Abstract

We address three-dimensional (3D) visualization and recognition of microorganisms using single-exposure on-line (SEOL) digital holography. A coherent 3D microscope-based Mach-Zehnder interferometer records a single on-line Fresnel digital hologram of microorganisms. Three-dimensional microscopic images are reconstructed numerically at different depths by an inverse Fresnel transformation. For recognition, microbiological objects are segmented by processing the background diffraction field. Gabor-based wavelets extract feature vectors with multi-oriented and multi-scaled Gabor kernels. We apply a rigid graph matching (RGM) algorithm to localize predefined shape features of biological samples. Preliminary experimental and simulation results using sphacelaria alga and tribonema aequale alga microorganisms are presented. To the best of our knowledge, this is the first report on 3D visualization and recognition of microorganisms using on-line digital holography with single-exposure.

© 2005 Optical Society of America

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References

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Appl. Opt. (4)

Appl. Phy. Lett. (1)

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

Biotechnology and Bioengineering (1)

S.-K. Treskatis, V. Orgeldinger, H. wolf, and E. D. Gilles, �??Morphological characterization of filamentous microorganisms in submerged cultures by on-line digital image analysis and Pattern recognition,�?? Biotechnology and Bioengineering 53, 191-201 (1997)
[CrossRef] [PubMed]

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 metazoa populations in wastewater treatment plants by image anlaysis and discriminant analysis,�?? Environmentrics 15, 381-390 (2004)
[CrossRef]

IEEE Trans. (1)

T. S. Lee, �??Image representation using 2D Gabor wavelets,�?? IEEE Trans. on PAMI. 18, 959-971 (1996)
[CrossRef]

IEEE Trans. Part B (1)

T. Luo, K. Kramer, D. B. Goldgof, L. O. Hall, S. Samson, A. Remsen, and T. Hopkins, �??Recognizing plankton images from the shadow image particle profiling evaluation recorder,�?? IEEE Trans. on systems, man, and cybernetics Part B 34, 1753-1762 (2004).
[CrossRef]

IEEE Trans. Computers (1)

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, and W. Konen, �??Distortion invariant object recognition in the dynamic link architecture,�?? IEEE Trans. Computers 42, 300- 311 (1993).
[CrossRef]

IEEE Trans. On AES. (1)

F. Sadjadi, �??Improved target classification using optimum polarimetric SAR signatures,�?? IEEE Trans. On AES. 38, 38-49 (2002).

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. 40, 837-850 (2004)

J. Opt. Soc. Am. (1)

J. G. Daugman, �??Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,�?? J. Opt. Soc. Am. 2, 1160-1169 (1985).
[CrossRef]

J. Opt. Soc. Am. A. (1)

H. Sjoberg, F. Goudail, and P. Refregier, �??Optimal algorithms for target location in nonhomogeneous binary images,�?? J. Opt. Soc. Am. A. 15, 2976-2985 (1998)
[CrossRef]

Opt Lett. (1)

T. Zhang and I. Yamaguchi, �??Three-dimensional microscopy with phase-shifting digital holography,�?? Opt Lett. 23, 1221 (1998).
[CrossRef]

Opt. Eng. (2)

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]

T. M. Kreis and W. P. O. Juptner, �??Suppression of the dc term in digital holography,�?? Opt. Eng. 36, 2357- 2360 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Real-time imaging (1)

M. G. Forero, F. Sroubek, and G. Cristobal, �??Identification of tuberculosis bacteria based on shape and color,�?? Real-time imaging 10, 251-262 (2004)
[CrossRef]

Other (4)

J. M. S. Cabral, M. Mota, and J. Tramper eds., Multiphase bioreactor design: chap2 image analysis and multiphase bioreactor, (Taylor & Francis, London 2001)
[CrossRef]

J. W. Lengeler, G. Drews, and H. G. Schlegel, Biology of the prokaryotes, (Blackwell science, New York, 1999).

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

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

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Figures (7)

Fig. 1.
Fig. 1.

Frameworks of the 3D visualization and recognition of microbiological objects.

Fig. 2.
Fig. 2.

Experimental setup for recording an on-line digital hologram of a microscopic 3D biological object; Ar: Argon laser, SF: Spatial filter, L: lens, D: diaphragm, BS1, BS2: beam splitter; M1, M2: mirror; MO: microscope objective; CCD: charge coupled device array.

Fig. 3.
Fig. 3.

Coordinate system for digital hologram and image reconstruction of 3D microorganisms.

