Abstract

Autofocus is an important technique for high-speed image acquisition in the second-generation DNA sequencing system, and this paper studies the passive focus algorithm for the system, which consists of two parts: focus measurement (FM) and focus search (FS). Based on the properties of DNA chips’ images, we choose the normalized variance as the FM algorithm and develop a new robust FS named adaptive prediction approximation combined search (APACS). APACS utilizes golden section search (GSS) to approximate the focus position and engages the curve-fitting search (CFS) to predict the position simultaneously in every step of GSS. When the difference between consecutive predictions meets the set precision, the search finishes. Otherwise, it ends as GSS. In APACS, we also propose an estimation method, named the combination of centroid estimation and overdetermined equations estimation by least squares solution, to calculate the initial vector for the nonlinear equations in APACS prediction, which reduces the iterations and accelerates the search. The simulation and measured results demonstrate that APACS not only maintains the stability but also reduces the focus time compared with GSS and CFS, which indicates APACS is a robust and fast FS for the fluorescence microscope in a sequencing system.

© 2014 Optical Society of America

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  1. L. Shih, “Autofocus survey: a comparison of algorithms,” Proc. SPIE 6502, 65020B (2007).
    [CrossRef]
  2. Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).
    [CrossRef]
  3. J. F. Schlag, A. C. Sanderson, C. P. Neuman, and F. C. Wimberly, Implementation of Automatic Focusing Algorithms for a Computer Vision System with Camera Control (Citeseer, 1983).
  4. N. Kehtarnavaz and H. J. Oh, “Development and real-time implementation of a rule-based auto-focus algorithm,” Real-Time Imaging 9, 197–203 (2003).
    [CrossRef]
  5. C.-Y. Chen, R.-C. Hwang, and Y.-J. Chen, “A passive auto-focus camera control system,” Appl. Soft Comput. 10, 296–303 (2010).
    [CrossRef]
  6. H.-L. Shen, Z.-H. Zheng, W. Wang, X. Du, S.-J. Shao, and J. H. Xin, “Autofocus for multispectral camera using focus symmetry,” Appl. Opt. 51, 2616–2623 (2012).
    [CrossRef]
  7. M. Gamadia, V. Peddigari, N. Kehtarnavaz, S.-Y. Lee, and G. Cook, “Real-time implementation of autofocus on the TI DSC processor,” Proc. SPIE 5297, 10–18 (2004).
    [CrossRef]
  8. R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
    [CrossRef]
  9. O. Osibote, R. Dendere, S. Krishnan, and T. Douglas, “Automated focusing in bright-field microscopy for tuberculosis detection,” J. Microsc. 240, 155–163 (2010).
    [CrossRef]
  10. F. C. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
    [CrossRef]
  11. J. M. Tenenbaum, “Accommodation in computer vision,” Ph.D. thesis (Stanford University, 1970).
  12. T. Yeo, S. Ong, and R. Sinniah, “Autofocusing for tissue microscopy,” in Image and Vision Computing (1993), pp. 629–639.
  13. M. A. Bueno-Ibarra and L. Acho, “Fast autofocus algorithm for automated microscopes,” Opt. Eng. 44, 063601 (2005).
    [CrossRef]
  14. J. H. Price and D. A. Gough, “Comparison of phase-contrast and fluorescence digital autofocus for scanning microscopy,” Cytometry 16, 283–297 (1994).
    [CrossRef]
  15. D. Vollath, “Automatic focusing by correlative methods,” J. Microsc. 147, 279–288 (1987).
    [CrossRef]
  16. A. Santos, C. Ortiz de Solorzano, J. J. Vaquero, J. Pena, N. Malpica, and F. Del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188, 264–272 (1997).
    [CrossRef]
  17. Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing algorithm selection in computer microscopy,” in 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2005), pp. 70–76.
  18. Y. Yao, B. Abidi, N. Doggaz, and M. Abidi, “Evaluation of sharpness measures and search algorithms for the auto focusing of high-magnification images,” in Defense and Security Symposium (International Society for Optics and Photonics, 2006), p. 62460G.
  19. M. Rahman and N. Kehtarnavaz, “Real-time face-priority auto focus for digital and cell-phone cameras,” IEEE Trans. Consum. Electron. 54, 1506–1513 (2008).
    [CrossRef]
  20. J. He, R. Zhou, and Z. Hong, “Modified fast climbing search auto-focus algorithm with adaptive step size searching technique for digital camera,” IEEE Trans. Consum. Electron. 49, 257–262 (2003).
    [CrossRef]
  21. K. Ooi, K. Izumi, M. Nozaki, and I. Takeda, “An advanced autofocus system for video camera using quasi condition reasoning,” IEEE Trans. Consum. Electron. 36, 526–530 (1990).
    [CrossRef]
  22. R. A. Jarvis, “Focus optimization criteria for computer image processing,” Microscope 24, 163–180 (1976).
  23. E. P. Krotkov, Active Computer Vision by Cooperative Focus and Stereo (Springer-Verlag, 1989).
  24. J. Baina and J. Dublet, “Automatic focus and iris control for video cameras,” in Fifth International Conference on Image Processing and its Applications (IET, 1995), pp. 232–235.
  25. M. Subbarao and J.-K. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 864–870 (1998).
    [CrossRef]
  26. E. Krotkov, “Focusing,” Int. J. Comput. Vis. 1, 223–237 (1956).
  27. D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Autofocus algorithm for dispersion correction in optical coherence tomography,” Appl. Opt. 42, 3038–3046 (2003).
    [CrossRef]
  28. Q. Wu, F. Merchant, and K. Castleman, Microscope Image Processing (Elsevier, 2010).
  29. S. Yazdanfar, K. B. Kenny, K. Tasimi, A. D. Corwin, E. L. Dixon, and R. J. Filkins, “Simple and robust image-based autofocusing for digital microscopy,” Opt. Express 16, 8670–8677 (2008).
    [CrossRef]
  30. H. Anton, Elementary Linear Algebra (Wiley, 2010).

