Abstract

A multispectral camera acquires spectral color images with high fidelity by splitting the light spectrum into more than three bands. Because of the shift of focal length with wavelength, the focus of each channel should be mechanically adjusted in order to obtain sharp images. Because progressive adjustment is quite time consuming, the clear focus must be determined by using a limited number of images. This paper exploits the symmetry of focus measure distribution and proposes a simple yet efficient autofocus method. The focus measures are computed using first-order image derivatives, and the focus curve is obtained by spline interpolation. The optimal focus position, which maximizes the symmetry of the focus measure distribution, is then computed according to distance metrics. The effectiveness of the proposed method is validated in the multispectral camera system, and it is also applicable to relevant imaging systems.

© 2012 Optical Society of America

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    [CrossRef]

2011

J. Brauers and T. Aach, “Geometric calibration of lens and filter distortions for multispectral filter-wheel cameras,” IEEE Trans. Image Process. 20, 496–505 (2011).
[CrossRef]

2010

L. C. Chiu and C. S. Fuh, “An efficient auto focus method for digital still camera based on focus value curve prediction model,” J. Inf. Sci. Eng. 26, 1261–1272 (2010).

S. O. Shim and T. S. Choi, “A novel iterative shape from focus algorithm based on combinatorial optimization,” Patt. Recogn. 43, 3338–3347 (2010).
[CrossRef]

2008

S. Y. Lee, Y. Kumar, J. M. Cho, S. W. Lee, and S. W. Kim, “Enhanced autofocus algorithm using robust focus measure and fuzzy reasoning,” IEEE Trans. Circuits Syst. Video Technol. 18, 1237–1246 (2008).
[CrossRef]

J. Gerhardt and J. Y. Hardeberg, “Spectral color reproduction minimizing spectral and perceptual color differences,” Color Res. Appl. 33, 494–504 (2008).
[CrossRef]

2007

2006

C. M. Chen, C. M. Hong, and H. C. Chuang, “Efficient auto-focus algorithm utilizing discrete difference equation prediction model for digital still cameras,” IEEE Trans. Consum. Electron. 52, 1135–1143 (2006).
[CrossRef]

2005

K. R. Park and J. Kim, “A real-time focusing algorithm for iris recognition camera,” IEEE Trans. Syst. Man Cybern. 35, 441–444 (2005).
[CrossRef]

A. Mansouri, F. S. Marzani, J. Y. Hardeberg, and P. Gouton, “Optical calibration of a multispectral imaging system based on interference filters,” Opt. Eng. 44, 027004 (2005).
[CrossRef]

2004

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]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

2003

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]

2001

P. L. Vora, J. E. Farrell, J. D. Tietz, and D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

2000

1999

K. S. Choi, J. S. Lee, and S. J. Ko, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827(1999).
[CrossRef]

1998

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

1994

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Patt. Anal. Mach. Intell. 16, 824–831 (1994).
[CrossRef]

1991

M. Swain and D. Ballard, “Color indexing,” Int. J. Comput. Vis. 7, 11–32 (1991).
[CrossRef]

1990

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

1987

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Patt. Anal. Mach. Intell. PAMI-9, 523–531 (1987).
[CrossRef]

1951

S. Kullback and R. A. Leibler, “On information and sufficiency,” Ann. Math. Stat. 22,79–86 (1951).
[CrossRef]

Aach, T.

J. Brauers and T. Aach, “Geometric calibration of lens and filter distortions for multispectral filter-wheel cameras,” IEEE Trans. Image Process. 20, 496–505 (2011).
[CrossRef]

J. Brauers and T. Aach, “Longitudinal aberrations caused by optical filters and their compensation in multispectral imaging,” in IEEE International Conference on Image Processing (ICIP) (IEEE, 2008), pp. 525–528.

Anderson, M.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A standard default color space for the Internet: sRGB,” Version 1.10, ICC (1996).

Aslantas, A.

Ballard, D.

M. Swain and D. Ballard, “Color indexing,” Int. J. Comput. Vis. 7, 11–32 (1991).
[CrossRef]

Bishop, C. M.

C. M. Bishop, Pattern Recognition and Machine Learning (Springer, 2006).

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Brainard, D. H.

P. L. Vora, J. E. Farrell, J. D. Tietz, and D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

Brauers, J.

J. Brauers and T. Aach, “Geometric calibration of lens and filter distortions for multispectral filter-wheel cameras,” IEEE Trans. Image Process. 20, 496–505 (2011).
[CrossRef]

J. Brauers and T. Aach, “Longitudinal aberrations caused by optical filters and their compensation in multispectral imaging,” in IEEE International Conference on Image Processing (ICIP) (IEEE, 2008), pp. 525–528.

