Abstract

Abstract

We develop a 3D region tracking method based on Maximum A Posteriori (MAP) tracker and adapt it to digital hologram sequences to efficiently track biological microorganisms in holographic microscopy data. In our approach, the target surface is modeled as the iso-surface of a level set function which is evolved at each frame via level set Hamilton Jacobian update rule in Euler-Lagrangian framework. The statistical characteristics of the target microorganism versus the background are exploited to evolve the interface at each frame, thus the algorithm works independent of the shape or morphology of the target. We use the bivariate Gaussian distribution to model the reconstructed hologram data which enables us to take into account the correlation between the amplitude and phase of the reconstructed wavefront to obtain a more accurate tracking solution.

© 2007 Optical Society of America

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References

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  1. J.W. Goodman, Introduction to Fourier Optics3nd ed., Roberts & Company, Englewood Colorado (2005).
  2. Y. Frauel, T.J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proceedings. of the IEEE 94, 636–653 (2006).
    [Crossref]
  3. E. Tajahuerce, O. Matoba, and B. Javidi, “Shift-Invariant Three-Dimensional Object Recognition by Means of Digital Holography,” Appl. Opt. 40, 3877–3886 (2001)
    [Crossref]
  4. 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, 6187–6192 (2002).
    [Crossref] [PubMed]
  5. T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45, 4873–4877 (2006).
    [Crossref] [PubMed]
  6. B. Javidi, S. Yeom, I. Moon, and M. Daneshpanah, “Real-time automated 3D sensing, detection, and recognition of dynamic biological micro-organic events,” Opt. Express 14, 3806–3829 (2006).
    [Crossref] [PubMed]
  7. A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of microorganisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A 24, 163–168 (2007).
    [Crossref]
  8. M. DaneshPanah and B. Javidi “Segmentation of 3D holographic images using bivariate jointly distributed region snake,” Opt. Express 14, 5143–5153 (2006).
    [Crossref] [PubMed]
  9. P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, and G. Pierattini, “Digital holographic microscope with automatic focus tracking by detecting sample displacement in real time,” Opt. Lett. 28, 1257–1259 (2003).
    [Crossref] [PubMed]
  10. F. Sadjadi, ed., Selected Papers on Automatic Target Recognition, SPIE-CDROM, (2000).
  11. P. Refregier, Noise Theory and Application to Physics, Springer (2005)
  12. F. Sadjadi and A. Mahalonobis, “Target adaptive polarimetric SAR target discrimination using MACH filters,” Appl. Opt. 45, 7365–7374 (2006).
  13. H. Kwon and N. M. Nasrabadi, “Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens.,  43, 388–397 (2005).
    [Crossref]
  14. A. Mahalonobis, R. Muise, and S. Stanfill, “Performance evaluation of quadratic correlation filters for target detection and discrimination in IR imagery,” Appl. Opt. 43, 5198–5205 (2004).
  15. A. Blake and A. Yuille eds, Active Vision, MIT Press, Cambridge (1992).
  16. F. Goudail and P. Refregier, “Optimal target tracking on image sequences with a deterministic background,” J. Opt. Soc. Am. A 14, 3197–3207 (1997)
    [Crossref]
  17. S.C. Zhu and A. Yuille, “Region competition: unifying snakes, region growing, and bayes/mdl for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 884–900 (1996).
    [Crossref]
  18. A. Yilmaz, X. Li, and M. Shah, “Contour based object tracking with occlusion handling in video acquired using mobile cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1531–1536 (2004).
    [Crossref] [PubMed]
  19. M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models”, Proc. ICCV, 259–268 (1987).
  20. J. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics Computer Vision and Material Sciences. Cambridge Univ. Press (1999).

2007 (1)

A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of microorganisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A 24, 163–168 (2007).
[Crossref]

2006 (5)

2005 (1)

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

2004 (2)

A. Mahalonobis, R. Muise, and S. Stanfill, “Performance evaluation of quadratic correlation filters for target detection and discrimination in IR imagery,” Appl. Opt. 43, 5198–5205 (2004).

