Abstract

We present an effective method for defocus map estimation from a single natural image. It is inspired by the observation that defocusing can significantly affect the spectrum amplitude at the object edge locations in an image. By establishing the relationship between the amount of spatially varying defocus blur and spectrum contrast at edge locations, we first estimate the blur amount at these edge locations, then a full defocus map can be obtained by propagating the blur amount at edge locations over the entire image with a nonhomogeneous optimization procedure. The proposed method takes into consideration not only the affect of light refraction but also the blur texture of an image. Experimental results demonstrate that our proposed method is more reliable in defocus map estimation compared to various state-of-the-art methods.

© 2013 Optical Society of America

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2011

2009

2008

M. Burger, P. Favaro, S. Soatto, and S. J. Osher, IEEE Trans. Pattern Anal. Mach. Intell. 30, 518 (2008).
[CrossRef]

D. Lischinski, A. Levin, and Y. Weiss, IEEE Trans. Pattern Anal. Mach. Intell. 30, 228 (2008).
[CrossRef]

2007

S. Bae and F. Durand, Comput. Graph. Forum 26, 571 (2007).

2005

P. Favaro and S. Soatto, IEEE Trans. Pattern Anal. Mach. Intell. 27, 406 (2005).
[CrossRef]

2004

E. Eisemann and F. Durand, ACM Trans. Graph. 23, 673 (2004).
[CrossRef]

D. Lischinski, A. Levin, and Y. Weiss, ACM Trans. Graph. 23, 689 (2004).
[CrossRef]

1998

J. H. Elder and S. W. Zucker, IEEE Trans. Pattern Anal. Mach. Intell. 20, 699 (1998).
[CrossRef]

1986

J. Canny, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 679 (1986).
[CrossRef]

Bae, S.

S. Bae and F. Durand, Comput. Graph. Forum 26, 571 (2007).

Birch, P.

Brown, M. S.

Y.-W. Tai and M. S. Brown, in Proceedings of the IEEE International Conference on Image Processing (ICIP) (IEEE, 2009), pp. 1797–1800.

Buchanan, A.

Burger, M.

M. Burger, P. Favaro, S. Soatto, and S. J. Osher, IEEE Trans. Pattern Anal. Mach. Intell. 30, 518 (2008).
[CrossRef]

Canny, J.

J. Canny, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 679 (1986).
[CrossRef]

Changyin, Z.

O. Cossairt, Z. Changyin, and S. Nayar, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2010), pp. 1110–1117.

Chatwin, C.

Chaudhuri, S.

V. P. Namboodiri and S. Chaudhuri, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2008), pp. 1–6.

Cossairt, O.

O. Cossairt, Z. Changyin, and S. Nayar, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2010), pp. 1110–1117.

Durand, F.

S. Bae and F. Durand, Comput. Graph. Forum 26, 571 (2007).

E. Eisemann and F. Durand, ACM Trans. Graph. 23, 673 (2004).
[CrossRef]

Eisemann, E.

E. Eisemann and F. Durand, ACM Trans. Graph. 23, 673 (2004).
[CrossRef]

Elder, J. H.

J. H. Elder and S. W. Zucker, IEEE Trans. Pattern Anal. Mach. Intell. 20, 699 (1998).
[CrossRef]

Favaro, P.

M. Burger, P. Favaro, S. Soatto, and S. J. Osher, IEEE Trans. Pattern Anal. Mach. Intell. 30, 518 (2008).
[CrossRef]

P. Favaro and S. Soatto, IEEE Trans. Pattern Anal. Mach. Intell. 27, 406 (2005).
[CrossRef]

Hecht, E.

E. Hecht, Optics 4th Series (Addison-Wesley, 2002).

Kang, S. B.

S. B. Kang, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2007), pp. 2025–2032.

Levin, A.

D. Lischinski, A. Levin, and Y. Weiss, IEEE Trans. Pattern Anal. Mach. Intell. 30, 228 (2008).
[CrossRef]

D. Lischinski, A. Levin, and Y. Weiss, ACM Trans. Graph. 23, 689 (2004).
[CrossRef]

Lischinski, D.

D. Lischinski, A. Levin, and Y. Weiss, IEEE Trans. Pattern Anal. Mach. Intell. 30, 228 (2008).
[CrossRef]

D. Lischinski, A. Levin, and Y. Weiss, ACM Trans. Graph. 23, 689 (2004).
[CrossRef]

Namboodiri, V. P.

V. P. Namboodiri and S. Chaudhuri, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2008), pp. 1–6.

Nayar, S.

O. Cossairt, Z. Changyin, and S. Nayar, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2010), pp. 1110–1117.

Osher, S. J.

M. Burger, P. Favaro, S. Soatto, and S. J. Osher, IEEE Trans. Pattern Anal. Mach. Intell. 30, 518 (2008).
[CrossRef]

Rombach, M. C.

Sim, T.

S. Zhuo and T. Sim, Pattern Recogn. 44, 1852 (2011).
[CrossRef]

Simonov, A. N.

Soatto, S.