Cai, P. Q.

Chandrasekar, S.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A standard default color space for the Internet: sRGB,” Version 1.10, ICC (1996).

Chen, C. M.

C. M. Chen, C. M. Hong, and H. C. Chuang, “Efficient auto-focus algorithm utilizing discrete difference equation prediction model for digital still cameras,” IEEE Trans. Consum. Electron. 52, 1135–1143 (2006).
[CrossRef]

Chiu, L. C.

L. C. Chiu and C. S. Fuh, “An efficient auto focus method for digital still camera based on focus value curve prediction model,” J. Inf. Sci. Eng. 26, 1261–1272 (2010).

Cho, J. M.

S. Y. Lee, Y. Kumar, J. M. Cho, S. W. Lee, and S. W. Kim, “Enhanced autofocus algorithm using robust focus measure and fuzzy reasoning,” IEEE Trans. Circuits Syst. Video Technol. 18, 1237–1246 (2008).
[CrossRef]

Choi, K. S.

K. S. Choi, J. S. Lee, and S. J. Ko, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827(1999).
[CrossRef]

Choi, T. S.

S. O. Shim and T. S. Choi, “A novel iterative shape from focus algorithm based on combinatorial optimization,” Patt. Recogn. 43, 3338–3347 (2010).
[CrossRef]

Chuang, H. C.

C. M. Chen, C. M. Hong, and H. C. Chuang, “Efficient auto-focus algorithm utilizing discrete difference equation prediction model for digital still cameras,” IEEE Trans. Consum. Electron. 52, 1135–1143 (2006).
[CrossRef]

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]

Farrell, J. E.

P. L. Vora, J. E. Farrell, J. D. Tietz, and D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

Fuh, C. S.

L. C. Chiu and C. S. Fuh, “An efficient auto focus method for digital still camera based on focus value curve prediction model,” J. Inf. Sci. Eng. 26, 1261–1272 (2010).

Gerhardt, J.

J. Gerhardt and J. Y. Hardeberg, “Spectral color reproduction minimizing spectral and perceptual color differences,” Color Res. Appl. 33, 494–504 (2008).
[CrossRef]

Gouton, P.

A. Mansouri, F. S. Marzani, J. Y. Hardeberg, and P. Gouton, “Optical calibration of a multispectral imaging system based on interference filters,” Opt. Eng. 44, 027004 (2005).
[CrossRef]

Haneishi, H.

Hardeberg, J. Y.

J. Gerhardt and J. Y. Hardeberg, “Spectral color reproduction minimizing spectral and perceptual color differences,” Color Res. Appl. 33, 494–504 (2008).
[CrossRef]

A. Mansouri, F. S. Marzani, J. Y. Hardeberg, and P. Gouton, “Optical calibration of a multispectral imaging system based on interference filters,” Opt. Eng. 44, 027004 (2005).
[CrossRef]

Hasegawa, T.

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]

Hernandez-Andres, J.

Hong, C. M.

C. M. Chen, C. M. Hong, and H. C. Chuang, “Efficient auto-focus algorithm utilizing discrete difference equation prediction model for digital still cameras,” IEEE Trans. Consum. Electron. 52, 1135–1143 (2006).
[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]

Hosoi, A.

Huang, W.

W. Huang and Z. Jing, “Evaluation of focus measures in multi-focus image fusion,” Patt. Recogn. Lett. 28, 493–500 (2007).
[CrossRef]

Izumi, K.

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

Jing, Z.

W. Huang and Z. Jing, “Evaluation of focus measures in multi-focus image fusion,” Patt. Recogn. Lett. 28, 493–500 (2007).
[CrossRef]

Kim, J.

K. R. Park and J. Kim, “A real-time focusing algorithm for iris recognition camera,” IEEE Trans. Syst. Man Cybern. 35, 441–444 (2005).
[CrossRef]

Kim, S. W.

S. Y. Lee, Y. Kumar, J. M. Cho, S. W. Lee, and S. W. Kim, “Enhanced autofocus algorithm using robust focus measure and fuzzy reasoning,” IEEE Trans. Circuits Syst. Video Technol. 18, 1237–1246 (2008).
[CrossRef]

Ko, S. J.

K. S. Choi, J. S. Lee, and S. J. Ko, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827(1999).
[CrossRef]

Kullback, S.

S. Kullback and R. A. Leibler, “On information and sufficiency,” Ann. Math. Stat. 22,79–86 (1951).
[CrossRef]

Kumar, Y.

