Abstract

We propose to apply statistical clustering algorithms on a three-dimensional profile of red blood cells (RBCs) obtained through digital holographic microscopy (DHM). We show that two classes of RBCs stored for 14 and 38 days can be effectively classified. Two-dimensional intensity images of these cells are virtually the same. DHM allows for measurement of the RBCs’ biconcave profile, resulting in a discriminative dataset. Two statistical clustering algorithms are compared. A model-based clustering approach classifies the pixels of an RBC and recognizes the RBC as either new or old based. The K-means algorithm is applied to the four-dimensional feature vector extracted from the RBC profile.

© 2011 Optical Society of America

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2010

A. R. Moradi, M. K. Ali, M. Daneshpanah, A. Anand, and B. Javidi, “Detection of calcium-induced morphological changes of living cells using optical traps,” IEEE Photonics J. 2, 775–783 (2010).
[CrossRef]

J. Laurie, D. Wyncoll, and C. Harrison, “New versus old blood—the debate continues,” Crit. Care 14, 130–131 (2010).
[CrossRef] [PubMed]

2009

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three dimensional identification and tracking of micro/nano biological organisms by computational holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

S. Borah and M. K. Ghose, “Performance analysis of AIM-K-means & K-means in quality cluster generation,” J. Comp. 1, 175–178 (2009).

2008

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358, 1229–1239 (2008).
[CrossRef] [PubMed]

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy and coulter counter,” Cytometry Part A 73, 895–903(2008).
[CrossRef]

L. Martinez and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express 16, 161–169 (2008).
[CrossRef]

2007

I. Moon and B. Javidi, “3D identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007).
[CrossRef] [PubMed]

2006

2005

2004

2002

T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: Analysis and implementation,” IEEE Trans. Pattern Anal. Machine Intell. 24, 881–892 (2002).
[CrossRef]

C. Fraley and A. E. Raftery, “Model-based clustering, discriminant analysis and density estimation,” J. Am. Stat. Assoc. 97, 611–631 (2002).
[CrossRef]

1999

1993

J. D. Banfield and A. E. Raftery, “Model-based Gaussian and non-Gaussian clustering,” Biometrics 49, 803–821 (1993).
[CrossRef]

1979

J. A. Hartigan and M. A. Wong, “Algorithm AS 136: A K-means clustering algorithm,” J. Royal Statistical Soc. C 28, 100–108(1979).
[CrossRef]

1977

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Statistical Soc. B 39, 1–38 (1977).

Alfieri, D.

Ali, M. K.

A. R. Moradi, M. K. Ali, M. Daneshpanah, A. Anand, and B. Javidi, “Detection of calcium-induced morphological changes of living cells using optical traps,” IEEE Photonics J. 2, 775–783 (2010).
[CrossRef]

Anand, A.

A. R. Moradi, M. K. Ali, M. Daneshpanah, A. Anand, and B. Javidi, “Detection of calcium-induced morphological changes of living cells using optical traps,” IEEE Photonics J. 2, 775–783 (2010).
[CrossRef]

Aspert, N.

Banfield, J. D.

J. D. Banfield and A. E. Raftery, “Model-based Gaussian and non-Gaussian clustering,” Biometrics 49, 803–821 (1993).
[CrossRef]

Barbul, A.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy and coulter counter,” Cytometry Part A 73, 895–903(2008).
[CrossRef]

Berger, A. J.

Blackstone, E. H.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358, 1229–1239 (2008).
[CrossRef] [PubMed]

Borah, S.

S. Borah and M. K. Ghose, “Performance analysis of AIM-K-means & K-means in quality cluster generation,” J. Comp. 1, 175–178 (2009).

Carapezza, E.

Charrière, F.

Colomb, T.

Coppola, G.

Cuche, E.

Daneshpanah, M.

