Abstract

Electronic devices endowed with camera platforms require new and powerful machine vision applications, which commonly include moving object detection strategies. To obtain high-quality results, the most recent strategies estimate nonparametrically background and foreground models and combine them by means of a Bayesian classifier. However, typical classifiers are limited by the use of constant prior values and they do not allow the inclusion of additional spatiodependent prior information. In this Letter, we propose an alternative Bayesian classifier that, unlike those reported before, allows the use of additional prior information obtained from any source and depending on the spatial position of each pixel.

© 2012 Optical Society of America

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  1. K. Sangani, Eng. Technol. 5, 28 (2010).
    [CrossRef]
  2. Y. Sheikh, O. Javed, and T. Kanade, in Proceedings of IEEE 12th International Conference on Computer Vision (IEEE, 2009), pp. 1219–1225.
  3. B. Zhang, Y. Gao, S. Zhao, and B. Zhong, IEEE Trans. Circuits Syst. Video Technol. 21, 29 (2011).
    [CrossRef]
  4. M. Cristani, M. Farenzena, D. Bloisi, and V. Murino, EURASIP J. Adv. Sig. Proc. 2010, 343057 (2010).
    [CrossRef]
  5. A. Tavakkoli, M. Nicolescu, G. Bebis, and M. Nicolescu, Machine Vis. Appl. 20, 395 (2009).
    [CrossRef]
  6. S. Y. Elhabian, K. M. El-Sayed, and S. H. Ahmed, Rec. Pat. Comput. Sci. 1, 32 (2008).
    [CrossRef]
  7. A. Elgammal, R. Duraiswami, D. Harwood, and L. S. Davis, Proc. IEEE 90, 1151 (2002).
    [CrossRef]
  8. T. Tanaka, A. Shimada, R. Taniguchi, T. Yamashita, and D. Arita, Comput. Vis. Image Underst. 113, 63 (2009).
    [CrossRef]
  9. Y. Sheikh and M. Shah, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1778 (2005).
    [CrossRef]
  10. X. Zhang and J. Yang, Electron. Lett. 44, 851 (2008).
    [CrossRef]
  11. C. Cuevas, D. Berjón, F. Morán, and N. García, IEEE Trans. Consum. Electron. 58, 117 (2012).
    [CrossRef]
  12. Q. Baig, T. D. Vu, and O. Aycard, in Proceedings of IEEE International Conference on Intelligent Computer Communication and Processing (IEEE, 2009), pp. 401–408.
  13. H. Yang, J. Tian, Y. Chu, Q. Tang, and J. Liu, IEEE Signal Process. Lett. 15, 497 (2008).
    [CrossRef]
  14. F. A. Sadjadi and C. S. L. Chun, Opt. Lett. 28. 531 (2003).
    [CrossRef]
  15. R. S. DiPietro, D. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, Proc. SPIE 7695, 1 (2010).
    [CrossRef]
  16. P. Carvalho, G. Rocha, and M. P. Hobson, Mon. Not. R. Astron. Soc. 393, 681 (2009).
    [CrossRef]
  17. W. Zhang, Q. M. J. Wu, G. H. Wang, and H. B. Yin, IEEE Trans. Multimedia 12, 300 (2010).
    [CrossRef]
  18. N. Martel-Brison and A. Zaccarin, in Proceedings of the 1st ACM Workshop on Vision Networks for Behavior Analysis (ACM, 2008), pp. 93–100.