A. Yilmaz, X. Li, and M. Shah, “Contour based object tracking with occlusion handling in video acquired using mobile cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1531–1536 (2004).
[Crossref] [PubMed]

2003 (1)

2002 (1)

2001 (1)

1997 (1)

F. Goudail and P. Refregier, “Optimal target tracking on image sequences with a deterministic background,” J. Opt. Soc. Am. A 14, 3197–3207 (1997)
[Crossref]

1996 (1)

S.C. Zhu and A. Yuille, “Region competition: unifying snakes, region growing, and bayes/mdl for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 884–900 (1996).
[Crossref]

1987 (1)

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models”, Proc. ICCV, 259–268 (1987).

Bertaux, N.

Blake, A.

A. Blake and A. Yuille eds, Active Vision, MIT Press, Cambridge (1992).

Coppola, G.

Daneshpanah, M.

De Nicola, S.

eds, A. Yuille

A. Blake and A. Yuille eds, Active Vision, MIT Press, Cambridge (1992).

Ferraro, P.

Finizio, A.

Frauel, Y.

Y. Frauel, T.J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proceedings. of the IEEE 94, 636–653 (2006).
[Crossref]

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, 6187–6192 (2002).
[Crossref] [PubMed]

Goodman, J.W.

J.W. Goodman, Introduction to Fourier Optics3nd ed., Roberts & Company, Englewood Colorado (2005).

Goudail, F.

F. Goudail and P. Refregier, “Optimal target tracking on image sequences with a deterministic background,” J. Opt. Soc. Am. A 14, 3197–3207 (1997)
[Crossref]

Javidi, B.

Kass, M.

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models”, Proc. ICCV, 259–268 (1987).

Kwon, H.

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

Li, X.

A. Yilmaz, X. Li, and M. Shah, “Contour based object tracking with occlusion handling in video acquired using mobile cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1531–1536 (2004).
[Crossref] [PubMed]

Mahalonobis, A.

Matoba, O.

Moon, I.

Muise, R.

Murata, S.

Nasrabadi, N. M.

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

Naughton, T. J.

Naughton, T.J.

Y. Frauel, T.J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proceedings. of the IEEE 94, 636–653 (2006).
[Crossref]

Nitanai, E.

Nomura, T.

Numata, T.

Pierattini, G.

Refregier, P.

F. Goudail and P. Refregier, “Optimal target tracking on image sequences with a deterministic background,” J. Opt. Soc. Am. A 14, 3197–3207 (1997)
[Crossref]

P. Refregier, Noise Theory and Application to Physics, Springer (2005)

Sadjadi, F.

Sethian, J.

J. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics Computer Vision and Material Sciences. Cambridge Univ. Press (1999).

Shah, M.

A. Yilmaz, X. Li, and M. Shah, “Contour based object tracking with occlusion handling in video acquired using mobile cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1531–1536 (2004).
[Crossref] [PubMed]

Stanfill, S.

Stern, A.

A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of microorganisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A 24, 163–168 (2007).
[Crossref]

Tajahuerce, E.

Y. Frauel, T.J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proceedings. of the IEEE 94, 636–653 (2006).
[Crossref]

E. Tajahuerce, O. Matoba, and B. Javidi, “Shift-Invariant Three-Dimensional Object Recognition by Means of Digital Holography,” Appl. Opt. 40, 3877–3886 (2001)
[Crossref]

Terzopoulos, D.

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models”, Proc. ICCV, 259–268 (1987).

Witkin, A.

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models”, Proc. ICCV, 259–268 (1987).

Yeom, S.

Yilmaz, A.

A. Yilmaz, X. Li, and M. Shah, “Contour based object tracking with occlusion handling in video acquired using mobile cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1531–1536 (2004).
[Crossref] [PubMed]

Yuille, A.

S.C. Zhu and A. Yuille, “Region competition: unifying snakes, region growing, and bayes/mdl for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 884–900 (1996).
[Crossref]

Zhu, S.C.

