Abstract

Focus measure plays a fundamental role in the shape from focus technique. In this Letter, we suggest a focus measure in the S-transform domain that is based on the energy of high-frequency components. A localized spectrum by using variable window size provides a more accurate method of measuring image sharpness as compared to other focus measures proposed in spectral domains. An optimal focus measure is obtained by selecting an appropriate frequency-dependent window width. The performance of the proposed focus measure is compared with those of existing focus measures in terms of three-dimensional shape recovery. Experimental results demonstrate the effectiveness of the proposed focus measure.

© 2010 Optical Society of America

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References

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  1. A. N. Simonov and M. C. Rombach, Opt. Lett.  34, 2111 (2009).
    [CrossRef] [PubMed]
  2. M. B. Ahmad and T. S. Choi, IEEE Trans. Circuits Syst. Video Technol.  15, 566 (2005).
    [CrossRef]
  3. A. S. Malik and T. S. Choi, Pattern Recogn.  40, 154 (2007).
    [CrossRef]
  4. S. K. Nayar and Y. Nakagawa, IEEE Trans. Pattern Anal. Mach. Intell.  16, 824 (1994).
    [CrossRef]
  5. M. T. Mahmood, S. O. Shim, and T. S. Choi, Opt. Eng.  48, 057203 (2009).
    [CrossRef]
  6. L. Sang-Yong, Y. Kumar, C. Ji-Man, L. Sang-Won, and K. Soo-Won, IEEE Trans. Circuits Syst. Video Technol.  18, 1237 (2008).
    [CrossRef]
  7. R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process.  44, 998 (1996).
    [CrossRef]
  8. R. A. Brown, M. L. Lauzon, and R. Frayne, IEEE Trans. Signal Process.  58, 281 (2010).
    [CrossRef]
  9. E. Sejdic, I. Djurovic, and J. Jiang, EURASIP J. Adv. Signal Process.  672941, 13 (2008).

2010 (1)

R. A. Brown, M. L. Lauzon, and R. Frayne, IEEE Trans. Signal Process.  58, 281 (2010).
[CrossRef]

2009 (2)

M. T. Mahmood, S. O. Shim, and T. S. Choi, Opt. Eng.  48, 057203 (2009).
[CrossRef]

A. N. Simonov and M. C. Rombach, Opt. Lett.  34, 2111 (2009).
[CrossRef] [PubMed]

2008 (2)

L. Sang-Yong, Y. Kumar, C. Ji-Man, L. Sang-Won, and K. Soo-Won, IEEE Trans. Circuits Syst. Video Technol.  18, 1237 (2008).
[CrossRef]

E. Sejdic, I. Djurovic, and J. Jiang, EURASIP J. Adv. Signal Process.  672941, 13 (2008).

2007 (1)

A. S. Malik and T. S. Choi, Pattern Recogn.  40, 154 (2007).
[CrossRef]

2005 (1)

M. B. Ahmad and T. S. Choi, IEEE Trans. Circuits Syst. Video Technol.  15, 566 (2005).
[CrossRef]

1996 (1)

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process.  44, 998 (1996).
[CrossRef]

1994 (1)

S. K. Nayar and Y. Nakagawa, IEEE Trans. Pattern Anal. Mach. Intell.  16, 824 (1994).
[CrossRef]

Ahmad, M. B.

M. B. Ahmad and T. S. Choi, IEEE Trans. Circuits Syst. Video Technol.  15, 566 (2005).
[CrossRef]

Brown, R. A.

R. A. Brown, M. L. Lauzon, and R. Frayne, IEEE Trans. Signal Process.  58, 281 (2010).
[CrossRef]

Choi, T. S.

M. T. Mahmood, S. O. Shim, and T. S. Choi, Opt. Eng.  48, 057203 (2009).
[CrossRef]

A. S. Malik and T. S. Choi, Pattern Recogn.  40, 154 (2007).
[CrossRef]

M. B. Ahmad and T. S. Choi, IEEE Trans. Circuits Syst. Video Technol.  15, 566 (2005).
[CrossRef]

Djurovic, I.

E. Sejdic, I. Djurovic, and J. Jiang, EURASIP J. Adv. Signal Process.  672941, 13 (2008).

Frayne, R.

R. A. Brown, M. L. Lauzon, and R. Frayne, IEEE Trans. Signal Process.  58, 281 (2010).
[CrossRef]

Jiang, J.

E. Sejdic, I. Djurovic, and J. Jiang, EURASIP J. Adv. Signal Process.  672941, 13 (2008).

Ji-Man, C.

L. Sang-Yong, Y. Kumar, C. Ji-Man, L. Sang-Won, and K. Soo-Won, IEEE Trans. Circuits Syst. Video Technol.  18, 1237 (2008).
[CrossRef]

Kumar, Y.

L. Sang-Yong, Y. Kumar, C. Ji-Man, L. Sang-Won, and K. Soo-Won, IEEE Trans. Circuits Syst. Video Technol.  18, 1237 (2008).
[CrossRef]

Lauzon, M. L.

R. A. Brown, M. L. Lauzon, and R. Frayne, IEEE Trans. Signal Process.  58, 281 (2010).
[CrossRef]

Lowe, R. P.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process.  44, 998 (1996).
[CrossRef]

Mahmood, M. T.

M. T. Mahmood, S. O. Shim, and T. S. Choi, Opt. Eng.  48, 057203 (2009).
[CrossRef]

Malik, A. S.

