreis, ed., Handbook of Holographic Interferometry, (Wiley, VCH, 2005).

N. Mukhopadhyay, ed., Probability and Statistical Inference, (Marcel Dekker, New York, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

Experimental setup for recording SEOL digital hologram of a 3D biological microorganism; Ar: Argon laser, BS1, BS2: beam splitter; M1, M2: mirror; MO: microscope objective; CCD: charge coupled device array.

Fig. 2.
Fig. 2.

Frameworks for shape tolerant 3D biological microorganism recognition based on the single-exposure on-line (SEOL) digital holography.

Fig. 3.
Fig. 3.

The design procedure for shape tolerant 3D biological microorganism recognition. The windows of sample segment are extracted in the restored 3D image from SEOL digital hologram.

Fig. 4.
Fig. 4.

The statistical inference method to implement the proposed 3D biological microorganism recognition system.

Fig. 5.
Fig. 5.

The histogram of (a) real part, (b) imaginary part of the preprocessed (segmentation and edge detection) 3D image.

Fig. 6.
Fig. 6.

The magnified algae’s images by use of a 10 × microscope objective: (a) sphacelaria’s 2D image and (b) polysiphonia’s 2D image.

Fig. 7.
Fig. 7.

sphacelaria’s phase contrast image after applying segmentation and edge detection algorithm at distance d =180 mm as the reference by use of a 10 × microscope objective.

Fig. 8.
Fig. 8.

Experimental results for input algae by use of a 10 × microscope objective: (a) sphacelaria’s intensity image at distance d = 180 mm and (b) polysiphonia’s intensity image at distance d =180 mm.

Fig. 9.
Fig. 9.

The average (a) MSD, (b) MAD calculated by the complex amplitude between the reference segments and the input segments versus the sample size of sampling segments.

Fig. 10.
Fig. 10.

(a) T-test for the equality of the location parameter between two sampling segments versus a sample size, (b) F-test for the equality of the dispersion parameter between two sampling segments versus a trial number with a sample size 500.

Equations (18)

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

MSD = i = 0 N 1 { R i ( x , y ) E [ S ( x , y ) ] } 2 i = 0 N 1 { R i ( x , y ) } 2 MAD = i = 0 N 1 R i ( x , y ) E [ S ( x , y ) ] i = 0 N 1 R i ( x , y ) ,
T = N R + N S 2 N R V [ R ] + N S V [ S ] × E [ R ] E [ S ] { ( N R ) 1 + ( N S ) 1 } 1 / 2 ,
H 0 : μ R = μ S , H 1 : μ R μ S
T = 1 V ¯ p E [ R ] E [ S ] { ( N R ) 1 + ( N S ) 1 } 1 / 2 ,
P { ( E [ R ] E [ S ] ) t N R + N S 2 , 1 α 1 / 2 V ¯ p [ ( N R 1 + N S 1 ) 1 / 2 ]
< μ R μ S < ( E [ R ] E [ S ] ) + t N R + N S 2 , 1 α 1 / 2 V ¯ P [ ( N R 1 + N S 1 ) 1 / 2 ] } = 1 α 1 .
F ( N R 1 ) , ( N S 1 ) = { N R / ( N R 1 ) } V [ R ] / σ R 2 { N S / ( N S 1 ) } V [ S ] / σ S 2 ,
H 0 : μ R 2 = μ S 2 , H 1 : μ R 2 μ S 2 ,
F ( N R 1 ) , ( N S 1 ) = { N R / ( N R 1 ) } V [ R ] { N S / ( N S 1 ) } V [ S ] = V ̂ [ R ] V ̂ [ S ]
P { F ( N R 1 ) , ( N S 1 ) , α 2 / 2 1 [ V ̂ [ R ] V ̂ [ S ] ] < σ R 2 σ S 2 < F ( N R 1 ) , ( N S 1 ) , 1 α 2 / 2 1 [ V ̂ [ R ] V ̂ [ S ] ] } = 1 α 2 ,
O H ( x , y ) = d 0 δ 2 d 0 + δ 2 exp [ j 2 πz / λ ] jλz exp [ j π λz + ( x 2 + y 2 ) ] ×
O ( ξ , η ; z ) exp [ j π λz ( ξ 2 + η 2 ) ] exp [ j 2 π λz ( + ) ] dzdξdη ,
R ( x , y ) = A R ( x , y ) exp [ j φ R ( x , y ) ] ,
I ( x , y ) = O H ( x , y ) + R ( x , y ) 2
= A H ( x , y ) 2 + A R 2 + 2 A H ( x , y ) A R cos [ Φ H ( x , y ) φ R ] .
H ( x , y ) = I ( x , y ) O ( x , y ) 2 R ( x , y ) 2 ,
O ( x , y ) 2 n x = 0 N x 1 n y = 0 N y 1 { 1 L x L x l x = 1 L x l y = 1 L y [ H ( n x + l x , n y + l y ) R ( n x + l x , n y + l y ) 2 ] } ,
O′ ( ξ , η ) = IFrT { H ( x , y ) } = IFrT ( FrT { H ( x , y ) } × exp { jπλ d o [ u 2 ( Δ x N x ) 2 + v 2 ( Δ y N y ) 2 ] } ) ,

Metrics