2012 (2)

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

H.-L. Shen, Z.-H. Zheng, W. Wang, X. Du, S.-J. Shao, and J. H. Xin, “Autofocus for multispectral camera using focus symmetry,” Appl. Opt. 51, 2616–2623 (2012).
[CrossRef]

2010 (2)

O. Osibote, R. Dendere, S. Krishnan, and T. Douglas, “Automated focusing in bright-field microscopy for tuberculosis detection,” J. Microsc. 240, 155–163 (2010).
[CrossRef]

C.-Y. Chen, R.-C. Hwang, and Y.-J. Chen, “A passive auto-focus camera control system,” Appl. Soft Comput. 10, 296–303 (2010).
[CrossRef]

2008 (2)

M. Rahman and N. Kehtarnavaz, “Real-time face-priority auto focus for digital and cell-phone cameras,” IEEE Trans. Consum. Electron. 54, 1506–1513 (2008).
[CrossRef]

S. Yazdanfar, K. B. Kenny, K. Tasimi, A. D. Corwin, E. L. Dixon, and R. J. Filkins, “Simple and robust image-based autofocusing for digital microscopy,” Opt. Express 16, 8670–8677 (2008).
[CrossRef]

2007 (1)

L. Shih, “Autofocus survey: a comparison of algorithms,” Proc. SPIE 6502, 65020B (2007).
[CrossRef]

2005 (1)

M. A. Bueno-Ibarra and L. Acho, “Fast autofocus algorithm for automated microscopes,” Opt. Eng. 44, 063601 (2005).
[CrossRef]

2004 (2)

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).
[CrossRef]

M. Gamadia, V. Peddigari, N. Kehtarnavaz, S.-Y. Lee, and G. Cook, “Real-time implementation of autofocus on the TI DSC processor,” Proc. SPIE 5297, 10–18 (2004).
[CrossRef]

2003 (3)

N. Kehtarnavaz and H. J. Oh, “Development and real-time implementation of a rule-based auto-focus algorithm,” Real-Time Imaging 9, 197–203 (2003).
[CrossRef]

D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Autofocus algorithm for dispersion correction in optical coherence tomography,” Appl. Opt. 42, 3038–3046 (2003).
[CrossRef]

J. He, R. Zhou, and Z. Hong, “Modified fast climbing search auto-focus algorithm with adaptive step size searching technique for digital camera,” IEEE Trans. Consum. Electron. 49, 257–262 (2003).
[CrossRef]

1998 (1)

M. Subbarao and J.-K. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 864–870 (1998).
[CrossRef]

1997 (1)

