Abstract

We present methods that automatically select a linear or nonlinear classifier for red blood cell (RBC) classification by analyzing the equality of the covariance matrices in Gabor-filtered holographic images. First, the phase images of the RBCs are numerically reconstructed from their holograms, which are recorded using off-axis digital holographic microscopy (DHM). Second, each RBC is segmented using a marker-controlled watershed transform algorithm and the inner part of the RBC is identified and analyzed. Third, the Gabor wavelet transform is applied to the segmented cells to extract a series of features, which then undergo a multivariate statistical test to evaluate the equality of the covariance matrices of the different shapes of the RBCs using selected features. When these covariance matrices are not equal, a nonlinear classification scheme based on quadratic functions is applied; otherwise, a linear classification is applied. We used the stomatocyte, discocyte, and echinocyte RBC for classifier training and testing. Simulation results demonstrated that 10 of the 14 RBC features are useful in RBC classification. Experimental results also revealed that the covariance matrices of the three main RBC groups are not equal and that a nonlinear classification method has a much lower misclassification rate. The proposed automated RBC classification method has the potential for use in drug testing and the diagnosis of RBC-related diseases.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2015 (6)

F. Yi, I. Moon, and Y. H. Lee, “Three-dimensional counting of morphologically normal human red blood cells via digital holographic microscopy,” J. Biomed. Opt. 20(1), 016005 (2015).
[Crossref] [PubMed]

J. Li, X. Li, B. Yang, and X. Sun, “Segmentation-based Image Copy-move Forgery Detection Scheme,” IEEE Trans. Inf. Forensics Security 10(3), 507–518 (2015).
[Crossref]

Y. Zheng, B. Jeon, D. Xu, Q. M. Wu, and H. Zhang, “Image segmentation by generalized hierarchical fuzzy C-means algorithm,” Journal of Intelligent and Fuzzy Systems: Applications in Engineering and Technology 28(2), 961–973 (2015).

X. Wen, L. Shao, Y. Xue, and W. Fang, “A rapid learning algorithm for vehicle classification,” Inf. Sci. 295, 395–406 (2015).
[Crossref]

B. Gu, V. S. Sheng, K. Y. Tay, W. Romano, and S. Li, “Incremental support vector learning for ordinal regression,” IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1403–1416 (2015).
[Crossref] [PubMed]

B. Rappaz, I. Moon, F. Yi, B. Javidi, P. Marquet, and G. Turcatti, “Automated multi-parameter measurement of cardiomyocytes dynamics with digital holographic microscopy,” Opt. Express 23(10), 13333–13347 (2015).
[Crossref] [PubMed]

2014 (3)

A. Anand and B. Javidi, “Digital holographic microscopy for automated 3D cell identification: an overview,” Chin. Opt. Lett. 12(6), 060012 (2014).
[Crossref]

P. Guo, J. Wang, B. Li, and S. Lee, “A variable threshold-value authentication architecture for wireless mesh networks,” Journal of Internet Technology 15(6), 929–936 (2014).

H. Lee and Y. Chen, “Cell morphology based classification for red cells in blood smear images,” Pattern Recognit. Lett. 49, 155–161 (2014).
[Crossref]

2013 (3)

F. Yi, I. Moon, B. Javidi, D. Boss, and P. Marquet, “Automated segmentation of multiple red blood cells with digital holographic microscopy,” J. Biomed. Opt. 18(2), 26006 (2013).
[Crossref] [PubMed]

I. Moon, F. Yi, Y. H. Lee, B. Javidi, D. Boss, and P. Marquet, “Automated quantitative analysis of 3D morphology and mean corpuscular hemoglobin in human red blood cells stored in different periods,” Opt. Express 21(25), 30947–30957 (2013).
[Crossref] [PubMed]

F. Yi, I. Moon, and Y. H. Lee, “Extraction of target specimens from bioholographic images using interactive graph cuts,” J. Biomed. Opt. 18(12), 126015 (2013).
[Crossref] [PubMed]

2012 (7)

I. Seroussi, D. Veikherman, N. Ofer, S. Yehudai-Resheff, and K. Keren, “Segmentation and tracking of live cells in phase-contrast images using directional gradient vector flow for snakes,” J. Microsc. 247(2), 137–146 (2012).
[Crossref] [PubMed]

D. Zhang, M. Islam, G. Lu, and I. Sumana, “Rotation invariant curvelet features for region based image retrieval,” Int. J. Comput. Vis. 98(2), 187–201 (2012).
[Crossref]

I. Moon, B. Javidi, F. Yi, D. Boss, and P. Marquet, “Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells,” Opt. Express 20(9), 10295–10309 (2012).
[Crossref] [PubMed]

