Abstract

We propose a new method based on the minimization of the stochastic complexity for fast and efficient tracking adapted to video images with a static camera. The obtained criterion combines the advantages of background-subtraction-based techniques and those of using measures of similarities to a target model without requiring any tuning of a weighting parameter. It is then demonstrated that this approach can be implemented with a fast integral image technique to estimate the location and the rectangular shape of the target in a few milliseconds.

© 2008 Optical Society of America

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References

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  1. J. Rissanen, Stochastic Complexity in Statistical Inquiry, Vol. 15 of Series in Computer Science (World Scientific, 1989).
  2. P. Viola and M. Jones, in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), p. 511.
  3. C. Stauffer and W. E. L. Grimson, IEEE Trans. Pattern Anal. Mach. Intell. 22, 747 (2000).
    [CrossRef]
  4. Y. Sheikh and M. Shah, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1778 (2005).
    [CrossRef] [PubMed]
  5. L. Li, W. Huang, I. Yu-Hua Gu, and Q. Tian, IEEE Trans. Image Process. 13, 1459 (2004).
    [CrossRef]
  6. M. Isard and A. Blake, International J. Comp. Vis. 29, 5 (1998).
  7. D. Comaniciu, V. Ramesh, and P. Meer, IEEE Trans. Pattern Anal. Mach. Intell. 25, 564 (2003).
    [CrossRef]
  8. B. Zhang, W. Tian, and Z. Jin, Chin. Opt. Lett. 4, 569 (2006).
  9. R. Han, Z. Jing, and Y. Li, Chin. Opt. Lett. 6, 168 (2008).
    [CrossRef]
  10. O. Ruch and P. Réfrégier, Opt. Lett. 26, 977 (2001).
    [CrossRef]
  11. H.-L. Shen and J. H. Xin, Opt. Lett. 32, 96 (2007).
    [CrossRef]

2008 (1)

2007 (1)

2006 (1)

2005 (1)

Y. Sheikh and M. Shah, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1778 (2005).
[CrossRef] [PubMed]

2004 (1)

L. Li, W. Huang, I. Yu-Hua Gu, and Q. Tian, IEEE Trans. Image Process. 13, 1459 (2004).
[CrossRef]

2003 (1)

D. Comaniciu, V. Ramesh, and P. Meer, IEEE Trans. Pattern Anal. Mach. Intell. 25, 564 (2003).
[CrossRef]

2001 (1)

2000 (2)

P. Viola and M. Jones, in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), p. 511.

C. Stauffer and W. E. L. Grimson, IEEE Trans. Pattern Anal. Mach. Intell. 22, 747 (2000).
[CrossRef]

1998 (1)

M. Isard and A. Blake, International J. Comp. Vis. 29, 5 (1998).

1989 (1)

J. Rissanen, Stochastic Complexity in Statistical Inquiry, Vol. 15 of Series in Computer Science (World Scientific, 1989).

Blake, A.

M. Isard and A. Blake, International J. Comp. Vis. 29, 5 (1998).

Comaniciu, D.

D. Comaniciu, V. Ramesh, and P. Meer, IEEE Trans. Pattern Anal. Mach. Intell. 25, 564 (2003).
[CrossRef]

Grimson, W. E. L.

C. Stauffer and W. E. L. Grimson, IEEE Trans. Pattern Anal. Mach. Intell. 22, 747 (2000).
[CrossRef]

Han, R.

Huang, W.

L. Li, W. Huang, I. Yu-Hua Gu, and Q. Tian, IEEE Trans. Image Process. 13, 1459 (2004).
[CrossRef]

Isard, M.

M. Isard and A. Blake, International J. Comp. Vis. 29, 5 (1998).

Jin, Z.

Jing, Z.

Jones, M.

P. Viola and M. Jones, in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), p. 511.

Li, L.

L. Li, W. Huang, I. Yu-Hua Gu, and Q. Tian, IEEE Trans. Image Process. 13, 1459 (2004).
[CrossRef]

Li, Y.

Meer, P.

D. Comaniciu, V. Ramesh, and P. Meer, IEEE Trans. Pattern Anal. Mach. Intell. 25, 564 (2003).
[CrossRef]

Ramesh, V.

D. Comaniciu, V. Ramesh, and P. Meer, IEEE Trans. Pattern Anal. Mach. Intell. 25, 564 (2003).
[CrossRef]

Réfrégier, P.

Rissanen, J.

J. Rissanen, Stochastic Complexity in Statistical Inquiry, Vol. 15 of Series in Computer Science (World Scientific, 1989).

Ruch, O.

Shah, M.

Y. Sheikh and M. Shah, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1778 (2005).
[CrossRef] [PubMed]

Sheikh, Y.