A. Santos, C. Ortiz de Solorzano, J. J. Vaquero, J. Pena, N. Malpica, and F. Del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188, 264–272 (1997).
[CrossRef]

1994 (1)

J. H. Price and D. A. Gough, “Comparison of phase-contrast and fluorescence digital autofocus for scanning microscopy,” Cytometry 16, 283–297 (1994).
[CrossRef]

1990 (1)

K. Ooi, K. Izumi, M. Nozaki, and I. Takeda, “An advanced autofocus system for video camera using quasi condition reasoning,” IEEE Trans. Consum. Electron. 36, 526–530 (1990).
[CrossRef]

1987 (1)

D. Vollath, “Automatic focusing by correlative methods,” J. Microsc. 147, 279–288 (1987).
[CrossRef]

1985 (1)

F. C. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
[CrossRef]

1976 (1)

R. A. Jarvis, “Focus optimization criteria for computer image processing,” Microscope 24, 163–180 (1976).

1956 (1)

E. Krotkov, “Focusing,” Int. J. Comput. Vis. 1, 223–237 (1956).

Abidi, B.

Y. Yao, B. Abidi, N. Doggaz, and M. Abidi, “Evaluation of sharpness measures and search algorithms for the auto focusing of high-magnification images,” in Defense and Security Symposium (International Society for Optics and Photonics, 2006), p. 62460G.

Abidi, M.

Y. Yao, B. Abidi, N. Doggaz, and M. Abidi, “Evaluation of sharpness measures and search algorithms for the auto focusing of high-magnification images,” in Defense and Security Symposium (International Society for Optics and Photonics, 2006), p. 62460G.

Acho, L.

M. A. Bueno-Ibarra and L. Acho, “Fast autofocus algorithm for automated microscopes,” Opt. Eng. 44, 063601 (2005).
[CrossRef]

Anton, H.

H. Anton, Elementary Linear Algebra (Wiley, 2010).

Baina, J.

J. Baina and J. Dublet, “Automatic focus and iris control for video cameras,” in Fifth International Conference on Image Processing and its Applications (IET, 1995), pp. 232–235.

Boppart, S. A.

Bueno, G.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

Bueno-Ibarra, M. A.

M. A. Bueno-Ibarra and L. Acho, “Fast autofocus algorithm for automated microscopes,” Opt. Eng. 44, 063601 (2005).
[CrossRef]

Castleman, K.

Q. Wu, F. Merchant, and K. Castleman, Microscope Image Processing (Elsevier, 2010).

Chen, C.-Y.

C.-Y. Chen, R.-C. Hwang, and Y.-J. Chen, “A passive auto-focus camera control system,” Appl. Soft Comput. 10, 296–303 (2010).
[CrossRef]

Chen, Y.-J.

C.-Y. Chen, R.-C. Hwang, and Y.-J. Chen, “A passive auto-focus camera control system,” Appl. Soft Comput. 10, 296–303 (2010).
[CrossRef]

Cook, G.

M. Gamadia, V. Peddigari, N. Kehtarnavaz, S.-Y. Lee, and G. Cook, “Real-time implementation of autofocus on the TI DSC processor,” Proc. SPIE 5297, 10–18 (2004).
[CrossRef]

Corwin, A. D.

Cristobal, G.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

del Milagro Fernandez, M.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

Del Pozo, F.

A. Santos, C. Ortiz de Solorzano, J. J. Vaquero, J. Pena, N. Malpica, and F. Del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188, 264–272 (1997).
[CrossRef]

Dendere, R.

O. Osibote, R. Dendere, S. Krishnan, and T. Douglas, “Automated focusing in bright-field microscopy for tuberculosis detection,” J. Microsc. 240, 155–163 (2010).
[CrossRef]

Deniz, O.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

Dixon, E. L.

Doggaz, N.

Y. Yao, B. Abidi, N. Doggaz, and M. Abidi, “Evaluation of sharpness measures and search algorithms for the auto focusing of high-magnification images,” in Defense and Security Symposium (International Society for Optics and Photonics, 2006), p. 62460G.

Douglas, T.

O. Osibote, R. Dendere, S. Krishnan, and T. Douglas, “Automated focusing in bright-field microscopy for tuberculosis detection,” J. Microsc. 240, 155–163 (2010).
[CrossRef]

Du, X.

Dublet, J.

