Abstract

Traditional unsupervised change detection methods need to generate a difference image (DI) for subsequent processing to produce a binary change map. In addition, few methods explore global structures. This Letter presents a novel unsupervised change detection approach based on low rank matrix completion. Other than generating a DI, the changed pixels are modeled as the estimated missing values for matrix completion, where the changed pixels are represented by a sparse term. A common low rank matrix is recovered by two temporal images. The changed pixels are separated out from the low rank matrix, in which the local information is introduced via graph cuts. The global and local structures are utilized in our model. Experimental results validate the effectiveness of the proposed approach. The proposed method is a new view for change detection.

© 2013 Optical Society of America

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  1. Z. Yetgin, IEEE Trans. Geosci. Remote Sens. 50, 1919 (2012).
    [CrossRef]
  2. M. Gong, Z. Zhou, and J. Ma, IEEE Trans. Image Process. 21, 2141 (2012).
    [CrossRef]
  3. T. Celik, IEEE Trans. Geosci. Remote Sens. 6, 772 (2009).
    [CrossRef]
  4. S. Patra, S. Ghosh, and A. Ghosh, Int. J. Remote Sens. 32, 6071 (2011).
    [CrossRef]
  5. N. S. Mishra, S. Ghosh, and A. Ghosh, Appl. Soft Comput. 12, 2683 (2012).
    [CrossRef]
  6. E. J. Candès and B. Recht, Found. Comput. Math. 9, 717 (2009).
    [CrossRef]
  7. J. Liu, P. Musialski, P. Wonka, and J. Ye, IEEE Trans. Pattern Anal. Mach. Intell. 35, 208 (2013).
    [CrossRef]
  8. L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang, and Y. Ma, in Proceedings of Asian Conference on Computer Vision (2011), p. 703.
  9. V. Kolmogorov and R. Zabin, IEEE Trans. Pattern Anal. Mach. Intell. 26, 147 (2004).
    [CrossRef]
  10. Z. Lin, M. Chen, and Y. Ma, “The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices,” arXiv:10095055 (2010).
  11. G. Ye, D. Liu, I.-H. Jhuo, and S.-F. Chang, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2012), p. 3021.
  12. K.-C. Toh and S. Yun, Pacific J. Optim. 6, 615 (2010).
  13. E. J. Candès, X. Li, Y. Ma, and J. Wright, J. ACM 58, 1 (2011).
    [CrossRef]

2013 (1)

J. Liu, P. Musialski, P. Wonka, and J. Ye, IEEE Trans. Pattern Anal. Mach. Intell. 35, 208 (2013).
[CrossRef]

2012 (3)

Z. Yetgin, IEEE Trans. Geosci. Remote Sens. 50, 1919 (2012).
[CrossRef]

M. Gong, Z. Zhou, and J. Ma, IEEE Trans. Image Process. 21, 2141 (2012).
[CrossRef]

N. S. Mishra, S. Ghosh, and A. Ghosh, Appl. Soft Comput. 12, 2683 (2012).
[CrossRef]

2011 (2)

S. Patra, S. Ghosh, and A. Ghosh, Int. J. Remote Sens. 32, 6071 (2011).
[CrossRef]

E. J. Candès, X. Li, Y. Ma, and J. Wright, J. ACM 58, 1 (2011).
[CrossRef]

2010 (1)

K.-C. Toh and S. Yun, Pacific J. Optim. 6, 615 (2010).

2009 (2)

E. J. Candès and B. Recht, Found. Comput. Math. 9, 717 (2009).
[CrossRef]

T. Celik, IEEE Trans. Geosci. Remote Sens. 6, 772 (2009).
[CrossRef]

2004 (1)

V. Kolmogorov and R. Zabin, IEEE Trans. Pattern Anal. Mach. Intell. 26, 147 (2004).
[CrossRef]

Candès, E. J.

E. J. Candès, X. Li, Y. Ma, and J. Wright, J. ACM 58, 1 (2011).
[CrossRef]

E. J. Candès and B. Recht, Found. Comput. Math. 9, 717 (2009).
[CrossRef]

Celik, T.

T. Celik, IEEE Trans. Geosci. Remote Sens. 6, 772 (2009).
[CrossRef]

Chang, S.-F.

G. Ye, D. Liu, I.-H. Jhuo, and S.-F. Chang, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2012), p. 3021.

Chen, M.

Z. Lin, M. Chen, and Y. Ma, “The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices,” arXiv:10095055 (2010).

Ganesh, A.

L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang, and Y. Ma, in Proceedings of Asian Conference on Computer Vision (2011), p. 703.

Ghosh, A.