S. Y. Lee, Y. Kumar, J. M. Cho, S. W. Lee, and S. W. Kim, “Enhanced autofocus algorithm using robust focus measure and fuzzy reasoning,” IEEE Trans. Circuits Syst. Video Technol. 18, 1237–1246 (2008).
[CrossRef]

Lee, J. S.

K. S. Choi, J. S. Lee, and S. J. Ko, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827(1999).
[CrossRef]

Lee, S. W.

S. Y. Lee, Y. Kumar, J. M. Cho, S. W. Lee, and S. W. Kim, “Enhanced autofocus algorithm using robust focus measure and fuzzy reasoning,” IEEE Trans. Circuits Syst. Video Technol. 18, 1237–1246 (2008).
[CrossRef]

Lee, S. Y.

S. Y. Lee, Y. Kumar, J. M. Cho, S. W. Lee, and S. W. Kim, “Enhanced autofocus algorithm using robust focus measure and fuzzy reasoning,” IEEE Trans. Circuits Syst. Video Technol. 18, 1237–1246 (2008).
[CrossRef]

Leibler, R. A.

S. Kullback and R. A. Leibler, “On information and sufficiency,” Ann. Math. Stat. 22,79–86 (1951).
[CrossRef]

Lopez-Alvarez, M. A.

Mansouri, A.

A. Mansouri, F. S. Marzani, J. Y. Hardeberg, and P. Gouton, “Optical calibration of a multispectral imaging system based on interference filters,” Opt. Eng. 44, 027004 (2005).
[CrossRef]

Marzani, F. S.

A. Mansouri, F. S. Marzani, J. Y. Hardeberg, and P. Gouton, “Optical calibration of a multispectral imaging system based on interference filters,” Opt. Eng. 44, 027004 (2005).
[CrossRef]

Miyake, Y.

Motta, R.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A standard default color space for the Internet: sRGB,” Version 1.10, ICC (1996).

Nakagawa, Y.

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Patt. Anal. Mach. Intell. 16, 824–831 (1994).
[CrossRef]

Nayar, S. K.

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Patt. Anal. Mach. Intell. 16, 824–831 (1994).
[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]

Nozaki, M.

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

Ooi, K.

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

Park, K. R.

K. R. Park and J. Kim, “A real-time focusing algorithm for iris recognition camera,” IEEE Trans. Syst. Man Cybern. 35, 441–444 (2005).
[CrossRef]

Pentland, A. P.

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Patt. Anal. Mach. Intell. PAMI-9, 523–531 (1987).
[CrossRef]

Romero, J.

Shao, S. J.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Shen, H. L.

Shim, S. O.

S. O. Shim and T. S. Choi, “A novel iterative shape from focus algorithm based on combinatorial optimization,” Patt. Recogn. 43, 3338–3347 (2010).
[CrossRef]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Stokes, M.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A standard default color space for the Internet: sRGB,” Version 1.10, ICC (1996).

Subbarao, M.

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

M. Subbarao, “Depth recovery from blurred edges,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 1988), pp. 498–503.

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]

Swain, M.

M. Swain and D. Ballard, “Color indexing,” Int. J. Comput. Vis. 7, 11–32 (1991).
[CrossRef]

Takeda, I.

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

Tenenbaum, J. M.

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

Tietz, J. D.

P. L. Vora, J. E. Farrell, J. D. Tietz, and D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

Tsumura, N.

Tyan, J. K.

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

Volero, E. M.

Vora, P. L.

P. L. Vora, J. E. Farrell, J. D. Tietz, and D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Xin, J. H.

Yokoyama, Y.

Zhou, R.

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]

Ann. Math. Stat.

S. Kullback and R. A. Leibler, “On information and sufficiency,” Ann. Math. Stat. 22,79–86 (1951).
[CrossRef]

Appl. Opt.

Color Res. Appl.

J. Gerhardt and J. Y. Hardeberg, “Spectral color reproduction minimizing spectral and perceptual color differences,” Color Res. Appl. 33, 494–504 (2008).
[CrossRef]

IEEE Trans. Circuits Syst. Video Technol.

S. Y. Lee, Y. Kumar, J. M. Cho, S. W. Lee, and S. W. Kim, “Enhanced autofocus algorithm using robust focus measure and fuzzy reasoning,” IEEE Trans. Circuits Syst. Video Technol. 18, 1237–1246 (2008).
[CrossRef]

IEEE Trans. Consum. Electron.