J. Baina and J. Dublet, “Automatic focus and iris control for video cameras,” in Fifth International Conference on Image Processing and its Applications (IET, 1995), pp. 232–235.

Duthaler, S.

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).
[CrossRef]

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing algorithm selection in computer microscopy,” in 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2005), pp. 70–76.

Escalante-Ramirez, B.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

Filkins, R. J.

Gamadia, M.

M. Gamadia, V. Peddigari, N. Kehtarnavaz, S.-Y. Lee, and G. Cook, “Real-time implementation of autofocus on the TI DSC processor,” Proc. SPIE 5297, 10–18 (2004).
[CrossRef]

Garcia-Rojo, M.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

Gough, D. A.

J. H. Price and D. A. Gough, “Comparison of phase-contrast and fluorescence digital autofocus for scanning microscopy,” Cytometry 16, 283–297 (1994).
[CrossRef]

Groen, F. C.

F. C. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
[CrossRef]

He, J.

J. He, R. Zhou, and Z. Hong, “Modified fast climbing search auto-focus algorithm with adaptive step size searching technique for digital camera,” IEEE Trans. Consum. Electron. 49, 257–262 (2003).
[CrossRef]

Hong, Z.

J. He, R. Zhou, and Z. Hong, “Modified fast climbing search auto-focus algorithm with adaptive step size searching technique for digital camera,” IEEE Trans. Consum. Electron. 49, 257–262 (2003).
[CrossRef]

Hwang, R.-C.

C.-Y. Chen, R.-C. Hwang, and Y.-J. Chen, “A passive auto-focus camera control system,” Appl. Soft Comput. 10, 296–303 (2010).
[CrossRef]

Izumi, K.

K. Ooi, K. Izumi, M. Nozaki, and I. Takeda, “An advanced autofocus system for video camera using quasi condition reasoning,” IEEE Trans. Consum. Electron. 36, 526–530 (1990).
[CrossRef]

Jarvis, R. A.

R. A. Jarvis, “Focus optimization criteria for computer image processing,” Microscope 24, 163–180 (1976).

Kehtarnavaz, N.

M. Rahman and N. Kehtarnavaz, “Real-time face-priority auto focus for digital and cell-phone cameras,” IEEE Trans. Consum. Electron. 54, 1506–1513 (2008).
[CrossRef]

M. Gamadia, V. Peddigari, N. Kehtarnavaz, S.-Y. Lee, and G. Cook, “Real-time implementation of autofocus on the TI DSC processor,” Proc. SPIE 5297, 10–18 (2004).
[CrossRef]

N. Kehtarnavaz and H. J. Oh, “Development and real-time implementation of a rule-based auto-focus algorithm,” Real-Time Imaging 9, 197–203 (2003).
[CrossRef]

Kenny, K. B.

Krishnan, S.

O. Osibote, R. Dendere, S. Krishnan, and T. Douglas, “Automated focusing in bright-field microscopy for tuberculosis detection,” J. Microsc. 240, 155–163 (2010).
[CrossRef]

Krotkov, E.

E. Krotkov, “Focusing,” Int. J. Comput. Vis. 1, 223–237 (1956).

Krotkov, E. P.

E. P. Krotkov, Active Computer Vision by Cooperative Focus and Stereo (Springer-Verlag, 1989).

Lee, S.-Y.

M. Gamadia, V. Peddigari, N. Kehtarnavaz, S.-Y. Lee, and G. Cook, “Real-time implementation of autofocus on the TI DSC processor,” Proc. SPIE 5297, 10–18 (2004).
[CrossRef]

Ligthart, G.

F. C. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
[CrossRef]

Malpica, N.

A. Santos, C. Ortiz de Solorzano, J. J. Vaquero, J. Pena, N. Malpica, and F. Del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188, 264–272 (1997).
[CrossRef]

Marks, D. L.

Merchant, F.

Q. Wu, F. Merchant, and K. Castleman, Microscope Image Processing (Elsevier, 2010).

Nava, R.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

Nelson, B. J.

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).
[CrossRef]

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing algorithm selection in computer microscopy,” in 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2005), pp. 70–76.

Neuman, C. P.

J. F. Schlag, A. C. Sanderson, C. P. Neuman, and F. C. Wimberly, Implementation of Automatic Focusing Algorithms for a Computer Vision System with Camera Control (Citeseer, 1983).

Nozaki, M.