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

E. H. Seeley and R. M. Caprioli, “3D imaging by mass spectrometry: a new frontier,” Anal. Chem. 84(5), 2105–2110 (2012).
[Crossref] [PubMed]

M. A. Robinson, D. J. Graham, and D. G. Castner, “ToF-SIMS depth profiling of cells: z-correction, 3D imaging, and sputter rate of individual NIH/3T3 fibroblasts,” Anal. Chem. 84(11), 4880–4885 (2012).
[Crossref] [PubMed]

2011 (4)

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification computational 3-D holographic microscopy,” Opt. Photonics News 22(6), 18–23 (2011).
[Crossref]

R. Liu, D. K. Dey, D. Boss, P. Marquet, and B. Javidi, “Recognition and classification of red blood cells using digital holographic microscopy and data clustering with discriminant analysis,” J. Opt. Soc. Am. A 28(6), 1204–1210 (2011).
[Crossref] [PubMed]

J. Gall, A. Yao, N. Razavi, L. Van Gool, and V. Lempitsky, “Hough forests for object detection, tracking, and action recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 33(11), 2188–2202 (2011).
[Crossref] [PubMed]

M. Winter, E. Wait, B. Roysam, S. K. Goderie, R. A. Ali, E. Kokovay, S. Temple, and A. R. Cohen, “Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing,” Nat. Protoc. 6(12), 1942–1952 (2011).
[Crossref] [PubMed]

2010 (1)

J. Laurie, D. Wyncoll, and C. Harrison, “New versus old blood - the debate continues,” Crit. Care 14(2), 130–131 (2010).
[Crossref] [PubMed]

2009 (1)

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional identification and tracking of micro/nanobiological organisms by computational holographic microscopy,” Proc. IEEE 97(6), 990–1010 (2009).
[Crossref]

2008 (2)

I. Moon and B. Javidi, “3-D visualization and identification of biological microorganisms using partially temporal incoherent light in-line computational holographic imaging,” IEEE Trans. Med. Imaging 27(12), 1782–1790 (2008).
[Crossref] [PubMed]

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, and E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358(12), 1229–1239 (2008).
[Crossref] [PubMed]

2007 (1)

I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4(13), 305–313 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (2)

1999 (1)

1989 (1)

I. Fogel and D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61(2), 103–113 (1989).
[Crossref]

1977 (1)

J. W. Bacus and J. H. Weens, “An automated method of differential red blood cell classification with application to the diagnosis of anemia,” J. Histochem. Cytochem. 25(7), 614–632 (1977).
[Crossref] [PubMed]

Abrahamsson, S.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Agard, D. A.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Ali, R. A.

M. Winter, E. Wait, B. Roysam, S. K. Goderie, R. A. Ali, E. Kokovay, S. Temple, and A. R. Cohen, “Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing,” Nat. Protoc. 6(12), 1942–1952 (2011).
[Crossref] [PubMed]

Anand, A.

A. Anand and B. Javidi, “Digital holographic microscopy for automated 3D cell identification: an overview,” Chin. Opt. Lett. 12(6), 060012 (2014).
[Crossref]

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification computational 3-D holographic microscopy,” Opt. Photonics News 22(6), 18–23 (2011).
[Crossref]

Aspert, N.

Bacus, J. W.

J. W. Bacus and J. H. Weens, “An automated method of differential red blood cell classification with application to the diagnosis of anemia,” J. Histochem. Cytochem. 25(7), 614–632 (1977).
[Crossref] [PubMed]

Bargmann, C. I.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Blackstone, E. H.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, and E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358(12), 1229–1239 (2008).
[Crossref] [PubMed]

Boss, D.

Caprioli, R. M.

E. H. Seeley and R. M. Caprioli, “3D imaging by mass spectrometry: a new frontier,” Anal. Chem. 84(5), 2105–2110 (2012).
[Crossref] [PubMed]

Carapezza, E.

Castner, D. G.

M. A. Robinson, D. J. Graham, and D. G. Castner, “ToF-SIMS depth profiling of cells: z-correction, 3D imaging, and sputter rate of individual NIH/3T3 fibroblasts,” Anal. Chem. 84(11), 4880–4885 (2012).
[Crossref] [PubMed]

Charrière, F.

Chen, J.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Chen, Y.

H. Lee and Y. Chen, “Cell morphology based classification for red cells in blood smear images,” Pattern Recognit. Lett. 49, 155–161 (2014).
[Crossref]

Cohen, A. R.