2012

C. Cuevas, D. Berjón, F. Morán, and N. García, IEEE Trans. Consum. Electron. 58, 117 (2012).
[CrossRef]

2011

B. Zhang, Y. Gao, S. Zhao, and B. Zhong, IEEE Trans. Circuits Syst. Video Technol. 21, 29 (2011).
[CrossRef]

2010

M. Cristani, M. Farenzena, D. Bloisi, and V. Murino, EURASIP J. Adv. Sig. Proc. 2010, 343057 (2010).
[CrossRef]

K. Sangani, Eng. Technol. 5, 28 (2010).
[CrossRef]

R. S. DiPietro, D. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, Proc. SPIE 7695, 1 (2010).
[CrossRef]

W. Zhang, Q. M. J. Wu, G. H. Wang, and H. B. Yin, IEEE Trans. Multimedia 12, 300 (2010).
[CrossRef]

2009

P. Carvalho, G. Rocha, and M. P. Hobson, Mon. Not. R. Astron. Soc. 393, 681 (2009).
[CrossRef]

T. Tanaka, A. Shimada, R. Taniguchi, T. Yamashita, and D. Arita, Comput. Vis. Image Underst. 113, 63 (2009).
[CrossRef]

A. Tavakkoli, M. Nicolescu, G. Bebis, and M. Nicolescu, Machine Vis. Appl. 20, 395 (2009).
[CrossRef]

2008

S. Y. Elhabian, K. M. El-Sayed, and S. H. Ahmed, Rec. Pat. Comput. Sci. 1, 32 (2008).
[CrossRef]

X. Zhang and J. Yang, Electron. Lett. 44, 851 (2008).
[CrossRef]

H. Yang, J. Tian, Y. Chu, Q. Tang, and J. Liu, IEEE Signal Process. Lett. 15, 497 (2008).
[CrossRef]

2005

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

2003

2002

A. Elgammal, R. Duraiswami, D. Harwood, and L. S. Davis, Proc. IEEE 90, 1151 (2002).
[CrossRef]

Ahmed, S. H.

S. Y. Elhabian, K. M. El-Sayed, and S. H. Ahmed, Rec. Pat. Comput. Sci. 1, 32 (2008).
[CrossRef]

Arita, D.

T. Tanaka, A. Shimada, R. Taniguchi, T. Yamashita, and D. Arita, Comput. Vis. Image Underst. 113, 63 (2009).
[CrossRef]

Aycard, O.

Q. Baig, T. D. Vu, and O. Aycard, in Proceedings of IEEE International Conference on Intelligent Computer Communication and Processing (IEEE, 2009), pp. 401–408.

Baig, Q.

Q. Baig, T. D. Vu, and O. Aycard, in Proceedings of IEEE International Conference on Intelligent Computer Communication and Processing (IEEE, 2009), pp. 401–408.

Bebis, G.

A. Tavakkoli, M. Nicolescu, G. Bebis, and M. Nicolescu, Machine Vis. Appl. 20, 395 (2009).
[CrossRef]

Berjón, D.

C. Cuevas, D. Berjón, F. Morán, and N. García, IEEE Trans. Consum. Electron. 58, 117 (2012).
[CrossRef]

Bloisi, D.

M. Cristani, M. Farenzena, D. Bloisi, and V. Murino, EURASIP J. Adv. Sig. Proc. 2010, 343057 (2010).
[CrossRef]

Carvalho, P.

P. Carvalho, G. Rocha, and M. P. Hobson, Mon. Not. R. Astron. Soc. 393, 681 (2009).
[CrossRef]

Chu, Y.

H. Yang, J. Tian, Y. Chu, Q. Tang, and J. Liu, IEEE Signal Process. Lett. 15, 497 (2008).
[CrossRef]

Chun, C. S. L.

Cooley, T.

R. S. DiPietro, D. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, Proc. SPIE 7695, 1 (2010).
[CrossRef]

Cristani, M.

M. Cristani, M. Farenzena, D. Bloisi, and V. Murino, EURASIP J. Adv. Sig. Proc. 2010, 343057 (2010).
[CrossRef]

Cuevas, C.

C. Cuevas, D. Berjón, F. Morán, and N. García, IEEE Trans. Consum. Electron. 58, 117 (2012).
[CrossRef]

Davis, L. S.

A. Elgammal, R. Duraiswami, D. Harwood, and L. S. Davis, Proc. IEEE 90, 1151 (2002).
[CrossRef]

DiPietro, R. S.

R. S. DiPietro, D. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, Proc. SPIE 7695, 1 (2010).
[CrossRef]

Duraiswami, R.

A. Elgammal, R. Duraiswami, D. Harwood, and L. S. Davis, Proc. IEEE 90, 1151 (2002).
[CrossRef]

Elgammal, A.