N. S. Mishra, S. Ghosh, and A. Ghosh, Appl. Soft Comput. 12, 2683 (2012).
[CrossRef]

S. Patra, S. Ghosh, and A. Ghosh, Int. J. Remote Sens. 32, 6071 (2011).
[CrossRef]

Ghosh, S.

N. S. Mishra, S. Ghosh, and A. Ghosh, Appl. Soft Comput. 12, 2683 (2012).
[CrossRef]

S. Patra, S. Ghosh, and A. Ghosh, Int. J. Remote Sens. 32, 6071 (2011).
[CrossRef]

Gong, M.

M. Gong, Z. Zhou, and J. Ma, IEEE Trans. Image Process. 21, 2141 (2012).
[CrossRef]

Jhuo, I.-H.

G. Ye, D. Liu, I.-H. Jhuo, and S.-F. Chang, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2012), p. 3021.

Kolmogorov, V.

V. Kolmogorov and R. Zabin, IEEE Trans. Pattern Anal. Mach. Intell. 26, 147 (2004).
[CrossRef]

Li, X.

E. J. Candès, X. Li, Y. Ma, and J. Wright, J. ACM 58, 1 (2011).
[CrossRef]

Lin, Z.

Z. Lin, M. Chen, and Y. Ma, “The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices,” arXiv:10095055 (2010).

Liu, D.

G. Ye, D. Liu, I.-H. Jhuo, and S.-F. Chang, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2012), p. 3021.

Liu, J.

J. Liu, P. Musialski, P. Wonka, and J. Ye, IEEE Trans. Pattern Anal. Mach. Intell. 35, 208 (2013).
[CrossRef]

Ma, J.

M. Gong, Z. Zhou, and J. Ma, IEEE Trans. Image Process. 21, 2141 (2012).
[CrossRef]

Ma, Y.

E. J. Candès, X. Li, Y. Ma, and J. Wright, J. ACM 58, 1 (2011).
[CrossRef]

L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang, and Y. Ma, in Proceedings of Asian Conference on Computer Vision (2011), p. 703.

Z. Lin, M. Chen, and Y. Ma, “The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices,” arXiv:10095055 (2010).

Matsushita, Y.

L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang, and Y. Ma, in Proceedings of Asian Conference on Computer Vision (2011), p. 703.

Mishra, N. S.

N. S. Mishra, S. Ghosh, and A. Ghosh, Appl. Soft Comput. 12, 2683 (2012).
[CrossRef]

Musialski, P.

J. Liu, P. Musialski, P. Wonka, and J. Ye, IEEE Trans. Pattern Anal. Mach. Intell. 35, 208 (2013).
[CrossRef]

Patra, S.

S. Patra, S. Ghosh, and A. Ghosh, Int. J. Remote Sens. 32, 6071 (2011).
[CrossRef]

Recht, B.

E. J. Candès and B. Recht, Found. Comput. Math. 9, 717 (2009).
[CrossRef]

Shi, B.

L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang, and Y. Ma, in Proceedings of Asian Conference on Computer Vision (2011), p. 703.

Toh, K.-C.

K.-C. Toh and S. Yun, Pacific J. Optim. 6, 615 (2010).

Wang, Y.

L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang, and Y. Ma, in Proceedings of Asian Conference on Computer Vision (2011), p. 703.

Wonka, P.

J. Liu, P. Musialski, P. Wonka, and J. Ye, IEEE Trans. Pattern Anal. Mach. Intell. 35, 208 (2013).
[CrossRef]

Wright, J.

E. J. Candès, X. Li, Y. Ma, and J. Wright, J. ACM 58, 1 (2011).
[CrossRef]

Wu, L.

L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang, and Y. Ma, in Proceedings of Asian Conference on Computer Vision (2011), p. 703.

Ye, G.

G. Ye, D. Liu, I.-H. Jhuo, and S.-F. Chang, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2012), p. 3021.

Ye, J.

J. Liu, P. Musialski, P. Wonka, and J. Ye, IEEE Trans. Pattern Anal. Mach. Intell. 35, 208 (2013).
[CrossRef]

Yetgin, Z.

Z. Yetgin, IEEE Trans. Geosci. Remote Sens. 50, 1919 (2012).
[CrossRef]

Yun, S.

K.-C. Toh and S. Yun, Pacific J. Optim. 6, 615 (2010).

Zabin, R.

V. Kolmogorov and R. Zabin, IEEE Trans. Pattern Anal. Mach. Intell. 26, 147 (2004).
[CrossRef]

Zhou, Z.