M. Winter, E. Wait, B. Roysam, S. K. Goderie, R. A. Ali, E. Kokovay, S. Temple, and A. R. Cohen, “Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing,” Nat. Protoc. 6(12), 1942–1952 (2011).
[Crossref] [PubMed]

Colomb, T.

Cuche, E.

Dahan, M.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Daneshpanah, M.

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification computational 3-D holographic microscopy,” Opt. Photonics News 22(6), 18–23 (2011).
[Crossref]

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional identification and tracking of micro/nanobiological organisms by computational holographic microscopy,” Proc. IEEE 97(6), 990–1010 (2009).
[Crossref]

Darzacq, X.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Davidson, M. W.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

Depeursinge, C.

Dey, D. K.

Dugast Darzacq, C.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Fang, W.

X. Wen, L. Shao, Y. Xue, and W. Fang, “A rapid learning algorithm for vehicle classification,” Inf. Sci. 295, 395–406 (2015).
[Crossref]

Fawcett, T.

T. Fawcett, “An Introduction to ROC Analysis,” Pattern Recognit. Lett. 27(8), 861–874 (2006).
[Crossref]

Figueroa, P.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, and E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358(12), 1229–1239 (2008).
[Crossref] [PubMed]

Fiolka, R.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

Fogel, I.

I. Fogel and D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61(2), 103–113 (1989).
[Crossref]

Gall, J.

J. Gall, A. Yao, N. Razavi, L. Van Gool, and V. Lempitsky, “Hough forests for object detection, tracking, and action recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 33(11), 2188–2202 (2011).
[Crossref] [PubMed]

Goderie, S. K.

M. Winter, E. Wait, B. Roysam, S. K. Goderie, R. A. Ali, E. Kokovay, S. Temple, and A. R. Cohen, “Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing,” Nat. Protoc. 6(12), 1942–1952 (2011).
[Crossref] [PubMed]

Graham, D. J.

M. A. Robinson, D. J. Graham, and D. G. Castner, “ToF-SIMS depth profiling of cells: z-correction, 3D imaging, and sputter rate of individual NIH/3T3 fibroblasts,” Anal. Chem. 84(11), 4880–4885 (2012).
[Crossref] [PubMed]

Gu, B.

B. Gu, V. S. Sheng, K. Y. Tay, W. Romano, and S. Li, “Incremental support vector learning for ordinal regression,” IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1403–1416 (2015).
[Crossref] [PubMed]

Guo, P.

P. Guo, J. Wang, B. Li, and S. Lee, “A variable threshold-value authentication architecture for wireless mesh networks,” Journal of Internet Technology 15(6), 929–936 (2014).

Gustafsson, M. G.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

Hajj, B.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Harrison, C.

J. Laurie, D. Wyncoll, and C. Harrison, “New versus old blood - the debate continues,” Crit. Care 14(2), 130–131 (2010).
[Crossref] [PubMed]

Hoeltge, G. A.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, and E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358(12), 1229–1239 (2008).
[Crossref] [PubMed]

Islam, M.

D. Zhang, M. Islam, G. Lu, and I. Sumana, “Rotation invariant curvelet features for region based image retrieval,” Int. J. Comput. Vis. 98(2), 187–201 (2012).
[Crossref]

Javidi, B.

B. Rappaz, I. Moon, F. Yi, B. Javidi, P. Marquet, and G. Turcatti, “Automated multi-parameter measurement of cardiomyocytes dynamics with digital holographic microscopy,” Opt. Express 23(10), 13333–13347 (2015).
[Crossref] [PubMed]

A. Anand and B. Javidi, “Digital holographic microscopy for automated 3D cell identification: an overview,” Chin. Opt. Lett. 12(6), 060012 (2014).
[Crossref]

I. Moon, F. Yi, Y. H. Lee, B. Javidi, D. Boss, and P. Marquet, “Automated quantitative analysis of 3D morphology and mean corpuscular hemoglobin in human red blood cells stored in different periods,” Opt. Express 21(25), 30947–30957 (2013).
[Crossref] [PubMed]

F. Yi, I. Moon, B. Javidi, D. Boss, and P. Marquet, “Automated segmentation of multiple red blood cells with digital holographic microscopy,” J. Biomed. Opt. 18(2), 26006 (2013).
[Crossref] [PubMed]

I. Moon, B. Javidi, F. Yi, D. Boss, and P. Marquet, “Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells,” Opt. Express 20(9), 10295–10309 (2012).
[Crossref] [PubMed]

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification computational 3-D holographic microscopy,” Opt. Photonics News 22(6), 18–23 (2011).
[Crossref]