A. Elgammal, R. Duraiswami, D. Harwood, and L. S. Davis, Proc. IEEE 90, 1151 (2002).
[CrossRef]

Elhabian, S. Y.

S. Y. Elhabian, K. M. El-Sayed, and S. H. Ahmed, Rec. Pat. Comput. Sci. 1, 32 (2008).
[CrossRef]

El-Sayed, K. M.

S. Y. Elhabian, K. M. El-Sayed, and S. H. Ahmed, Rec. Pat. Comput. Sci. 1, 32 (2008).
[CrossRef]

Farenzena, M.

M. Cristani, M. Farenzena, D. Bloisi, and V. Murino, EURASIP J. Adv. Sig. Proc. 2010, 343057 (2010).
[CrossRef]

Gao, Y.

B. Zhang, Y. Gao, S. Zhao, and B. Zhong, IEEE Trans. Circuits Syst. Video Technol. 21, 29 (2011).
[CrossRef]

García, N.

C. Cuevas, D. Berjón, F. Morán, and N. García, IEEE Trans. Consum. Electron. 58, 117 (2012).
[CrossRef]

Harwood, D.

A. Elgammal, R. Duraiswami, D. Harwood, and L. S. Davis, Proc. IEEE 90, 1151 (2002).
[CrossRef]

Hobson, M. P.

P. Carvalho, G. Rocha, and M. P. Hobson, Mon. Not. R. Astron. Soc. 393, 681 (2009).
[CrossRef]

Jacobson, J.

R. S. DiPietro, D. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, Proc. SPIE 7695, 1 (2010).
[CrossRef]

Javed, O.

Y. Sheikh, O. Javed, and T. Kanade, in Proceedings of IEEE 12th International Conference on Computer Vision (IEEE, 2009), pp. 1219–1225.

Kanade, T.

Y. Sheikh, O. Javed, and T. Kanade, in Proceedings of IEEE 12th International Conference on Computer Vision (IEEE, 2009), pp. 1219–1225.

Liu, J.

H. Yang, J. Tian, Y. Chu, Q. Tang, and J. Liu, IEEE Signal Process. Lett. 15, 497 (2008).
[CrossRef]

Lockwood, R.

R. S. DiPietro, D. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, Proc. SPIE 7695, 1 (2010).
[CrossRef]

Manolakis, D.

R. S. DiPietro, D. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, Proc. SPIE 7695, 1 (2010).
[CrossRef]

Martel-Brison, N.

N. Martel-Brison and A. Zaccarin, in Proceedings of the 1st ACM Workshop on Vision Networks for Behavior Analysis (ACM, 2008), pp. 93–100.

Morán, F.

C. Cuevas, D. Berjón, F. Morán, and N. García, IEEE Trans. Consum. Electron. 58, 117 (2012).
[CrossRef]

Murino, V.

M. Cristani, M. Farenzena, D. Bloisi, and V. Murino, EURASIP J. Adv. Sig. Proc. 2010, 343057 (2010).
[CrossRef]

Nicolescu, M.

A. Tavakkoli, M. Nicolescu, G. Bebis, and M. Nicolescu, Machine Vis. Appl. 20, 395 (2009).
[CrossRef]

A. Tavakkoli, M. Nicolescu, G. Bebis, and M. Nicolescu, Machine Vis. Appl. 20, 395 (2009).
[CrossRef]

Rocha, G.

P. Carvalho, G. Rocha, and M. P. Hobson, Mon. Not. R. Astron. Soc. 393, 681 (2009).
[CrossRef]

Sadjadi, F. A.

Sangani, K.

K. Sangani, Eng. Technol. 5, 28 (2010).
[CrossRef]

Shah, M.

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

Sheikh, Y.

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

Y. Sheikh, O. Javed, and T. Kanade, in Proceedings of IEEE 12th International Conference on Computer Vision (IEEE, 2009), pp. 1219–1225.

Shimada, A.

T. Tanaka, A. Shimada, R. Taniguchi, T. Yamashita, and D. Arita, Comput. Vis. Image Underst. 113, 63 (2009).
[CrossRef]

Tanaka, T.

T. Tanaka, A. Shimada, R. Taniguchi, T. Yamashita, and D. Arita, Comput. Vis. Image Underst. 113, 63 (2009).
[CrossRef]

Tang, Q.