A. R. Moradi, M. K. Ali, M. Daneshpanah, A. Anand, and B. Javidi, “Detection of calcium-induced morphological changes of living cells using optical traps,” IEEE Photonics J. 2, 775–783 (2010).
[CrossRef]

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three dimensional identification and tracking of micro/nano biological organisms by computational holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

De Nicola, S.

Dempster, A. P.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Statistical Soc. B 39, 1–38 (1977).

Depeursinge, C.

Dey, D. K.

S. Ghosh and D. K. Dey, “Clustering: a pervasive data analytic technique,” Multivariate Statistical Methods, A.Sengupta, ed., Macmillan Advanced Research Series (Macmillan, 2009), pp. 171–201.

S. Ghosh and D. K. Dey, “Model based penalized clustering for multivariate data,” in Advances in Multivariate Statistical Methods, A.Sengupta, ed. (World Scientific, 2009), pp. 53–72.
[CrossRef]

Dubois, F.

Elkan, C.

C. Elkan, “Using the triangle inequality to accelerate k-means,” in Proceedings of the Twentieth International Conference on Machine Learning (ICML), 2003), pp. 147–153.

Emery, Y.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy and coulter counter,” Cytometry Part A 73, 895–903(2008).
[CrossRef]

P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holography microscopy a non-invasive quantitative contrast imaging technique allowing visualization of living cells,” Opt. Lett. 30468–470(2005).
[CrossRef] [PubMed]

Feld, M. S.

Ferraro, P.

Figueroa, P.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358, 1229–1239 (2008).
[CrossRef] [PubMed]

Finizio, A.

Frahling, G.

G. Frahling and C. Sohler, “A fast k-means implementation using coresets,” in Proceedings of the Twenty-Second Annual Symposium on Computational Geometry (SoCG) (Association for Computing Machinery, 2006), pp. 135–143.

Fraley, C.

C. Fraley and A. E. Raftery, “Model-based clustering, discriminant analysis and density estimation,” J. Am. Stat. Assoc. 97, 611–631 (2002).
[CrossRef]

Frauel, Y.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proc. IEEE 94, 636–654 (2006).
[CrossRef]

Ghose, M. K.

S. Borah and M. K. Ghose, “Performance analysis of AIM-K-means & K-means in quality cluster generation,” J. Comp. 1, 175–178 (2009).

Ghosh, S.

S. Ghosh and D. K. Dey, “Clustering: a pervasive data analytic technique,” Multivariate Statistical Methods, A.Sengupta, ed., Macmillan Advanced Research Series (Macmillan, 2009), pp. 171–201.

S. Ghosh and D. K. Dey, “Model based penalized clustering for multivariate data,” in Advances in Multivariate Statistical Methods, A.Sengupta, ed. (World Scientific, 2009), pp. 53–72.
[CrossRef]

Harrison, C.

J. Laurie, D. Wyncoll, and C. Harrison, “New versus old blood—the debate continues,” Crit. Care 14, 130–131 (2010).
[CrossRef] [PubMed]

Hartigan, J. A.

J. A. Hartigan and M. A. Wong, “Algorithm AS 136: A K-means clustering algorithm,” J. Royal Statistical Soc. C 28, 100–108(1979).
[CrossRef]

Hoeltge, G. A.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358, 1229–1239 (2008).
[CrossRef] [PubMed]

Horowitz, G.

Itzkan, I.

Javidi, B.

A. R. Moradi, M. K. Ali, M. Daneshpanah, A. Anand, and B. Javidi, “Detection of calcium-induced morphological changes of living cells using optical traps,” IEEE Photonics J. 2, 775–783 (2010).
[CrossRef]

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three dimensional identification and tracking of micro/nano biological organisms by computational holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

L. Martinez and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express 16, 161–169 (2008).
[CrossRef]

I. Moon and B. Javidi, “3D identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007).
[CrossRef] [PubMed]

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proc. IEEE 94, 636–654 (2006).
[CrossRef]

B. Javidi, I. Moon, and S. Yeom, “Real-time 3D sensing and identification of microorganisms,” Opt. Photon. News Magazine 17, 16–21 (2006).
[CrossRef]

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 13, 4492–4506 (2005).
[CrossRef] [PubMed]

Joannes, L.