R. Liu, D. K. Dey, D. Boss, P. Marquet, and B. Javidi, “Recognition and classification of red blood cells using digital holographic microscopy and data clustering with discriminant analysis,” J. Opt. Soc. Am. A 28(6), 1204–1210 (2011).
[Crossref] [PubMed]

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional identification and tracking of micro/nanobiological organisms by computational holographic microscopy,” Proc. IEEE 97(6), 990–1010 (2009).
[Crossref]

I. Moon and B. Javidi, “3-D visualization and identification of biological microorganisms using partially temporal incoherent light in-line computational holographic imaging,” IEEE Trans. Med. Imaging 27(12), 1782–1790 (2008).
[Crossref] [PubMed]

I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4(13), 305–313 (2007).
[Crossref] [PubMed]

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(12), 4492–4506 (2005).
[Crossref] [PubMed]

I. Moon and B. Javidi, “Shape tolerant three-dimensional recognition of biological microorganisms using digital holography,” Opt. Express 13(23), 9612–9622 (2005).
[Crossref] [PubMed]

Jeon, B.

Y. Zheng, B. Jeon, D. Xu, Q. M. Wu, and H. Zhang, “Image segmentation by generalized hierarchical fuzzy C-means algorithm,” Journal of Intelligent and Fuzzy Systems: Applications in Engineering and Technology 28(2), 961–973 (2015).

Katsov, A. Y.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Keren, K.

I. Seroussi, D. Veikherman, N. Ofer, S. Yehudai-Resheff, and K. Keren, “Segmentation and tracking of live cells in phase-contrast images using directional gradient vector flow for snakes,” J. Microsc. 247(2), 137–146 (2012).
[Crossref] [PubMed]

Koch, C. G.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, and E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358(12), 1229–1239 (2008).
[Crossref] [PubMed]

Kokovay, E.

M. Winter, E. Wait, B. Roysam, S. K. Goderie, R. A. Ali, E. Kokovay, S. Temple, and A. R. Cohen, “Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing,” Nat. Protoc. 6(12), 1942–1952 (2011).
[Crossref] [PubMed]

Kühn, J.

Laurie, J.

J. Laurie, D. Wyncoll, and C. Harrison, “New versus old blood - the debate continues,” Crit. Care 14(2), 130–131 (2010).
[Crossref] [PubMed]

Lee, H.

H. Lee and Y. Chen, “Cell morphology based classification for red cells in blood smear images,” Pattern Recognit. Lett. 49, 155–161 (2014).
[Crossref]

Lee, S.

P. Guo, J. Wang, B. Li, and S. Lee, “A variable threshold-value authentication architecture for wireless mesh networks,” Journal of Internet Technology 15(6), 929–936 (2014).

Lee, Y. H.

F. Yi, I. Moon, and Y. H. Lee, “Three-dimensional counting of morphologically normal human red blood cells via digital holographic microscopy,” J. Biomed. Opt. 20(1), 016005 (2015).
[Crossref] [PubMed]

I. Moon, F. Yi, Y. H. Lee, B. Javidi, D. Boss, and P. Marquet, “Automated quantitative analysis of 3D morphology and mean corpuscular hemoglobin in human red blood cells stored in different periods,” Opt. Express 21(25), 30947–30957 (2013).
[Crossref] [PubMed]

F. Yi, I. Moon, and Y. H. Lee, “Extraction of target specimens from bioholographic images using interactive graph cuts,” J. Biomed. Opt. 18(12), 126015 (2013).
[Crossref] [PubMed]

Lempitsky, V.

J. Gall, A. Yao, N. Razavi, L. Van Gool, and V. Lempitsky, “Hough forests for object detection, tracking, and action recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 33(11), 2188–2202 (2011).
[Crossref] [PubMed]

Li, B.

P. Guo, J. Wang, B. Li, and S. Lee, “A variable threshold-value authentication architecture for wireless mesh networks,” Journal of Internet Technology 15(6), 929–936 (2014).

Li, J.

J. Li, X. Li, B. Yang, and X. Sun, “Segmentation-based Image Copy-move Forgery Detection Scheme,” IEEE Trans. Inf. Forensics Security 10(3), 507–518 (2015).
[Crossref]

Li, L.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, and E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358(12), 1229–1239 (2008).
[Crossref] [PubMed]

Li, S.

B. Gu, V. S. Sheng, K. Y. Tay, W. Romano, and S. Li, “Incremental support vector learning for ordinal regression,” IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1403–1416 (2015).
[Crossref] [PubMed]

Li, X.