Fig. 4.
Fig. 4.

Experimental results for biological samples (sphacelaria and tribonema aequale) by use of a 10 × microscope objective: (a) sphacelaria’s 2D image and (b) sphacelaria’s digital hologram by SEOL digital holography; (c) and (d) sphacelaria’s reconstructed images by use of SEOL digital holography with only single hologram recording at distance d=180 mm and 190 mm, respectively; (e) sphacelaria’s reconstructed image at distance 180 mm using phase-shifting digital holography; (f) tribonema aequale’s reconstructed image at distance d=180 mm using SEOL digital holography.

Fig. 5.
Fig. 5.

Computational reconstruction, segmentation, and feature vector extraction of the sphacelaria sample A1, (a) reconstructed image at d=180 mm, (b) segmented image, real parts of Gabor coefficients when (c) u=1, (d) u=2, (e) u=3.

Fig. 6.
Fig. 6.

Recognition of sphacelaria, (a) reference sample A1 with the graph R, (b) RGM result of one test sample A8, (c) number of detections, (d) maximum similarity and minimum difference cost, (a) and (b) are presented by contrast reversal for better visualization.

Fig. 7.
Fig. 7.

Recognition of tribonema aequale, (a) reference sample B1 with the graph R, (b) RGM result of one test sample B2, (c) number of detections, (d) maximum similarity and minimum difference cost, (a) and (b) are presented by contrast reversal for better visualization.

Equations (22)

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

H P ( x , y ) = [ A H ( x , y ) ] 2 + A R 2 + 2 A H ( x , y ) A R × cos [ Φ H ( x , y ) φ R Δ φ P ] ,
U h ( x , y ) = A H ( x , y ) × cos [ Φ H ( x , y ) ] + j A H ( x , y ) × sin [ Φ H ( x , y ) ]
= { H 1 ( x , y ) A H ( x , y ) 2 A R 2 } ( 2 A R ) + j { H 2 ( x , y ) A H ( x , y ) 2 A R 2 } ( 2 A R ) ,
U h ' ( x , y ) = 2 A H ( x , y ) A R × cos ( Φ H ( x , y ) φ R ) = H 1 ( x , y ) A H ( x , y ) 2 A R 2 .
U o ' ( m ' , n ' ) = exp [ j π λ d ( Δ X 2 m ' 2 + Δ Y 2 n ' 2 ) ] ×
m = 1 N z n = 1 N y U h ' ( m , n ) exp [ j π λ d ( Δ x 2 m 2 + Δ y 2 n 2 ) ] exp [ j 2 π ( m m ' N x + n n ' N y ) ] ,
o ( m , n ) = { o ' ( m , n ) if o ' ( m , n ) < I s 0 otherwise ,
I s = min [ τ κ min , r max · max ( o ' ) ] ,
P s 1 N T i = 1 κ min h ( τ i ) ,
g ( x ) = k 2 σ 2 exp ( k 2 x 2 2 σ 2 ) [ exp ( j k · x ) exp ( σ 2 2 ) ] ,
h uv ( m , n ) = m ' = 1 N m n ' = 1 N n g uv ( m m ' , n n ' ) o ( m ' , n ' ) ,
v ( m , n ) = [ o ( m , n ) v = 1 V h 1 v ( m , n ) v = 1 V h Uv ( m , n ) ] t .
x k r = A ( θ r ) ( x k o x c o ) + p r , k = 1 , , K ,
A ( θ ) = [ cos θ sin θ sin θ cos θ ] ,
x k s ( θ , p ) = A ( θ ) ( x k o x c o ) + p , k = 1 , , K ,
Γ rs = 1 K k = 1 K γ k ( θ , p ) ,
γ k ( θ , p ) v [ x k r ] , v [ x k s ( θ , p ) ] v [ x k r ] v [ x k s ( θ , p ) ] , k = 1 , , K .
C rs = 1 K k = 1 K c k ( θ , p ) ,
c k ( θ , p ) = v [ x k r ] v [ x k s ( θ , p ) ] , k = 1 , , K .
Accept detection at p if Γ r j ̂ S ( θ ̂ j ̂ ; p ) > α Γ and C r j ̂ S ( θ ̂ j ̂ ; p ) < α C ,
j ̂ = max j Γ r 1 S ( θ ̂ 1 ; p ) , , Γ r J S ( θ ̂ J ; p ) ,
θ ̂ j = arg max θ Γ r j s ( θ , p ) .

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