JCC  Vol.1 No.6 , November 2013
A Simple Model for On-Sensor Phase-Detection Autofocusing Algorithm
Abstract

A simple model of the phase-detection autofocus device based on the partially masked sensor pixels is described. The cross-correlation function of the half-images registered by the masked pixels is proposed as a focus function. It is shown that—in such setting—focusing is equivalent to searching of the cross-correlation function maximum. Application of stochastic approximation algorithms to unimodal and non-unimodal focus functions is shortly discussed.


Cite this paper
Śliwiński, P. and Wachel, P. (2013) A Simple Model for On-Sensor Phase-Detection Autofocusing Algorithm. Journal of Computer and Communications, 1, 11-17. doi: 10.4236/jcc.2013.16003.
References

[1]   J. W. Goodman, “Statistical Optics,” Wiley-Interscience, New York, 2000.

[2]   P. Seitz and A. J. Theuwissen, “Single-Photon Imaging,” Springer, 2011. http://dx.doi.org/10.1007/978-3-642-18443-7

[3]   S. J. Ray, “Applied Photographic Optics,” 3rd Edition, Focal Press, Oxford, 2004.

[4]   J. Kiefer, “Sequential Minimax Search for a Maximum,” Proceedings of the American Mathematical Society, Vol. 4, No. 3, 1953, pp. 502-506. http://dx.doi.org/10.1090/S0002-9939-1953-0055639-3

[5]   H. J. Kushner and G. G. Yin, “Stochastic Approximation and Recursive Algorithms and Applications,” 2nd Edition, Springer, New York, 2003.

[6]   G. Lippmann, “Epreuves Reversibles Donnant la Sensation du Relief,” Journal of Theoretical and Applied Physics, Vol. 7, No. 1, 1908, pp. 821-825. http://dx.doi.org/10.1051/jphystap:019080070082100

[7]   L. Kovacs and T. Sziranyi, “Focus Area Extraction by Blind Deconvolution for Defining Regions of Interest,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 29, No. 6, 2007, pp. 1080-1085. http://dx.doi.org/10.1109/TPAMI.2007.1079

[8]   K. S. Pradeep and A. N. Rajagopalan, “Improving Shape from Focus Using Defocus Cue,” IEEE Transactions on Image Processing, Vol. 16, No. 7, 2007, pp. 1920-1925. http://dx.doi.org/10.1109/TIP.2007.899188

[9]   A. N. R. R. Hariharan, “Shape-from-Focus by Tensor Voting,” IEEE Transactions on Image Processing, Vol. 21, No. 7, 2012, pp. 3323-3328. http://dx.doi.org/10.1109/TIP.2012.2190612

[10]   M. Subbarao and J.-K. Tyan, “Selecting the Optimal Focus Measure for Autofocusing and Depth-from-Focus,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 20, No. 8, 1998, pp. 864-870. http://dx.doi.org/10.1109/34.709612

[11]   P. ?liwiński, “Auto-focusing with the Help of Orthogonal Series Transforms,” International Journal of Electronics and Telecommunications, Vol. 56, No. 1, 2010, pp. 31-37. http://dx.doi.org/10.2478/v10177-010-0004-5

[12]   A. Cohen and J.-P. D’Ales, “Nonlinear Approximation of Random Functions,” SIAM Journal of Applied Mathematics, Vol. 57, No. 2, 1997, pp. 518-540. http://dx.doi.org/10.1137/S0036139994279153

[13]   R. A. DeVore, B. Jawerth and B. Lucier, “Image Compression through Wavelet Transform Coding,” IEEE Transactions on Information Theory, Vol. 38, No. 2, 1992, pp. 719-746. http://dx.doi.org/10.1109/18.119733

[14]   A. Chambolle, R. A. DeVore, N. Y. Lee, and B. J. Lucier, “Nonlinear Wavelet Image-Processing—Variational-Problems, Compression, and Noise Removal through Wavelet Shrinkage,” IEEE Transactions on Image Processing, Vol. 7, No. 3, 1998, pp. 319-335. http://dx.doi.org/10.1109/83.661182

[15]   D. L. Donoho, M. Vetterli, R. A. DeVore and I. Daubechies, “Data Compression and Harmonic Analysis,” IEEE Transactions on Information Theory, Vol. 44, No. 6, 1998, pp. 2435-2476. http://dx.doi.org/10.1109/18.720544

[16]   R. M. Gray and L. D. Davisson, “An Introduction to Statistical Signal Processing,” Cambridge University Press, New York, 2011.