Y. Sheikh and M. Shah, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1778 (2005).
[CrossRef] [PubMed]

Shen, H.-L.

Stauffer, C.

C. Stauffer and W. E. L. Grimson, IEEE Trans. Pattern Anal. Mach. Intell. 22, 747 (2000).
[CrossRef]

Tian, Q.

L. Li, W. Huang, I. Yu-Hua Gu, and Q. Tian, IEEE Trans. Image Process. 13, 1459 (2004).
[CrossRef]

Tian, W.

Viola, P.

P. Viola and M. Jones, in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), p. 511.

Xin, J. H.

Yu-Hua Gu, I.

L. Li, W. Huang, I. Yu-Hua Gu, and Q. Tian, IEEE Trans. Image Process. 13, 1459 (2004).
[CrossRef]

Zhang, B.

Chin. Opt. Lett. (2)

IEEE Trans. Image Process. (1)

L. Li, W. Huang, I. Yu-Hua Gu, and Q. Tian, IEEE Trans. Image Process. 13, 1459 (2004).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (3)

D. Comaniciu, V. Ramesh, and P. Meer, IEEE Trans. Pattern Anal. Mach. Intell. 25, 564 (2003).
[CrossRef]

C. Stauffer and W. E. L. Grimson, IEEE Trans. Pattern Anal. Mach. Intell. 22, 747 (2000).
[CrossRef]

Y. Sheikh and M. Shah, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1778 (2005).
[CrossRef] [PubMed]

Opt. Lett. (2)

Other (3)

M. Isard and A. Blake, International J. Comp. Vis. 29, 5 (1998).

J. Rissanen, Stochastic Complexity in Statistical Inquiry, Vol. 15 of Series in Computer Science (World Scientific, 1989).

P. Viola and M. Jones, in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), p. 511.

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Figures (2)

Fig. 1
Fig. 1

Snowy video sequence ( 640 × 480   pixels ) . Comparison of the results obtained with the proposed stochastic complexity criterion (row 1) and the Bhattacharryya distance (row 2), when estimating both the target size and location (continuous contours) or only its location (dashed contours). Row 3, detection map obtained with a standard background subtraction method. Results obtained on the L * component of the L * a * b * color-space (average computation time with the proposed method: 1.1 ms per frame).

Fig. 2
Fig. 2

Tracking results obtained on two outdoor video sequences ( 640 × 480   pixels ) . Row 1, results obtained on the L * component of the L * a * b * color-space ( 2.0 ms per frame). Row 2, results obtained on the a * b * chromatic components of the L * a * b * color-space ( 1.9 ms per frame).

Equations (14)

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Δ t ( Ω ) = Δ shape t + Δ Ω t + Δ Ω C t .
Δ Ω C t = ( x , y ) Ω C log P ( x , y ) B ( s t ( x , y ) ) .
Δ Ω t = ( x , y ) Ω log P A ( s t ( x , y ) ) .
Δ Ω t = N Ω 2 log 2 π + N Ω 2 log σ A 2 + 1 2 ( x , y ) Ω f A t ( x , y ) ,
Δ Ω C t = N Ω C 2 log 2 π + 1 2 ( x , y ) Ω C f B t ( x , y ) ,
f A t ( x , y ) = ( s t ( x , y ) m A ) 2 σ A 2 ,
f B t ( x , y ) = log σ B 2 ( x , y ) + ( s t ( x , y ) m B ( x , y ) ) 2 σ B 2 ( x , y ) .
K t = 1 2 ( x , y ) Image f B t ( x , y ) ,
Δ Ω C t = K t + N Ω C 2 log 2 π 1 2 ( x , y ) Ω f B t ( x , y ) ,
Δ Ω t + Δ Ω C t = K t + N 2 log 2 π + N Ω 2 log σ A 2 + 1 2 ( x , y ) Ω [ f A t ( x , y ) f B t ( x , y ) ] ,
( x , y ) Ω f t ( x , y ) = F t ( x 1 , y 1 ) + F t ( x 2 , y 2 ) F t ( x 1 , y 2 ) F t ( x 2 , y 1 ) .
Δ Ω t + Δ Ω C t = K t + N log 2 π + N Ω 2 log Γ A + 1 2 ( x , y ) Ω [ f A t ( x , y ) f B t ( x , y ) ] ,
f A t ( x , y ) = [ s t ( x , y ) m A ] [ Γ A ] 1 [ s t ( x , y ) m A ] ,
f B t ( x , y ) = log Γ B ( x , y ) + [ s t ( x , y ) m B ( x , y ) ] [ Γ B ( x , y ) ] 1 [ s t ( x , y ) m B ( x , y ) ] ,

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