M. Burger, P. Favaro, S. Soatto, and S. J. Osher, IEEE Trans. Pattern Anal. Mach. Intell. 30, 518 (2008).
[CrossRef]

P. Favaro and S. Soatto, IEEE Trans. Pattern Anal. Mach. Intell. 27, 406 (2005).
[CrossRef]

Tai, Y.-W.

Y.-W. Tai and M. S. Brown, in Proceedings of the IEEE International Conference on Image Processing (ICIP) (IEEE, 2009), pp. 1797–1800.

Wai-Kuen, C.

Z. Wei and C. Wai-Kuen, in Proceedings of the IEEE 12th International Conference on Computer Vision Workshops (ICCV) (IEEE, 2009), pp. 1947–1954.

Wei, Z.

Z. Wei and C. Wai-Kuen, in Proceedings of the IEEE 12th International Conference on Computer Vision Workshops (ICCV) (IEEE, 2009), pp. 1947–1954.

Weiss, Y.

D. Lischinski, A. Levin, and Y. Weiss, IEEE Trans. Pattern Anal. Mach. Intell. 30, 228 (2008).
[CrossRef]

D. Lischinski, A. Levin, and Y. Weiss, ACM Trans. Graph. 23, 689 (2004).
[CrossRef]

Young, R.

Zhuo, S.

S. Zhuo and T. Sim, Pattern Recogn. 44, 1852 (2011).
[CrossRef]

Zucker, S. W.

J. H. Elder and S. W. Zucker, IEEE Trans. Pattern Anal. Mach. Intell. 20, 699 (1998).
[CrossRef]

ACM Trans. Graph.

E. Eisemann and F. Durand, ACM Trans. Graph. 23, 673 (2004).
[CrossRef]

D. Lischinski, A. Levin, and Y. Weiss, ACM Trans. Graph. 23, 689 (2004).
[CrossRef]

Comput. Graph. Forum

S. Bae and F. Durand, Comput. Graph. Forum 26, 571 (2007).

IEEE Trans. Pattern Anal. Mach. Intell.

D. Lischinski, A. Levin, and Y. Weiss, IEEE Trans. Pattern Anal. Mach. Intell. 30, 228 (2008).
[CrossRef]

P. Favaro and S. Soatto, IEEE Trans. Pattern Anal. Mach. Intell. 27, 406 (2005).
[CrossRef]

M. Burger, P. Favaro, S. Soatto, and S. J. Osher, IEEE Trans. Pattern Anal. Mach. Intell. 30, 518 (2008).
[CrossRef]

J. H. Elder and S. W. Zucker, IEEE Trans. Pattern Anal. Mach. Intell. 20, 699 (1998).
[CrossRef]

J. Canny, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 679 (1986).
[CrossRef]

Opt. Lett.

Pattern Recogn.

S. Zhuo and T. Sim, Pattern Recogn. 44, 1852 (2011).
[CrossRef]

Other

E. Hecht, Optics 4th Series (Addison-Wesley, 2002).

S. B. Kang, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2007), pp. 2025–2032.

V. P. Namboodiri and S. Chaudhuri, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2008), pp. 1–6.

O. Cossairt, Z. Changyin, and S. Nayar, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2010), pp. 1110–1117.

Z. Wei and C. Wai-Kuen, in Proceedings of the IEEE 12th International Conference on Computer Vision Workshops (ICCV) (IEEE, 2009), pp. 1947–1954.

Y.-W. Tai and M. S. Brown, in Proceedings of the IEEE International Conference on Image Processing (ICIP) (IEEE, 2009), pp. 1797–1800.

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Figures (5)

Fig. 1.
Fig. 1.

Focus and defocus for thin lens model.

Fig. 2.
Fig. 2.

Sparse defocus map refinement using JBF. (a) Original input defocus image, (b) sparse defocus map before JBF, and (c) sparse defocus map after JBF.

Fig. 3.
Fig. 3.

Comparison of our method with Bae and Durand’s method. (a) Input image, (b) Bae and Durand’s method, and (c) our method.

Fig. 4.
Fig. 4.

Comparison of our method with the inverse diffusion method. (a) Input image, (b) inverse diffusion method, and (c) our method.

Fig. 5.
Fig. 5.

Comparison of our method with Zhuo and Sim’s method. (a) Input image, (b) Zhuo and Sim’s method, and (c) our method.

Equations (10)

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d(X,λ)=f(X,λ)*p(X,λ)*s(λ),
g(x,y;σ1)=12πσ12exp(x2+y22σ12),
d(X)=f(X)*g(X,σ+σ1).
D(u,v)=F(u,v)G(u,v;σ+σ1),
C(i)=log(A(i))1NjBlog(A(j)),
C(i)=log(F(u,v)G(u,v;σ(i)+σ1))1NjBlog(F(u,v)G(u,v;σ(j)+σ1))),
σ(i)=1/exp(c(i))σ12,
E(m)=mTLm+λ(mm˜)TD(mm˜),
k|(i,j)ωk(δij1|ωk|(1+(Iiμk)T(Σk+ε|ωk|U3)1(Ijμk))),
(L+λD)m=λDm˜.

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