H. Yang, J. Tian, Y. Chu, Q. Tang, and J. Liu, IEEE Signal Process. Lett. 15, 497 (2008).
[CrossRef]

Taniguchi, R.

T. Tanaka, A. Shimada, R. Taniguchi, T. Yamashita, and D. Arita, Comput. Vis. Image Underst. 113, 63 (2009).
[CrossRef]

Tavakkoli, A.

A. Tavakkoli, M. Nicolescu, G. Bebis, and M. Nicolescu, Machine Vis. Appl. 20, 395 (2009).
[CrossRef]

Tian, J.

H. Yang, J. Tian, Y. Chu, Q. Tang, and J. Liu, IEEE Signal Process. Lett. 15, 497 (2008).
[CrossRef]

Vu, T. D.

Q. Baig, T. D. Vu, and O. Aycard, in Proceedings of IEEE International Conference on Intelligent Computer Communication and Processing (IEEE, 2009), pp. 401–408.

Wang, G. H.

W. Zhang, Q. M. J. Wu, G. H. Wang, and H. B. Yin, IEEE Trans. Multimedia 12, 300 (2010).
[CrossRef]

Wu, Q. M. J.

W. Zhang, Q. M. J. Wu, G. H. Wang, and H. B. Yin, IEEE Trans. Multimedia 12, 300 (2010).
[CrossRef]

Yamashita, T.

T. Tanaka, A. Shimada, R. Taniguchi, T. Yamashita, and D. Arita, Comput. Vis. Image Underst. 113, 63 (2009).
[CrossRef]

Yang, H.

H. Yang, J. Tian, Y. Chu, Q. Tang, and J. Liu, IEEE Signal Process. Lett. 15, 497 (2008).
[CrossRef]

Yang, J.

X. Zhang and J. Yang, Electron. Lett. 44, 851 (2008).
[CrossRef]

Yin, H. B.

W. Zhang, Q. M. J. Wu, G. H. Wang, and H. B. Yin, IEEE Trans. Multimedia 12, 300 (2010).
[CrossRef]

Zaccarin, A.

N. Martel-Brison and A. Zaccarin, in Proceedings of the 1st ACM Workshop on Vision Networks for Behavior Analysis (ACM, 2008), pp. 93–100.

Zhang, B.

B. Zhang, Y. Gao, S. Zhao, and B. Zhong, IEEE Trans. Circuits Syst. Video Technol. 21, 29 (2011).
[CrossRef]

Zhang, W.

W. Zhang, Q. M. J. Wu, G. H. Wang, and H. B. Yin, IEEE Trans. Multimedia 12, 300 (2010).
[CrossRef]

Zhang, X.

X. Zhang and J. Yang, Electron. Lett. 44, 851 (2008).
[CrossRef]

Zhao, S.

B. Zhang, Y. Gao, S. Zhao, and B. Zhong, IEEE Trans. Circuits Syst. Video Technol. 21, 29 (2011).
[CrossRef]

Zhong, B.

B. Zhang, Y. Gao, S. Zhao, and B. Zhong, IEEE Trans. Circuits Syst. Video Technol. 21, 29 (2011).
[CrossRef]

Comput. Vis. Image Underst.

T. Tanaka, A. Shimada, R. Taniguchi, T. Yamashita, and D. Arita, Comput. Vis. Image Underst. 113, 63 (2009).
[CrossRef]

Electron. Lett.

X. Zhang and J. Yang, Electron. Lett. 44, 851 (2008).
[CrossRef]

Eng. Technol.

K. Sangani, Eng. Technol. 5, 28 (2010).
[CrossRef]

EURASIP J. Adv. Sig. Proc.

M. Cristani, M. Farenzena, D. Bloisi, and V. Murino, EURASIP J. Adv. Sig. Proc. 2010, 343057 (2010).
[CrossRef]

IEEE Signal Process. Lett.

H. Yang, J. Tian, Y. Chu, Q. Tang, and J. Liu, IEEE Signal Process. Lett. 15, 497 (2008).
[CrossRef]

IEEE Trans. Circuits Syst. Video Technol.

