Efficiency Analysis of the Autofocusing Algorithm Based on Orthogonal Transforms

Open Access JCC

6. Final Remarks

In the paper we presented three implementations of the

image variance estimate evaluation which is the core and

the most computationally demanding part of the autofo-

cusing algorithm. We provided an experimental evidence

that the implementation based on the fast Haar transform

has a much better (by a wide margin) energy efficiency

than the remaining two implementations based on the

discrete cosine and the Walsh-Hadamard transforms.

Somehow unexpectedly, the experiments revealed that

there is no advantage of using the integer number Walsh-

Hadamard transform over the cosine one. Finally, having

in mind an ASIC implementation of the algorithm, we

also proposed the word-selection algorithm which deter-

mines the required precision of the image data with re-

spect to the size of the image data and to the variance of

the noise present in the data. The actual benefit of this

algorithm needs however to be verified experimentally.

Acknowledgements

The work is supported by the NCN gran t UMO-2011/01/

B/ST7/00666.

REFERENCES

[1] F. C. A. Groen, I. T. Young and G. Ligthart, “A Compar-

ison of Different Focus Functions for Use in Autofocus

Algorithms,” Cytometry, Vol . 6, No. 2, 1985, pp. 81-91.

http://dx.doi.org/10.1002/cyto.990060202

[2] M. Subbarao and J.-K. Tyan, “Selecting the Optimal Fo-

cus Measure for Autofocusing and Depth-from-Focus,”

IEEE Transactions on Pattern Analysis and Machine In-

telligence, Vol. 20, No. 8, 1998, pp. 864-870.

http://dx.doi.org/10.1109/34.709612

[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.

http://dx.doi.org/10.1109/TIP.2012.2190612

[4] E. Krotkov, “Focusing,” International Journal of Com-

puter Vision, Vol. 1, No. 3, 1987, pp. 223-237.

http://dx.doi.org/10.1007/BF00127822

[5] P. Śliwiński, “Autofocusing 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

[6] 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

[7] S. K. Nayar and Y. Nakagawa, “Shape from Focus,”

IEEE Transactions on Pattern Analysis and Machine In-

telligence, Vol. 16, No. 8, 1994, pp. 824-831.

http://dx.doi.org/10.1109/34.308479

[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] J. W. Goodman, “Statistical Optics,” Willey-Interscience,

New York, 2000.

[10] S. J. Ray, “Applied Photographic Optics,” 3rd Edition,

Focal Pre ss , 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 Scientif-

ic Computing,” Cambridge University Press, Cambridge,

1993.

[13] D. Taubman and M. Marcellin, “JPEG2000. Image Com-

pression Fundamentals, Standards and Practice,” Kluwer

Academic Publishers, 2002, Vol. 642.

http://dx.doi.org/10.1007/978-1-4615-0799-4

[14] G. Szego, “Orthogonal Polynomials,” 3rd Edition, Amer-

ican 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.

http://dx.doi.org/10.1109/TC.1976.1674569

[17] J. Arndt, “Matters Computational: Ideas, Algorithms,

Source Code,” Springer-Verlag New York, Inc., New

York, NY, USA, 2010.

[18] P. Śliwiński and P. Wachel, “Application of Stochastic

Counterpart Optimization to Contrast-Detection Autofo-

cusing,” International Conference on Advances in Com-

puting, Communications and Informatics (ICACCI 2013),

Mysore, India, 22-25 August 2013, pp. 333-337.

http://dx.doi.org/10.1109/ICACCI.2013.6637193

[19] W. Härdle, G. Kerkyacharian, D. Picard and A. Tsybakov,

“Wavelets, Approximation, and Statistical Applications,”

Springer-Verlag, New York, 1998.

http://dx.doi.org/10.1007/978-1-4612-2222-4

[20] L. Györfi, M. Kohler, A. Krzyżak and H. Walk, “A Dis-

tribution-Free Theory of Nonparametric Regression,”

Springer-Verlag, New York, 2002.

http://dx.doi.org/10.1007/b97848

[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. http://dx.doi.org/10.1109/TCAD.2003.818119