Kanungo, T.

T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: Analysis and implementation,” IEEE Trans. Pattern Anal. Machine Intell. 24, 881–892 (2002).
[CrossRef]

Koch, C. G.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358, 1229–1239 (2008).
[CrossRef] [PubMed]

Koo, T. W.

Korenstein, R.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy and coulter counter,” Cytometry Part A 73, 895–903(2008).
[CrossRef]

Kreis, T.

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

Kühn, J.

Laird, N. M.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Statistical Soc. B 39, 1–38 (1977).

Laurie, J.

J. Laurie, D. Wyncoll, and C. Harrison, “New versus old blood—the debate continues,” Crit. Care 14, 130–131 (2010).
[CrossRef] [PubMed]

Legros, J.-C.

Li, L.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358, 1229–1239 (2008).
[CrossRef] [PubMed]

MacQueen, J. B.

J. B. MacQueen, “Some methods for classification and analysis of multivariate observations,” in Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability(University of California, 1967), pp. 281–297.

Magistretti, P.

Magistretti, P. J.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy and coulter counter,” Cytometry Part A 73, 895–903(2008).
[CrossRef]

Marquet, P.

Martinez, L.

Matoba, O.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proc. IEEE 94, 636–654 (2006).
[CrossRef]

Mihaljevic, T.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358, 1229–1239 (2008).
[CrossRef] [PubMed]

Moon, I.

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three dimensional identification and tracking of micro/nano biological organisms by computational holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

I. Moon and B. Javidi, “3D identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007).
[CrossRef] [PubMed]

B. Javidi, I. Moon, and S. Yeom, “Real-time 3D sensing and identification of microorganisms,” Opt. Photon. News Magazine 17, 16–21 (2006).
[CrossRef]

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 13, 4492–4506 (2005).
[CrossRef] [PubMed]

Moradi, A. R.

A. R. Moradi, M. K. Ali, M. Daneshpanah, A. Anand, and B. Javidi, “Detection of calcium-induced morphological changes of living cells using optical traps,” IEEE Photonics J. 2, 775–783 (2010).
[CrossRef]

Mount, D. M.

T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: Analysis and implementation,” IEEE Trans. Pattern Anal. Machine Intell. 24, 881–892 (2002).
[CrossRef]

Murata, S.

Naughton, T.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proc. IEEE 94, 636–654 (2006).
[CrossRef]

Netanyahu, N. S.

T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: Analysis and implementation,” IEEE Trans. Pattern Anal. Machine Intell. 24, 881–892 (2002).
[CrossRef]

Nitanai, E.

Nomura, T.

Numata, T.

Osten, W.

Pedrini, G.

Piatko, C. D.

T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: Analysis and implementation,” IEEE Trans. Pattern Anal. Machine Intell. 24, 881–892 (2002).
[CrossRef]

Pierattini, G.

Raftery, A. E.

C. Fraley and A. E. Raftery, “Model-based clustering, discriminant analysis and density estimation,” J. Am. Stat. Assoc. 97, 611–631 (2002).
[CrossRef]

J. D. Banfield and A. E. Raftery, “Model-based Gaussian and non-Gaussian clustering,” Biometrics 49, 803–821 (1993).
[CrossRef]

Rappaz, B.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy and coulter counter,” Cytometry Part A 73, 895–903(2008).
[CrossRef]

P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holography microscopy a non-invasive quantitative contrast imaging technique allowing visualization of living cells,” Opt. Lett. 30468–470(2005).
[CrossRef] [PubMed]

Rubin, D. B.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Statistical Soc. B 39, 1–38 (1977).

Sessler, D. I.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358, 1229–1239 (2008).
[CrossRef] [PubMed]

Silverman, R.

T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: Analysis and implementation,” IEEE Trans. Pattern Anal. Machine Intell. 24, 881–892 (2002).
[CrossRef]

Sohler, C.