B. Zhang, Y. Gao, S. Zhao, and B. Zhong, IEEE Trans. Circuits Syst. Video Technol. 21, 29 (2011).
[CrossRef]

IEEE Trans. Consum. Electron.

C. Cuevas, D. Berjón, F. Morán, and N. García, IEEE Trans. Consum. Electron. 58, 117 (2012).
[CrossRef]

IEEE Trans. Multimedia

W. Zhang, Q. M. J. Wu, G. H. Wang, and H. B. Yin, IEEE Trans. Multimedia 12, 300 (2010).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

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

Machine Vis. Appl.

A. Tavakkoli, M. Nicolescu, G. Bebis, and M. Nicolescu, Machine Vis. Appl. 20, 395 (2009).
[CrossRef]

Mon. Not. R. Astron. Soc.

P. Carvalho, G. Rocha, and M. P. Hobson, Mon. Not. R. Astron. Soc. 393, 681 (2009).
[CrossRef]

Opt. Lett.

Proc. IEEE

A. Elgammal, R. Duraiswami, D. Harwood, and L. S. Davis, Proc. IEEE 90, 1151 (2002).
[CrossRef]

Proc. SPIE

R. S. DiPietro, D. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, Proc. SPIE 7695, 1 (2010).
[CrossRef]

Rec. Pat. Comput. Sci.

S. Y. Elhabian, K. M. El-Sayed, and S. H. Ahmed, Rec. Pat. Comput. Sci. 1, 32 (2008).
[CrossRef]

Other

Y. Sheikh, O. Javed, and T. Kanade, in Proceedings of IEEE 12th International Conference on Computer Vision (IEEE, 2009), pp. 1219–1225.

Q. Baig, T. D. Vu, and O. Aycard, in Proceedings of IEEE International Conference on Intelligent Computer Communication and Processing (IEEE, 2009), pp. 401–408.

N. Martel-Brison and A. Zaccarin, in Proceedings of the 1st ACM Workshop on Vision Networks for Behavior Analysis (ACM, 2008), pp. 93–100.

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Figures (1)

Fig. 1.
Fig. 1.

Bayesian classifier from the combination of spatioappearance background and foreground estimated models decomposed in: spatial marginal distributions, conditional appearance distributions, and prior probabilities. To facilitate the graphical representations only one appearance component and one spatial component have been considered.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

Mβ(xn)=Mβ(an,sn)=1Nβi=1Nβ|Σβ|1/2(2π)D+22exp(12(xnxβi)T(Σβ)1(xnxβi)),
Mϕ(xn)=Mϕ(an,sn)=αγ+(1α)Nϕi=1Nϕ|Σϕ|1/2(2π)D+22exp(12(xnxϕi)T(Σϕ)1(xnxϕi)),
Pr(ϕ|an,sn)=Pr(ϕ)Mϕ(an,sn)Pr(β)Mβ(an,sn)+Pr(ϕ)Mϕ(an,sn),
Pr(ϕ|an,sn)p(an|sn)=p(ϕ,an|sn)=Pr(ϕ|sn)p(an|sn,ϕ),
Pr(ϕ|an,sn)=Pr(ϕ|sn)p(an|sn,ϕ)Pr(β|sn)p(an|sn,β)+Pr(ϕ|sn)p(an|sn,ϕ),
Pr(ϕ|sn)=Pr(ϕ)p(sn|ϕ)Pr(β)p(sn|β)+Pr(ϕ)p(sn|ϕ)
p(sn|β)=Mβ(sn)=Mβ(an,sn)dan,
p(sn|ϕ)=Mϕ(sn)=Mϕ(an,sn)dan,
p(an|sn,β)=Mβ(an,sn)Mβ(sn),
p(an|sn,ϕ)=Mϕ(an,sn)Mϕ(sn),
Pr(ϕ|sn)=Pr(ϕ)Mϕ(sn)Pr(β)Mβ(sn)+Pr(ϕ)Mϕ(sn).
P˜r(ϕ|sn)Nϕ(sn)Mϕ(sn)Nβ(sn)Mβ(sn)+Nϕ(sn)Mϕ(sn),

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