J. Li, X. Li, B. Yang, and X. Sun, “Segmentation-based Image Copy-move Forgery Detection Scheme,” IEEE Trans. Inf. Forensics Security 10(3), 507–518 (2015).
[Crossref]

Liu, R.

Lu, G.

D. Zhang, M. Islam, G. Lu, and I. Sumana, “Rotation invariant curvelet features for region based image retrieval,” Int. J. Comput. Vis. 98(2), 187–201 (2012).
[Crossref]

Marquet, P.

B. Rappaz, I. Moon, F. Yi, B. Javidi, P. Marquet, and G. Turcatti, “Automated multi-parameter measurement of cardiomyocytes dynamics with digital holographic microscopy,” Opt. Express 23(10), 13333–13347 (2015).
[Crossref] [PubMed]

F. Yi, I. Moon, B. Javidi, D. Boss, and P. Marquet, “Automated segmentation of multiple red blood cells with digital holographic microscopy,” J. Biomed. Opt. 18(2), 26006 (2013).
[Crossref] [PubMed]

I. Moon, F. Yi, Y. H. Lee, B. Javidi, D. Boss, and P. Marquet, “Automated quantitative analysis of 3D morphology and mean corpuscular hemoglobin in human red blood cells stored in different periods,” Opt. Express 21(25), 30947–30957 (2013).
[Crossref] [PubMed]

I. Moon, B. Javidi, F. Yi, D. Boss, and P. Marquet, “Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells,” Opt. Express 20(9), 10295–10309 (2012).
[Crossref] [PubMed]

R. Liu, D. K. Dey, D. Boss, P. Marquet, and B. Javidi, “Recognition and classification of red blood cells using digital holographic microscopy and data clustering with discriminant analysis,” J. Opt. Soc. Am. A 28(6), 1204–1210 (2011).
[Crossref] [PubMed]

T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45(5), 851–863 (2006).
[Crossref] [PubMed]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38(34), 6994–7001 (1999).
[Crossref] [PubMed]

Mihaljevic, T.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, and E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358(12), 1229–1239 (2008).
[Crossref] [PubMed]

Mizuguchi, G.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Montfort, F.

Moon, I.

F. Yi, I. Moon, and Y. H. Lee, “Three-dimensional counting of morphologically normal human red blood cells via digital holographic microscopy,” J. Biomed. Opt. 20(1), 016005 (2015).
[Crossref] [PubMed]

B. Rappaz, I. Moon, F. Yi, B. Javidi, P. Marquet, and G. Turcatti, “Automated multi-parameter measurement of cardiomyocytes dynamics with digital holographic microscopy,” Opt. Express 23(10), 13333–13347 (2015).
[Crossref] [PubMed]

F. Yi, I. Moon, B. Javidi, D. Boss, and P. Marquet, “Automated segmentation of multiple red blood cells with digital holographic microscopy,” J. Biomed. Opt. 18(2), 26006 (2013).
[Crossref] [PubMed]

F. Yi, I. Moon, and Y. H. Lee, “Extraction of target specimens from bioholographic images using interactive graph cuts,” J. Biomed. Opt. 18(12), 126015 (2013).
[Crossref] [PubMed]

I. Moon, F. Yi, Y. H. Lee, B. Javidi, D. Boss, and P. Marquet, “Automated quantitative analysis of 3D morphology and mean corpuscular hemoglobin in human red blood cells stored in different periods,” Opt. Express 21(25), 30947–30957 (2013).
[Crossref] [PubMed]

I. Moon, B. Javidi, F. Yi, D. Boss, and P. Marquet, “Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells,” Opt. Express 20(9), 10295–10309 (2012).
[Crossref] [PubMed]

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification computational 3-D holographic microscopy,” Opt. Photonics News 22(6), 18–23 (2011).
[Crossref]

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional identification and tracking of micro/nanobiological organisms by computational holographic microscopy,” Proc. IEEE 97(6), 990–1010 (2009).
[Crossref]

I. Moon and B. Javidi, “3-D visualization and identification of biological microorganisms using partially temporal incoherent light in-line computational holographic imaging,” IEEE Trans. Med. Imaging 27(12), 1782–1790 (2008).
[Crossref] [PubMed]

I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4(13), 305–313 (2007).
[Crossref] [PubMed]

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(12), 4492–4506 (2005).
[Crossref] [PubMed]

I. Moon and B. Javidi, “Shape tolerant three-dimensional recognition of biological microorganisms using digital holography,” Opt. Express 13(23), 9612–9622 (2005).
[Crossref] [PubMed]

Mueller, F.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Ofer, N.