A. S. Malik and T. S. Choi, Pattern Recogn.  40, 154 (2007).
[CrossRef]

Mansinha, L.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process.  44, 998 (1996).
[CrossRef]

Nakagawa, Y.

S. K. Nayar and Y. Nakagawa, IEEE Trans. Pattern Anal. Mach. Intell.  16, 824 (1994).
[CrossRef]

Nayar, S. K.

S. K. Nayar and Y. Nakagawa, IEEE Trans. Pattern Anal. Mach. Intell.  16, 824 (1994).
[CrossRef]

Rombach, M. C.

Sang-Won, L.

L. Sang-Yong, Y. Kumar, C. Ji-Man, L. Sang-Won, and K. Soo-Won, IEEE Trans. Circuits Syst. Video Technol.  18, 1237 (2008).
[CrossRef]

Sang-Yong, L.

L. Sang-Yong, Y. Kumar, C. Ji-Man, L. Sang-Won, and K. Soo-Won, IEEE Trans. Circuits Syst. Video Technol.  18, 1237 (2008).
[CrossRef]

Sejdic, E.

E. Sejdic, I. Djurovic, and J. Jiang, EURASIP J. Adv. Signal Process.  672941, 13 (2008).

Shim, S. O.

M. T. Mahmood, S. O. Shim, and T. S. Choi, Opt. Eng.  48, 057203 (2009).
[CrossRef]

Simonov, A. N.

Soo-Won, K.

L. Sang-Yong, Y. Kumar, C. Ji-Man, L. Sang-Won, and K. Soo-Won, IEEE Trans. Circuits Syst. Video Technol.  18, 1237 (2008).
[CrossRef]

Stockwell, R. G.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process.  44, 998 (1996).
[CrossRef]

EURASIP J. Adv. Signal Process. (1)

E. Sejdic, I. Djurovic, and J. Jiang, EURASIP J. Adv. Signal Process.  672941, 13 (2008).

IEEE Trans. Circuits Syst. Video Technol. (2)

L. Sang-Yong, Y. Kumar, C. Ji-Man, L. Sang-Won, and K. Soo-Won, IEEE Trans. Circuits Syst. Video Technol.  18, 1237 (2008).
[CrossRef]

M. B. Ahmad and T. S. Choi, IEEE Trans. Circuits Syst. Video Technol.  15, 566 (2005).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. K. Nayar and Y. Nakagawa, IEEE Trans. Pattern Anal. Mach. Intell.  16, 824 (1994).
[CrossRef]

IEEE Trans. Signal Process. (2)

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process.  44, 998 (1996).
[CrossRef]

R. A. Brown, M. L. Lauzon, and R. Frayne, IEEE Trans. Signal Process.  58, 281 (2010).
[CrossRef]

Opt. Eng. (1)

M. T. Mahmood, S. O. Shim, and T. S. Choi, Opt. Eng.  48, 057203 (2009).
[CrossRef]

Opt. Lett. (1)

Pattern Recogn. (1)

A. S. Malik and T. S. Choi, Pattern Recogn.  40, 154 (2007).
[CrossRef]

Cited By

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Figures (2)

Fig. 1
Fig. 1

First row, sample frame extracted from each image sequence: (a) real cone, (b) coin, and (c) letter I. Second row: (d)–(f) all-in-focus images obtained through the proposed focus measure F ST .

Fig. 2
Fig. 2

Reconstructed 3D shapes of test objects (left-most column) real cone, (central column) coin, and (right-most column) letter I using (first row) F SML , (second row) F TEN , (third row) F GLV , (fourth row) F DWT , and (fifth row) F ST .

Tables (1)

Tables Icon

Table 1 Performance Comparison in Terms of RMSE

Equations (14)

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H ( ω ) = + h ( t ) g ( t ) e i 2 π ω t d t ,
χ ( τ , ω ) = | ω | 2 π + h ( t ) exp [ ( t τ ) 2 ω 2 2 ] e i 2 π ω t d t .
σ ( ω ) = α | ω | β ,     α , β > 0.
χ ( τ , ω ) = | ω | β α 2 π + h ( t ) exp [ ( t τ ) 2 ( | ω | β ) 2 2 α 2 ] e i 2 π ω t d t .
χ ( p T , n N T ) = n = 0 N 1 H ( n + n N T ) exp ( 2 π 2 n 2 n 2 ) exp ( i 2 π n p N ) ,
χ ( p T x , q T y , n N T x , m M T y ) = n = 0 N 1 m = 0 M 1 H ( n + n N T x , m + m M T y )
× exp ( 2 π 2 n 2 n 2 ) exp ( i 2 π n p N )
× exp ( 2 π 2 m 2 m 2 ) exp ( i 2 π m q M ) ,
F ST = p = 0 N 1 q = 0 M 1 n = 0 N 1 m = 0 M 1 χ ( p T x , q T y , n N T x , m M T y ) 2 ,
( n , m ) ( 0 , 0 ) .
I z ( x , y ) = F ST ( I z ( x , y ) ) ,     z = 1 , 2 , , Z .
I z ( x , y ) = x = x W x = x + W x = y W y = y + W z = z W z = z + W I z ( x , y ) .
D ( x , y ) = arg   max z ( I z ( x , y ) ) ,     z = 1 , 2 , , Z .
I aif ( x , y ) = I D ( x , y ) .

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