K. Ooi, K. Izumi, M. Nozaki, and I. Takeda, “An advanced autofocus system for video camera using quasi condition reasoning,” IEEE Trans. Consum. Electron. 36, 526–530 (1990).
[CrossRef]

Oh, H. J.

N. Kehtarnavaz and H. J. Oh, “Development and real-time implementation of a rule-based auto-focus algorithm,” Real-Time Imaging 9, 197–203 (2003).
[CrossRef]

Oldenburg, A. L.

Ong, S.

T. Yeo, S. Ong, and R. Sinniah, “Autofocusing for tissue microscopy,” in Image and Vision Computing (1993), pp. 629–639.

Ooi, K.

K. Ooi, K. Izumi, M. Nozaki, and I. Takeda, “An advanced autofocus system for video camera using quasi condition reasoning,” IEEE Trans. Consum. Electron. 36, 526–530 (1990).
[CrossRef]

Ortiz de Solorzano, C.

A. Santos, C. Ortiz de Solorzano, J. J. Vaquero, J. Pena, N. Malpica, and F. Del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188, 264–272 (1997).
[CrossRef]

Osibote, O.

O. Osibote, R. Dendere, S. Krishnan, and T. Douglas, “Automated focusing in bright-field microscopy for tuberculosis detection,” J. Microsc. 240, 155–163 (2010).
[CrossRef]

Peddigari, V.

M. Gamadia, V. Peddigari, N. Kehtarnavaz, S.-Y. Lee, and G. Cook, “Real-time implementation of autofocus on the TI DSC processor,” Proc. SPIE 5297, 10–18 (2004).
[CrossRef]

Pena, J.

A. Santos, C. Ortiz de Solorzano, J. J. Vaquero, J. Pena, N. Malpica, and F. Del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188, 264–272 (1997).
[CrossRef]

Price, J. H.

J. H. Price and D. A. Gough, “Comparison of phase-contrast and fluorescence digital autofocus for scanning microscopy,” Cytometry 16, 283–297 (1994).
[CrossRef]

Rahman, M.

M. Rahman and N. Kehtarnavaz, “Real-time face-priority auto focus for digital and cell-phone cameras,” IEEE Trans. Consum. Electron. 54, 1506–1513 (2008).
[CrossRef]

Redondo, R.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

Reynolds, J. J.

Salido, J.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

Sanderson, A. C.

J. F. Schlag, A. C. Sanderson, C. P. Neuman, and F. C. Wimberly, Implementation of Automatic Focusing Algorithms for a Computer Vision System with Camera Control (Citeseer, 1983).

Santos, A.

A. Santos, C. Ortiz de Solorzano, J. J. Vaquero, J. Pena, N. Malpica, and F. Del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188, 264–272 (1997).
[CrossRef]

Schlag, J. F.

J. F. Schlag, A. C. Sanderson, C. P. Neuman, and F. C. Wimberly, Implementation of Automatic Focusing Algorithms for a Computer Vision System with Camera Control (Citeseer, 1983).

Shao, S.-J.

Shen, H.-L.

Shih, L.

L. Shih, “Autofocus survey: a comparison of algorithms,” Proc. SPIE 6502, 65020B (2007).
[CrossRef]

Sinniah, R.

T. Yeo, S. Ong, and R. Sinniah, “Autofocusing for tissue microscopy,” in Image and Vision Computing (1993), pp. 629–639.

Subbarao, M.

M. Subbarao and J.-K. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 864–870 (1998).
[CrossRef]

Sun, Y.

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).
[CrossRef]

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing algorithm selection in computer microscopy,” in 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2005), pp. 70–76.

Takeda, I.

K. Ooi, K. Izumi, M. Nozaki, and I. Takeda, “An advanced autofocus system for video camera using quasi condition reasoning,” IEEE Trans. Consum. Electron. 36, 526–530 (1990).
[CrossRef]

Tasimi, K.

Tenenbaum, J. M.

J. M. Tenenbaum, “Accommodation in computer vision,” Ph.D. thesis (Stanford University, 1970).

Tyan, J.-K.

M. Subbarao and J.-K. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 864–870 (1998).
[CrossRef]

Valdiviezo, J. C.