I. Seroussi, D. Veikherman, N. Ofer, S. Yehudai-Resheff, and K. Keren, “Segmentation and tracking of live cells in phase-contrast images using directional gradient vector flow for snakes,” J. Microsc. 247(2), 137–146 (2012).
[Crossref] [PubMed]

Rappaz, B.

Razavi, N.

J. Gall, A. Yao, N. Razavi, L. Van Gool, and V. Lempitsky, “Hough forests for object detection, tracking, and action recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 33(11), 2188–2202 (2011).
[Crossref] [PubMed]

Rego, E. H.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

Robinson, M. A.

M. A. Robinson, D. J. Graham, and D. G. Castner, “ToF-SIMS depth profiling of cells: z-correction, 3D imaging, and sputter rate of individual NIH/3T3 fibroblasts,” Anal. Chem. 84(11), 4880–4885 (2012).
[Crossref] [PubMed]

Romano, W.

B. Gu, V. S. Sheng, K. Y. Tay, W. Romano, and S. Li, “Incremental support vector learning for ordinal regression,” IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1403–1416 (2015).
[Crossref] [PubMed]

Roysam, B.

M. Winter, E. Wait, B. Roysam, S. K. Goderie, R. A. Ali, E. Kokovay, S. Temple, and A. R. Cohen, “Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing,” Nat. Protoc. 6(12), 1942–1952 (2011).
[Crossref] [PubMed]

Sagi, D.

I. Fogel and D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61(2), 103–113 (1989).
[Crossref]

Seeley, E. H.

E. H. Seeley and R. M. Caprioli, “3D imaging by mass spectrometry: a new frontier,” Anal. Chem. 84(5), 2105–2110 (2012).
[Crossref] [PubMed]

Seroussi, I.

I. Seroussi, D. Veikherman, N. Ofer, S. Yehudai-Resheff, and K. Keren, “Segmentation and tracking of live cells in phase-contrast images using directional gradient vector flow for snakes,” J. Microsc. 247(2), 137–146 (2012).
[Crossref] [PubMed]

Sessler, D. I.

C. G. Koch, L. Li, D. I. Sessler, P. Figueroa, G. A. Hoeltge, T. Mihaljevic, and E. H. Blackstone, “Duration of red-cell storage and complications after cardiac surgery,” N. Engl. J. Med. 358(12), 1229–1239 (2008).
[Crossref] [PubMed]

Shao, L.

X. Wen, L. Shao, Y. Xue, and W. Fang, “A rapid learning algorithm for vehicle classification,” Inf. Sci. 295, 395–406 (2015).
[Crossref]

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

Sheng, V. S.

B. Gu, V. S. Sheng, K. Y. Tay, W. Romano, and S. Li, “Incremental support vector learning for ordinal regression,” IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1403–1416 (2015).
[Crossref] [PubMed]

Soule, P.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Stallinga, S.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Stern, A.

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional identification and tracking of micro/nanobiological organisms by computational holographic microscopy,” Proc. IEEE 97(6), 990–1010 (2009).
[Crossref]

Sumana, I.

D. Zhang, M. Islam, G. Lu, and I. Sumana, “Rotation invariant curvelet features for region based image retrieval,” Int. J. Comput. Vis. 98(2), 187–201 (2012).
[Crossref]

Sun, X.

J. Li, X. Li, B. Yang, and X. Sun, “Segmentation-based Image Copy-move Forgery Detection Scheme,” IEEE Trans. Inf. Forensics Security 10(3), 507–518 (2015).
[Crossref]

Tay, K. Y.

B. Gu, V. S. Sheng, K. Y. Tay, W. Romano, and S. Li, “Incremental support vector learning for ordinal regression,” IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1403–1416 (2015).
[Crossref] [PubMed]

Temple, S.

M. Winter, E. Wait, B. Roysam, S. K. Goderie, R. A. Ali, E. Kokovay, S. Temple, and A. R. Cohen, “Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing,” Nat. Protoc. 6(12), 1942–1952 (2011).
[Crossref] [PubMed]

Turcatti, G.

Van Gool, L.

J. Gall, A. Yao, N. Razavi, L. Van Gool, and V. Lempitsky, “Hough forests for object detection, tracking, and action recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 33(11), 2188–2202 (2011).
[Crossref] [PubMed]

Veikherman, D.

I. Seroussi, D. Veikherman, N. Ofer, S. Yehudai-Resheff, and K. Keren, “Segmentation and tracking of live cells in phase-contrast images using directional gradient vector flow for snakes,” J. Microsc. 247(2), 137–146 (2012).
[Crossref] [PubMed]

Wait, E.