M. Gong, Z. Zhou, and J. Ma, IEEE Trans. Image Process. 21, 2141 (2012).
[CrossRef]

Appl. Soft Comput. (1)

N. S. Mishra, S. Ghosh, and A. Ghosh, Appl. Soft Comput. 12, 2683 (2012).
[CrossRef]

Found. Comput. Math. (1)

E. J. Candès and B. Recht, Found. Comput. Math. 9, 717 (2009).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

Z. Yetgin, IEEE Trans. Geosci. Remote Sens. 50, 1919 (2012).
[CrossRef]

T. Celik, IEEE Trans. Geosci. Remote Sens. 6, 772 (2009).
[CrossRef]

IEEE Trans. Image Process. (1)

M. Gong, Z. Zhou, and J. Ma, IEEE Trans. Image Process. 21, 2141 (2012).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

J. Liu, P. Musialski, P. Wonka, and J. Ye, IEEE Trans. Pattern Anal. Mach. Intell. 35, 208 (2013).
[CrossRef]

V. Kolmogorov and R. Zabin, IEEE Trans. Pattern Anal. Mach. Intell. 26, 147 (2004).
[CrossRef]

Int. J. Remote Sens. (1)

S. Patra, S. Ghosh, and A. Ghosh, Int. J. Remote Sens. 32, 6071 (2011).
[CrossRef]

J. ACM (1)

E. J. Candès, X. Li, Y. Ma, and J. Wright, J. ACM 58, 1 (2011).
[CrossRef]

Pacific J. Optim. (1)

K.-C. Toh and S. Yun, Pacific J. Optim. 6, 615 (2010).

Other (3)

Z. Lin, M. Chen, and Y. Ma, “The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices,” arXiv:10095055 (2010).

G. Ye, D. Liu, I.-H. Jhuo, and S.-F. Chang, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2012), p. 3021.

L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang, and Y. Ma, in Proceedings of Asian Conference on Computer Vision (2011), p. 703.

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Figures (5)

Fig. 1.
Fig. 1.

Landsat-5 TM band 1 optical images. (a) Image acquired on July 22, 1985. (b) Image acquired on July 13, 2005. (c) Ground truth.

Fig. 2.
Fig. 2.

ESA/Envisat ASAR images. (a) Image acquired on April 12, 2007. (b) Image acquired on July 26, 2007. (c) Ground truth.

Fig. 3.
Fig. 3.

Total error ratio with δ and ε. (a) First dataset. (b) Second dataset.

Fig. 4.
Fig. 4.

Change detection results on the first dataset. (a) FCM. (b) RFLICM. (c) PCA-based method. (d) Common low rank matrix. (e) S1S2. (f) Our method.

Fig. 5.
Fig. 5.

Change detection results on the second dataset. (a) FCM. (b) RFLICM. (c) PCA-based method. (d) Common low rank matrix. (e) S1S2. (f) Our method.

Tables (3)

Tables Icon

Algorithm 1. Optimization Problem of Eq. (6)

Tables Icon

Table 1. Change Detection Performance Results on the First Dataset

Tables Icon

Table 2. Change Detection Performance Results on Second Dataset

Equations (14)

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

argminRr(R),s.t.Rmn=Xmn,(m,n)Ω,
argminRR*,s.t.WΩ(R)=WΩ(X).
argminRR*,s.t.WΩ(R)=WΩ(Xk),k=1,2,
argminR,P{0,1}R*+λP0,s.t.PcR=PcXk,k=1,2,
argminR,P{0,1},SR*+λP0+γk=12SkF2s.t.PcXk=Pc(R+Sk),
argminR,P{0,1},,SR*+λP1+γk=12SkF2+μG(P)s.t.PcXk=Pc(R+Sk),k=1,2,
L(R,P,S,Y)=R*+λP1+γk=12SkF2+μG(P)+α2k=12PcΔkF2+k=12Yk,PcΔk,
{(R,P,S)=argminR,P,SL(R,P,S,Y)Yk=Yk+αPc(XkRSk)α=θα,
argminRR*+k=12Yk,PcR+α2k=12PcΔkF2=argminR12αR*+12R(PR+12k=12Ek)F2,
{(Uh,Σh,Vh)=svd(12k=12Ek+PZh)Rh+1=Uh(Σh)1/(2α)VhTth+1=0.5(1+1+4th2)Zh+1=Rh+1+th1th+1(Rh+1Rh),
argminSkγSkF2+α2PcΔkF2+Yk,PcSk=argminSkγPSkF2+(γ+α2)PcSkJk1+2γ/αF2,
{(Sk)Pc=Pc(XkR+α1Yk)1+2γ/α(Sk)P=0.
argminP{0,1}λP1+μG(P)+k=12Yk,PcΔk+α2k=12PcΔkF2=argminP{0,1}λP1+μG(P)+α2k=12PcΔk+α1YkF2.
argminl{0,1}mnU(Pmn=l)+μG(P).

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