R. Redondo, G. Bueno, J. C. Valdiviezo, R. Nava, G. Cristobal, O. Deniz, M. Garcia-Rojo, J. Salido, M. del Milagro Fernandez, J. Vidal, and B. Escalante-Ramirez, “Autofocus evaluation for brightfield microscopy pathology,” J. Biomed. Opt. 17, 036008 (2012).
[CrossRef]

Vaquero, J. J.

A. Santos, C. Ortiz de Solorzano, J. J. Vaquero, J. Pena, N. Malpica, and F. Del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188, 264–272 (1997).
[CrossRef]

Vidal, J.

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Figures (6)

Fig. 1.
Fig. 1.

Sample images captured by the microscope system at different Z positions from the bottom up. The exposure time is 300 ms, and the bar in each image is 20 μm. As there exists depth of field in the system, (c) and (d) are two images in focus, while the other four are not.

Fig. 2.
Fig. 2.

FM curve of normalized variance, Sobel-Ten, and autocorrelation in 100 μm interval. Each curve consists of an FM value at 1001 positions along the Z axis, and the step size is 0.1 μm. The Y axis represents the normalized FM value, and the peaks’ Z position indicates the focus position. As we can see, the three FMs are all well-functioned. The peak width at half height of normalized variance among the three ones is the largest, and its monotony interval on each side of the peak is also the longest, making it more suitable for the curve-fitting strategy in our focus search APACS.

Fig. 3.
Fig. 3.

Flowcharts of GSS and APACS. (a) Flowchart of GSS. The [ak,bk] denotes the searched range after k steps. G1k and G2k denote the golden section points of the interval [ak,bk]. f(G1k) and f(G2k) represent the FM value of the two golden section points. AR denotes the accuracy requirement, and k denotes the searching steps. (b) Flowchart of APACS. The variable denoted here is same as (a) except for focus_now and focus_pre, which represent the two consecutive predictions of APACS. The parts highlighted in red are some important steps that are different from GSS.

Fig. 4.
Fig. 4.

Deviation of c¯ estimated by CE. The X axis shows the number of points of R generated by GSS, which are used for CE. And as the point quantity increases, the deviation decreases, because the points gathered during the GSS routine are actually approaching the focus position, which helps to stabilize the CE.

Fig. 5.
Fig. 5.

Deviation distribution of APACS. (a) This is the specific distribution of the deviation. The X axis represents the sample area, and the Y axis represents the mid-point position of the searched interval, while the Z axis represents the deviation. The actual focus position of each sample is near 50 μm. We can see that it is more precise when the focus position is next to the middle of the searched interval, and on the contrary when the focus position is located in either end of the interval, it is less accurate and larger focus bias and deviation occur, which, however, are still acceptable according to the set precision and depth of field. (b) This is the average distribution of the deviation, and the errorbar shows the standard deviation of the focus bias at each interval.

Fig. 6.
Fig. 6.

Average deviation distribution. When the focus position is relatively too far away from the mid-point of the interval, APACS may lead to a larger deviation compared with GSS. But the deviations are still within the depth of field.

Tables (4)

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Table 1. Computing Time for Fitting by Different Estimating Methods

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Table 2. CFS and APACS

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Table 3. GSS and APACS (Simulation)

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Table 4. GSS and APACS (On-the-Spot Survey)

Equations (13)

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

Fvar=1M*N*f(x,y)¯xy[f(x,y)f(x,y)¯]2.
F(z)=az2+bz+c,the focus position:b2a,
G(z)=a×e(zb)2c,the focus position:b,
L(z)=ab+(zc)2,the focus position:c.
Gold_ratio=512,G1=a+(1Gold_ratio)×(ba),G2=a+Gold_ratio×(ba).
R={(zi,f(zi))|All the points(i)acquired afternsteps inAPACS,1in}.
c¯=i=1n(zi×f(zi)i=1nf(zi)).
aL(z)×b=L(z)×(zc¯)2,
a=K1L(z2)K2L(z1)L(z2)L(z1),b=K1K2L(z2)L(z1),
[1L(z1)1L(z2)1L(zn)][ab]=[K1K2Kn],whereKi=L(zi)×(zic¯)2,
[ni=1nL(zi)i=1nL(zi)i=1nL(zi)2][ab]=[i=1nKii=1nKi×L(zi)],
a=M1×N22M2×N12N11×N22N21×N12,b=M1×N21M2×N11N21×N12N11×N22,
M1=i=1nKi,M2=i=1nKi×L(zi).

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