M. Winter, E. Wait, B. Roysam, S. K. Goderie, R. A. Ali, E. Kokovay, S. Temple, and A. R. Cohen, “Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing,” Nat. Protoc. 6(12), 1942–1952 (2011).
[Crossref] [PubMed]

Wang, J.

P. Guo, J. Wang, B. Li, and S. Lee, “A variable threshold-value authentication architecture for wireless mesh networks,” Journal of Internet Technology 15(6), 929–936 (2014).

Weens, J. H.

J. W. Bacus and J. H. Weens, “An automated method of differential red blood cell classification with application to the diagnosis of anemia,” J. Histochem. Cytochem. 25(7), 614–632 (1977).
[Crossref] [PubMed]

Wen, X.

X. Wen, L. Shao, Y. Xue, and W. Fang, “A rapid learning algorithm for vehicle classification,” Inf. Sci. 295, 395–406 (2015).
[Crossref]

Winter, M.

M. Winter, E. Wait, B. Roysam, S. K. Goderie, R. A. Ali, E. Kokovay, S. Temple, and A. R. Cohen, “Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing,” Nat. Protoc. 6(12), 1942–1952 (2011).
[Crossref] [PubMed]

Wisniewski, J.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Wu, C.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. Dugast Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2012).
[Crossref] [PubMed]

Wu, Q. M.

Y. Zheng, B. Jeon, D. Xu, Q. M. Wu, and H. Zhang, “Image segmentation by generalized hierarchical fuzzy C-means algorithm,” Journal of Intelligent and Fuzzy Systems: Applications in Engineering and Technology 28(2), 961–973 (2015).

Wyncoll, D.

J. Laurie, D. Wyncoll, and C. Harrison, “New versus old blood - the debate continues,” Crit. Care 14(2), 130–131 (2010).
[Crossref] [PubMed]

Xu, D.

Y. Zheng, B. Jeon, D. Xu, Q. M. Wu, and H. Zhang, “Image segmentation by generalized hierarchical fuzzy C-means algorithm,” Journal of Intelligent and Fuzzy Systems: Applications in Engineering and Technology 28(2), 961–973 (2015).

Xue, Y.

X. Wen, L. Shao, Y. Xue, and W. Fang, “A rapid learning algorithm for vehicle classification,” Inf. Sci. 295, 395–406 (2015).
[Crossref]

Yang, B.

J. Li, X. Li, B. Yang, and X. Sun, “Segmentation-based Image Copy-move Forgery Detection Scheme,” IEEE Trans. Inf. Forensics Security 10(3), 507–518 (2015).
[Crossref]

Yao, A.

J. Gall, A. Yao, N. Razavi, L. Van Gool, and V. Lempitsky, “Hough forests for object detection, tracking, and action recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 33(11), 2188–2202 (2011).
[Crossref] [PubMed]

Yehudai-Resheff, S.

I. Seroussi, D. Veikherman, N. Ofer, S. Yehudai-Resheff, and K. Keren, “Segmentation and tracking of live cells in phase-contrast images using directional gradient vector flow for snakes,” J. Microsc. 247(2), 137–146 (2012).
[Crossref] [PubMed]

Yeom, S.

Yi, F.

Zhang, D.

D. Zhang, M. Islam, G. Lu, and I. Sumana, “Rotation invariant curvelet features for region based image retrieval,” Int. J. Comput. Vis. 98(2), 187–201 (2012).
[Crossref]

Zhang, H.

Y. Zheng, B. Jeon, D. Xu, Q. M. Wu, and H. Zhang, “Image segmentation by generalized hierarchical fuzzy C-means algorithm,” Journal of Intelligent and Fuzzy Systems: Applications in Engineering and Technology 28(2), 961–973 (2015).

Zheng, Y.

Y. Zheng, B. Jeon, D. Xu, Q. M. Wu, and H. Zhang, “Image segmentation by generalized hierarchical fuzzy C-means algorithm,” Journal of Intelligent and Fuzzy Systems: Applications in Engineering and Technology 28(2), 961–973 (2015).

Anal. Chem. (2)

E. H. Seeley and R. M. Caprioli, “3D imaging by mass spectrometry: a new frontier,” Anal. Chem. 84(5), 2105–2110 (2012).
[Crossref] [PubMed]

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Appl. Opt. (2)

Biol. Cybern. (1)

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Chin. Opt. Lett. (1)

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IEEE Trans. Inf. Forensics Security (1)

J. Li, X. Li, B. Yang, and X. Sun, “Segmentation-based Image Copy-move Forgery Detection Scheme,” IEEE Trans. Inf. Forensics Security 10(3), 507–518 (2015).
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IEEE Trans. Med. Imaging (1)

I. Moon and B. Javidi, “3-D visualization and identification of biological microorganisms using partially temporal incoherent light in-line computational holographic imaging,” IEEE Trans. Med. Imaging 27(12), 1782–1790 (2008).
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F. Yi, I. Moon, and Y. H. Lee, “Extraction of target specimens from bioholographic images using interactive graph cuts,” J. Biomed. Opt. 18(12), 126015 (2013).
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Figures (8)

Fig. 1
Fig. 1

Schematic of off-axis DHM.