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

K. S. Choi, J. S. Lee, and S. J. Ko, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827(1999).
[CrossRef]

C. M. Chen, C. M. Hong, and H. C. Chuang, “Efficient auto-focus algorithm utilizing discrete difference equation prediction model for digital still cameras,” IEEE Trans. Consum. Electron. 52, 1135–1143 (2006).
[CrossRef]

IEEE Trans. Image Process.

J. Brauers and T. Aach, “Geometric calibration of lens and filter distortions for multispectral filter-wheel cameras,” IEEE Trans. Image Process. 20, 496–505 (2011).
[CrossRef]

P. L. Vora, J. E. Farrell, J. D. Tietz, and D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

IEEE Trans. Patt. Anal. Mach. Intell.

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

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Patt. Anal. Mach. Intell. 16, 824–831 (1994).
[CrossRef]

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Patt. Anal. Mach. Intell. PAMI-9, 523–531 (1987).
[CrossRef]

IEEE Trans. Syst. Man Cybern.

K. R. Park and J. Kim, “A real-time focusing algorithm for iris recognition camera,” IEEE Trans. Syst. Man Cybern. 35, 441–444 (2005).
[CrossRef]

Int. J. Comput. Vis.

M. Swain and D. Ballard, “Color indexing,” Int. J. Comput. Vis. 7, 11–32 (1991).
[CrossRef]

J. Inf. Sci. Eng.

L. C. Chiu and C. S. Fuh, “An efficient auto focus method for digital still camera based on focus value curve prediction model,” J. Inf. Sci. Eng. 26, 1261–1272 (2010).

J. Opt. Soc. Am. A

Microsc. Res. Tech.

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]

Opt. Eng.

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Figures (7)

Fig. 1.
Fig. 1.

Typical multispectral camera that consists of a digital camera and a filter wheel. Eight narrowband filters are installed in the filter wheel. Because of the wavelength-dependent refractive indices of the lens and filters, the appropriate lens position of each channel is adjusted by using a step motor.

Fig. 2.
Fig. 2.

Geometry of image formation and image blurring caused by the movement of the camera sensor or lens.

Fig. 3.
Fig. 3.

Focal length shift of a typical apochromatic lens with respect to the wavelength in the visible spectrum. As only three wavelengths are of equal focal length, the apochromatic lens is not suitable to a multispectral camera.

Fig. 4.
Fig. 4.

Distribution of focus measure at different channels. For clarity, only four out of eight distributions are displayed.

Fig. 5.
Fig. 5.

Illustration of symmetry computation. (a) Sampled lens position and its spline- interpolated curve. Three images corresponding to three lens positions (A, B, and C) are shown for visualization. (b) Focus measure distributions, p(k) and q(k), of the interpolated focus curve with respect to the trial lens position kT in (a).

Fig. 6.
Fig. 6.

(a) Absolute lens position errors Ek and (b) relative focus measure errors EF of various distance metrics, with respect to different step intervals.

Fig. 7.
Fig. 7.

Acquired multispectral images without and with autofocus. The images are transformed to sRGB space for visualization.

Tables (4)

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Table 1. Absolute Lens Position Errors Ek of Various Channels When Using the Norm-2 Distance Metric

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Table 2. Relative Focus Measure Errors EF of Various Channels When Using the Norm-2 Distance Metric

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Table 3. Numbers of Lens Positions Required for the Coarse-to-Fine Method and the Proposed Autofocus Method

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Table 4. Image Quality in the Case without (W/O) and with Autofocus, Evaluated in Terms of the PSNR and SSIM Metrics

Equations (19)

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1f=1u+1v,
I(x,y)=Iideal(x,y)*h(x,y),
h(x,y)=12πσ2exp(x2+y22σ2).
σ=βR,
R1=R2=Dd2v.
σ=βDd2v=ηd,
h(x,y)=12πη2d2exp((x2+y2)2η2d2).
F=1Kxy|Ix(x,y)|+|Iy(x,y)|,
Sx=(101202101),Sy=(121000121),
K=xyI(x,y).
p(k)=F(kTk),
q(k)=F(kT+k),
D1(p,q)=k|p(k)q(k)|,
D2(p,q)=(k(p(k)q(k))2)1/2.
DHIST(p,q)=1kmin(p(k),q(k))kp(k).
DKL(p,q)=kp(k)logp(k)q(k).
DKL(p,q)=kp(k)logp(k)q(k)+kq(k)logq(k)p(k)=k(p(k)q(k))logp(k)q(k).
Ek=|kactualkopt|.
EF=|FactualFopt|Factual×100%.

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