[17]   S. Yakowitz, P. L’ecuyer and F. Vázquez-Abad, “Global Stochastic Optimization with Low-Dispersion Point Sets,” Operations Research, Vol. 48, No. 6, 2000, pp. 939-950. http://dx.doi.org/10.1287/opre.48.6.939.12393

[18]   W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, “Numerical Recipes in C++: The Art of Scientific Computing,” Cambridge University Press, Cambridge, 2009.

[19]   J. Kiefer and J. Wolfowitz, “Stochastic Estimation of the Maximum of a Regression Function,” The Annals of Mathematical Statistics, Vol. 23, No. 3, 1952, pp. 462-466. http://dx.doi.org/10.1214/aoms/1177729392

[20]   C. Horn and S. Kulkarni, “Convergence of the Kiefer- Wolfowitz Algorithm under Arbitrary Disturbances,” American Control Conference, Vol. 3, 1994, pp. 2673-2674.

[21]   T. L. Lai, “Stochastic Ap-proximation: Invited Paper,” The Annals of Statistics, Vol. 31, No. 2, 2003, pp. 391-406. http://dx.doi.org/10.1214/aos/1051027873

[22]   R. Rubinstein, “Smoothed Functionals in Stochastic Optimization,” Mathematics of Operations Research, Vol. 8, No. 1, 1983, pp. 26-33. http://dx.doi.org/10.1287/moor.8.1.26

[23]   J. Kreimer and R. Y. Rubinstein, “Nondifferentiable Optimization via Smooth Approximation: General Analytical Approach,” Annals of Operations Research, Vol. 39, No. 1, 1992, pp. 97-119. http://dx.doi.org/10.1007/BF02060937

[24]   D. Q. Mayne and E. Polak, “Nondifferential Optimization via Adaptive Smoothing,” Journal of Optimization Theory and Applications, Vol. 43, No. 4, 1984, pp. 601-613. http://dx.doi.org/10.1007/BF00935008

[25]   B. T. Polyak and A. B. Juditsky, “Acceleration of Stochastic Approximation by Averaging,” SIAM Journal on Control and Optimization, Vol. 30, No. 4, 1992, pp. 838-855. http://dx.doi.org/10.1137/0330046

[26]   E. Krotkov, “Focusing,” International Journal of Computer Vision, Vol. 1, No. 3, 1987, pp. 223-237. http://dx.doi.org/10.1007/BF00127822

[27]   L. P. Devroye, “Progressive Global Random Search of Continuous Functions,” Mathematical Programming, Vol. 15, No. 1, 1978, pp. 330-342. http://dx.doi.org/10.1007/BF01609037

[28]   S. Yakowitz, “A Globally Convergent Stochastic Approximation,” SIAM Journal on Control and Optimization, Vol. 31, No. 1, 1993, pp. 30-40. http://dx.doi.org/10.1137/0331003

[29]   L. Devroye and A. Krzyzak, “Random Search under Additive Noise,” In: M. Dror, P. L’Ecuyer and F. Szidarovszky, Eds., Modeling Uncertainty, Springer, 2005, pp. 383-417.

[30]   I.-J. Wang, E. K. Chong and S. R. Kulkarni, “Equivalent Necessary and Sufficient Conditions on Noise Sequences for Stochastic Approximation Algorithms,” Advances in Applied Probability, Vol. 28, No. 3, 1996, pp. 784-801. http://dx.doi.org/10.2307/1428181

 
 
Top