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Erschienen in: Multimedia Systems 3/2015

01.06.2015 | Regular Paper

Nonlocal variational image segmentation models on graphs using the Split Bregman

verfasst von: Ke Lu, Qian Wang, Ning He, Daru Pan, Weiguo Pan

Erschienen in: Multimedia Systems | Ausgabe 3/2015

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Abstract

Variational functionals such as Mumford-Shah and Chan-Vese methods have a major impact on various areas of image processing. After over 10 years of investigation, they are still in widespread use today. These formulations optimize contours by evolution through gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In this paper, we propose an image segmentation model in a variational nonlocal means framework based on a weighted graph. The advantages of this model are twofold. First, the convexity global minimum (optimum) information is taken into account to achieve better segmentation results. Second, the proposed global convex energy functionals combine nonlocal regularization and local intensity fitting terms. The nonlocal total variational regularization term based on the graph is able to preserve the detailed structure of target objects. At the same time, the modified local binary fitting term introduced in the model as the local fitting term can efficiently deal with intensity inhomogeneity in images. Finally, we apply the Split Bregman method to minimize the proposed energy functional efficiently. The proposed model has been applied to segmentation of real medical and remote sensing images. Compared with other methods, the proposed model is superior in terms of both accuracy and efficient.

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Literatur
1.
Zurück zum Zitat Zha, Z.J., Hua, X.S., Mei, T., Wang, J., Qi, G.J., Wang, Z.: Joint multi-label multi-instance learning for image classification. In: IEEE Conference on CVPR 2008, pp. 1–8 (2008) Zha, Z.J., Hua, X.S., Mei, T., Wang, J., Qi, G.J., Wang, Z.: Joint multi-label multi-instance learning for image classification. In: IEEE Conference on CVPR 2008, pp. 1–8 (2008)
2.
Zurück zum Zitat Zha, Z.-J., Yang, L., Mei, T., Wang, M., Wang, Z.: Visual query suggestion. ACM Multimedia 2009, 15–24 (2009) Zha, Z.-J., Yang, L., Mei, T., Wang, M., Wang, Z.: Visual query suggestion. ACM Multimedia 2009, 15–24 (2009)
3.
Zurück zum Zitat Zha, Z.J., Yang, L., Mei, T., Wang, M., Wang, Z., Chua, T.S., Hua, X.S.: Visual query suggestion: Towards Capturing User Intent in Internet Image Search. ACM Trans. Multimedia Comput. Commun. Appl. (TOMMCAP): 6(3), Article No. 13 (2010) Zha, Z.J., Yang, L., Mei, T., Wang, M., Wang, Z., Chua, T.S., Hua, X.S.: Visual query suggestion: Towards Capturing User Intent in Internet Image Search. ACM Trans. Multimedia Comput. Commun. Appl. (TOMMCAP): 6(3), Article No. 13 (2010)
4.
Zurück zum Zitat Zha, Z.J., Wang, M., Zheng, Y.-T., Yang, Y., Hong, R., Chua, T.: Interactive video indexing with statistical active learning. IEEE Trans. Multimedia 14(1), 17–27 (2012)CrossRef Zha, Z.J., Wang, M., Zheng, Y.-T., Yang, Y., Hong, R., Chua, T.: Interactive video indexing with statistical active learning. IEEE Trans. Multimedia 14(1), 17–27 (2012)CrossRef
5.
Zurück zum Zitat Zha, Z.-J., Mei, T., Wang, J., Wang, Z., Hua, X.-S.: Graph based semi-supervised learning with multiple labels. J. Vis. Commun. Image Represent. 20(2), 97–103 (2009)CrossRef Zha, Z.-J., Mei, T., Wang, J., Wang, Z., Hua, X.-S.: Graph based semi-supervised learning with multiple labels. J. Vis. Commun. Image Represent. 20(2), 97–103 (2009)CrossRef
6.
Zurück zum Zitat Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vis. 321–331 (1988) Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vis. 321–331 (1988)
7.
Zurück zum Zitat Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22(1), 61–80 (1997)CrossRefMATH Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22(1), 61–80 (1997)CrossRefMATH
8.
Zurück zum Zitat Malladi, R., Sethian, J.A., Vemuri, B.C.: Evolutionary fronts for topology-independent shape modeling and recovery. Proc. Eur. Conf. Comput. Vis. 3–13 (1994) Malladi, R., Sethian, J.A., Vemuri, B.C.: Evolutionary fronts for topology-independent shape modeling and recovery. Proc. Eur. Conf. Comput. Vis. 3–13 (1994)
9.