Fig. 2
Fig. 2

Illustration of single RBC and the inner part of the cell.

Fig. 3
Fig. 3

Flowchart of the design of the RBC classification method.

Fig. 4
Fig. 4

Three reconstructed RBC phase images.

Fig. 5
Fig. 5

Segmented RBC phase images. Top row: segmented whole RBCs corresponding to the RBC phase images in Fig. 4. Bottom row: segmented inner part of the RBCs corresponding to the RBC phase images in Fig. 4.

Fig. 6
Fig. 6

Examples of the three types of RBCs.

Fig. 7
Fig. 7

The Gabor-wavelet-filtered RBC images. Top row: extracted RBCs. Bottom row: corresponding Gabor-wavelet-filtered RBCs.

Fig. 8
Fig. 8

Scatterplots of selected pairs of features for the three types of RBCs: (a) scatterplot for features F1 and F2, (b) scatterplot for features F5 and F11, (c) scatterplot for features F5 and F13, and (d) scatterplot for features F11 and F12.

Tables (4)

Tables Icon

Table 1 Feature Descriptions

Tables Icon

Table 2 Results of RBC Feature Analysis Using Stepwise Selection Method

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Table 3 Classification of the Three Types of RBCs Using the Holdout Procedure

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Table 4 Results of the Classification of the Three Types of RBCs Using Method in [2]

Equations (21)

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ψ( m,n )=exp{ [ α 2 ( mcosθ+nsinθ ) 2 + β 2 ( msinθ+ncosθ ) 2 ] } ×exp{ j2π f 0 ( mcosθ+nsinθ ) },
R ^ ( m , n )=R( m,n )ψ( m,n ),
S=N p 2 M 2 , φ ¯ = 1 N i=1 N φ i ,MCH= 10λ 2πα S φ ¯ ,MCHSD= MCH S ,
Per= N e ×1+ N o × 2 , Cir= Per 2 /S, Elo={ max(| N 0,4 N 2,6 |,| N 1,5 N 3,7 |),if| N 0,4 N 2,6 || N 1,5 N 3,7 | 0,if| N 0,4 N 2,6 |=| N 1,5 N 3,7 | ,
N j,k = i=1 a i=j or a i=k n 1
PCP= 1 25 -2i2 2j2 φ ij , SC= PCP φ max , Dvalue=PCP φ max ,
Λ( x| y 1 ,..., y p )= Λ( y 1 ,..., y p ,x ) Λ( y 1 ,..., y p ) ,
Λ= | E | | E+H | ,
E= i=1 k j=1 n ( y ij y ¯ i ) ( y ij y ¯ i ) T , H=n i=1 k ( y ¯ i y ¯ ) ( y ¯ i y ¯ ) T ,
F= 1Λ Λ v E p v H ,
H 0 : Σ 1 = Σ 2 == Σ k .
W= | S 1 | v 1 /2 | S 2 | v 2 /2 | S k | v k /2 | S pl | i v i /2 ,
S pl | i=1 k v i S i | | i=1 k v i | = E v E .
c 1 =[ i=1 k 1 v i 1 i=1 k v i ][ 2 p 2 +3p1 6(p+1)(k1) ],
u=2(1 c 1 )lnM,
D i 2 ( y )= ( y y ¯ i i ) T S pl -1 ( y y ¯ i i ),
S pl = 1 Nk i=1 k ( n i 1) S i .
D i 2 ( y )= y T S pl -1 y2 y ¯ i T S pl 1 y+ y ¯ i T S pl -1 y ¯ i .
D i 2 ( y )=2 y ¯ i T S pl 1 y+ y ¯ i T S pl 1 y ¯ i .
D i 2 (y)= ( y y ¯ i ) T S i 1 ( y y ¯ i ),
StomatocyteRBC: L 1 ( y )= ( y y ¯ 1 ) T S 1 1 ( y y ¯ 1 ), Discocyte RBC: L 2 ( y )= ( y y ¯ 2 ) T S 2 1 ( y y ¯ 2 ), EchinocyteRBC: L 3 ( y )= ( y y ¯ 3 ) T S 3 1 ( y y ¯ 3 ),

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