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Efficiency Analysis of the Autofocusing Algorithm Based on Orthogonal Transforms

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DOI: 10.4236/jcc.2013.16008    1,996 Downloads   3,196 Views  


Efficiency of the autofocusing algorithm implementations based on various orthogonal transforms is examined. The algorithm uses the variance of an image acquired by a sensor as a focus function. To compute the estimate of the variance we exploit the equivalence between that estimate and the image orthogonal expansion. Energy consumption of three implementations exploiting either of the following fast orthogonal transforms: the discrete cosine, the Walsh-Hadamard, and the Haar wavelet one, is evaluated and compared. Furthermore, it is conjectured that the computation precision can considerably be reduced if the image is heavily corrupted by the noise, and a simple problem of optimal word bit-length selection with respect to the signal variance is analyzed.

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Śliwiński, P. , Berezowski, K. , Patronik, P. and Wachel, P. (2013) Efficiency Analysis of the Autofocusing Algorithm Based on Orthogonal Transforms. Journal of Computer and Communications, 1, 41-45. doi: 10.4236/jcc.2013.16008.


[1] F. C. A. Groen, I. T. Young and G. Ligthart, “A Comparison of Different Focus Functions for Use in Autofocus Algorithms,” Cytometry, Vol. 6, No. 2, 1985, pp. 81-91.
[2] 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.
[3] A. N. R. R. Hariharan, “Shape-from-Focus by Tensor Voting,” IEEE Transactions on Image Processing, Vol. 21, No. 7, 2012, pp. 3323-3328.
[4] E. Krotkov, “Focusing,” International Journal of Computer Vision, Vol. 1, No. 3, 1987, pp. 223-237.
[5] P. Sliwiński, “Autofocusing with the Help of Orthogonal Series Transforms,” International Journal of Electronics and Telecommunications, Vol. 56, No. 1, 2010, pp. 31- 37.
[6] J. Kiefer, “Sequential Minimax Search for a Maximum,” Proceedings of the American Mathematical Society, Vol. 4, No. 3, 1953, pp. 502-506.
[7] S. K. Nayar and Y. Nakagawa, “Shape from Focus,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 16, No. 8, 1994, pp. 824-831.
[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.
[9] J. W. Goodman, “Statistical Optics,” Willey-Interscience, New York, 2000.
[10] S. J. Ray, “Applied Photographic Optics,” 3rd Edition, Focal Press, Oxford, 2004.
[11] K. Beauchamp, “Applications of Walsh and Related Functions,” Academic Press, Waltham, 1984.
[12] W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, “Numerical Recipes in C: The Art of Scientific Computing,” Cambridge University Press, Cambridge, 1993.
[13] D. Taubman and M. Marcellin, “JPEG2000. Image Compression Fundamentals, Standards and Practice,” Kluwer Academic Publishers, 2002, Vol. 642.
[14] G. Szego, “Orthogonal Polynomials,” 3rd Edition, American Mathematical Society, Providence, RI, 1974.
[15] V. Mathews and G. Sicuranza, “Polynomial Signal Processing,” Wiley, New York, 2000.
[16] B. Fino and V. Algazi, “Unified Matrix Treatment of the fast Walsh-Hadamard Transform,” IEEE Transactions on Computers, Vol. 100, No. 11, 1976, pp. 1142-1146.
[17] J. Arndt, “Matters Computational: Ideas, Algorithms, Source Code,” Springer-Verlag New York, Inc., New York, NY, USA, 2010.
[18] P. Sliwiński and P. Wachel, “Application of Stochastic Counterpart Optimization to Contrast-Detection Autofocusing,” International Conference on Advances in Computing, Communications and Informatics (ICACCI 2013), Mysore, India, 22-25 August 2013, pp. 333-337.
[19] W. Härdle, G. Kerkyacharian, D. Picard and A. Tsybakov, “Wavelets, Approximation, and Statistical Applications,” Springer-Verlag, New York, 1998.
[20] L. Györfi, M. Kohler, A. Krzyzak and H. Walk, “A Distribution-Free Theory of Nonparametric Regression,” Springer-Verlag, New York, 2002.
[21] G. Constantinides, P. Cheung and W. Luk, “Wordlength Optimization for Linear Digital Signal Processing,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 22, No. 10, 2003, pp. 1432-1442.

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