S.C. Zhu and A. Yuille, “Region competition: unifying snakes, region growing, and bayes/mdl for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 884–900 (1996).
[Crossref]

Appl. Opt. (5)

IEEE Trans. Geosci. Remote Sens. (1)

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

IEEE Trans. Pattern Anal. Mach. Intell. (2)

S.C. Zhu and A. Yuille, “Region competition: unifying snakes, region growing, and bayes/mdl for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 884–900 (1996).
[Crossref]

A. Yilmaz, X. Li, and M. Shah, “Contour based object tracking with occlusion handling in video acquired using mobile cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1531–1536 (2004).
[Crossref] [PubMed]

J. Opt. Soc. Am. (2)

A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of microorganisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A 24, 163–168 (2007).
[Crossref]

F. Goudail and P. Refregier, “Optimal target tracking on image sequences with a deterministic background,” J. Opt. Soc. Am. A 14, 3197–3207 (1997)
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Proc. ICCV (1)

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models”, Proc. ICCV, 259–268 (1987).

Proceedings. of the IEEE (1)

Y. Frauel, T.J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proceedings. of the IEEE 94, 636–653 (2006).
[Crossref]

Other (5)

J.W. Goodman, Introduction to Fourier Optics3nd ed., Roberts & Company, Englewood Colorado (2005).

J. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics Computer Vision and Material Sciences. Cambridge Univ. Press (1999).

F. Sadjadi, ed., Selected Papers on Automatic Target Recognition, SPIE-CDROM, (2000).

P. Refregier, Noise Theory and Application to Physics, Springer (2005)

A. Blake and A. Yuille eds, Active Vision, MIT Press, Cambridge (1992).

Supplementary Material (2)

» Media 1: MOV (332 KB)     
» Media 2: MOV (1962 KB)     

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Figures (3)

Fig 1.
Fig 1.

Single Exposure On Line digital holography setup. The diffracted field from the specimen is magnified by a 100x/0.8NA microscope objective.

Fig 2.
Fig 2.

Diatom alga with 100x/0.8NA microscope objective (a) (332 KB) Movie of magnitude reconstruction in 1µm steps along optical axis [Media 1], (b) phase of a single plane of reconstruction in focus. (c) Magnitude of three planes in the reconstruction volume.

Fig 3.
Fig 3.

(1.91MB) A sequence of cross sections of the reconstructed volume from diatom algae being contoured by the iso-surface of the proposed 3D tracker. [Media 2]

Equations (10)

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P ( r 0 ) = r κ P tar [ V ( l + 1 ) ( r ) V ( t ) , T ( t ) ] w ( r ) P bck [ V ( t + 1 ) ( r ) | V ( t ) , T ( t ) ] 1 w ( r ) ,
E ( r 0 ) = log { P ( r 0 ) } = r κ w ( r ) log P tar ( r ) r κ ( 1 w ( r ) ) log P bck ( r ) log P ( T ( t + 1 ) )
φ ( p , t + 1 ) = φ ( p , t ) + F ( p ) ijk φ ,
E r = ( r κ w ( r ) log P tar ( r ) + r κ ( 1 w ( r ) ) log P bck ( r ) + log P ( T ( t + 1 ) ) ) n ,
log P ( T ( t + 1 ) ) = . n = . ( φ ( p , t ) ) ( φ ( p , t ) ) ,
F ( p ) = r κ w ( r ) log P tar ( r ) r κ ( 1 w ( r ) ) log P bck ( r ) + . ( φ ( p , t ) φ ( p , t ) ) .
T ̂ ( t + 1 ) = arg max T 3 { P ( T ( t + 1 ) V ( t + 1 ) , V ( t ) , T ( t ) ) } .
T ̂ ( t + 1 ) = arg max T 3 { P ( V ( t + 1 ) | V ( t ) , T ( t ) , T ( t + 1 ) ) × P ( T ( t + 1 ) | V ( t ) , T ( t ) ) }
r κ w ( r ) log P ( r ) = N ( w ) log ( 2 π σ ̂ φ σ ̂ α 1 ρ ̂ 2 ) + 1 2 ( σ ̂ φ ) 2 r κ ( φ ( r ) μ ̂ φ ) 2
+ 1 2 ( σ ̂ α 1 ρ ̂ 2 ) 2 r κ ( α ( r ) μ ̂ α ρ ̂ σ ̂ α ( φ ( r ) μ ̂ φ ) σ ̂ φ ) 2

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