G. Frahling and C. Sohler, “A fast k-means implementation using coresets,” in Proceedings of the Twenty-Second Annual Symposium on Computational Geometry (SoCG) (Association for Computing Machinery, 2006), pp. 135–143.

Stern, A.

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three dimensional identification and tracking of micro/nano biological organisms by computational holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

Tahajuerce, E.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proc. IEEE 94, 636–654 (2006).
[CrossRef]

Tiziani, H. J.

Wong, M. A.

J. A. Hartigan and M. A. Wong, “Algorithm AS 136: A K-means clustering algorithm,” J. Royal Statistical Soc. C 28, 100–108(1979).
[CrossRef]

Wu, A. Y.

T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: Analysis and implementation,” IEEE Trans. Pattern Anal. Machine Intell. 24, 881–892 (2002).
[CrossRef]

Wyncoll, D.

J. Laurie, D. Wyncoll, and C. Harrison, “New versus old blood—the debate continues,” Crit. Care 14, 130–131 (2010).
[CrossRef] [PubMed]

Yeom, S.

Zhang, Y.

Appl. Opt.

Biometrics

J. D. Banfield and A. E. Raftery, “Model-based Gaussian and non-Gaussian clustering,” Biometrics 49, 803–821 (1993).
[CrossRef]

Crit. Care

J. Laurie, D. Wyncoll, and C. Harrison, “New versus old blood—the debate continues,” Crit. Care 14, 130–131 (2010).
[CrossRef] [PubMed]

Cytometry Part A

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy and coulter counter,” Cytometry Part A 73, 895–903(2008).
[CrossRef]

IEEE Photonics J.

A. R. Moradi, M. K. Ali, M. Daneshpanah, A. Anand, and B. Javidi, “Detection of calcium-induced morphological changes of living cells using optical traps,” IEEE Photonics J. 2, 775–783 (2010).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell.

T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: Analysis and implementation,” IEEE Trans. Pattern Anal. Machine Intell. 24, 881–892 (2002).
[CrossRef]

J. Am. Stat. Assoc.

C. Fraley and A. E. Raftery, “Model-based clustering, discriminant analysis and density estimation,” J. Am. Stat. Assoc. 97, 611–631 (2002).
[CrossRef]

J. Comp.

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Figures (4)

Fig. 1
Fig. 1

3D holographic microscopy imaging. (a) Schematic of the experimental setup; R, reference wave; O, object wave; M, mirror; BS, beam splitter; MO, microscope objective lens. (b) Sample hologram of a RBC recorded by the system. (c) Reconstructed phase image of the sample RBC.

Fig. 2
Fig. 2

Flow chart of the general K-means algorithm.

Fig. 3
Fig. 3

Plots of height(s) versus radius for one RBC (a) multiple heights versus radius, (b) mean height versus radius.

Fig. 4
Fig. 4

Three landmark points on the curve of one RBC.

Tables (2)

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Table 1 RBC Classification Result by Model-Based Clustering

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Table 2 Feature Vectors and K-Means Clustering Result

Equations (6)

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l ( θ k , τ k , z i k | x ) = log i = 1 n { [ k = 1 G ϕ k ( y i | θ k ) z i k ] τ 1 z i 1 ... τ G z i G } = i = 1 n k = 1 G z i k log [ τ k ϕ k ( y i | θ k ) ] .
z ^ i k τ ^ k f k ( y i | θ ^ k ) j = 1 G τ ^ k f k ( y i | θ ^ k ) .
τ ^ k n k n , μ ^ k i = 1 n z ^ i k y i n k , n k i = 1 n z ^ i k .
Pr [ y class j ] = τ j f j k = 1 G τ k f k ( y ) .
f j ( y | θ k ) = k = 1 G τ j k ϕ ( y | μ j k , Σ j k ) .
arg min k k = 1 K x i k D 2 ( x i , m k ) ,

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