Zurück zum Zitat Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Gradient flows and geometric active contour models. Proc. Int. Conf. Comput. Vis. 810–815 (1995) Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Gradient flows and geometric active contour models. Proc. Int. Conf. Comput. Vis. 810–815 (1995)
10.
Zurück zum Zitat Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)CrossRefMATHMathSciNet Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)CrossRefMATHMathSciNet
11.
Zurück zum Zitat Cohen, L.D., Cohen, I.: Finite-element methods for active contour models and balloons for 2-d and 3-d images. IEEE Trans. Pattern Anal. Mach. Intell. 1131–1147 (1993) Cohen, L.D., Cohen, I.: Finite-element methods for active contour models and balloons for 2-d and 3-d images. IEEE Trans. Pattern Anal. Mach. Intell. 1131–1147 (1993)
12.
Zurück zum Zitat Leroy, B., Herlin, I., Cohen, L.D.: Multi-resolution algorithms for active contour models. Proc. 12th Int. Conf. Analysis and Optimization of Systems. 58–65 (1996) Leroy, B., Herlin, I., Cohen, L.D.: Multi-resolution algorithms for active contour models. Proc. 12th Int. Conf. Analysis and Optimization of Systems. 58–65 (1996)
13.
Zurück zum Zitat Xiang, Y., Chung, A.C.S., Ye, J.: An active contour model for image segmentation based on elastic interaction. J. Comput. Phys. 219, 455–476 (2006)CrossRefMATHMathSciNet Xiang, Y., Chung, A.C.S., Ye, J.: An active contour model for image segmentation based on elastic interaction. J. Comput. Phys. 219, 455–476 (2006)CrossRefMATHMathSciNet
14.
Zurück zum Zitat He, N., Lu, K.: An improved geometric active contour model for concrete CT image segmentation based on edge flow. Chin. J. Electron. 19(4), 687–690 (2010) He, N., Lu, K.: An improved geometric active contour model for concrete CT image segmentation based on edge flow. Chin. J. Electron. 19(4), 687–690 (2010)
15.
Zurück zum Zitat Leventon, M.E., Grimson, W.E.L., Faugeras, O.D.: Statistical shape influencing geodesic active contours. In: Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 316–323 (2000) Leventon, M.E., Grimson, W.E.L., Faugeras, O.D.: Statistical shape influencing geodesic active contours. In: Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 316–323 (2000)
16.
Zurück zum Zitat Xu, C., Prince, J.: Generalized gradient vector flow external forces for active contours. Signal Process. 131–139 (1998) Xu, C., Prince, J.: Generalized gradient vector flow external forces for active contours. Signal Process. 131–139 (1998)
17.
Zurück zum Zitat Dakua, S.P., Sahambi, J.S.: Modified active contour model and Random Walk approach for left ventricular cardiac MR image segmentation. Int. J. Numer. Methods Biomed. Eng. 7(29), 1350–1361 (2011)MathSciNet Dakua, S.P., Sahambi, J.S.: Modified active contour model and Random Walk approach for left ventricular cardiac MR image segmentation. Int. J. Numer. Methods Biomed. Eng. 7(29), 1350–1361 (2011)MathSciNet
18.
Zurück zum Zitat Wang, X.F., Huang, D.S., Xu, H.: An efficient local Chan-Vese model for image segmentation. Pattern Recognit. 43(2010), 603–618 (2010)CrossRefMATH Wang, X.F., Huang, D.S., Xu, H.: An efficient local Chan-Vese model for image segmentation. Pattern Recognit. 43(2010), 603–618 (2010)CrossRefMATH
19.
Zurück zum Zitat Miyoun, J., Gabriel, P., Laurent, D.C.: Nonlocal active contours. EMMCVPR SIAM J. Imag. Sci. 5(3), 1022–1054 (2011) Miyoun, J., Gabriel, P., Laurent, D.C.: Nonlocal active contours. EMMCVPR SIAM J. Imag. Sci. 5(3), 1022–1054 (2011)
20.
Zurück zum Zitat He, N., Zhang, P., Lu, K.: A new deformable model using level sets for shape segmentation. J. Electron. 26(3), 353–358 (2009) He, N., Zhang, P., Lu, K.: A new deformable model using level sets for shape segmentation. J. Electron. 26(3), 353–358 (2009)
21.
Zurück zum Zitat Ke, L., Ning, H., Jian, X.: Content-based similarity for 3D model retrieval and classification. Prog. Nat. Sci. 19(4), 495–499 (2009)CrossRef Ke, L., Ning, H., Jian, X.: Content-based similarity for 3D model retrieval and classification. Prog. Nat. Sci. 19(4), 495–499 (2009)CrossRef
22.
Zurück zum Zitat Lu, K., He, N., Li, L.: Non local means based denoising for medical images. Comput. Math. Methods Med. 2012, Article ID 438617 (2012). doi:10.1155/2012/438617 Lu, K., He, N., Li, L.: Non local means based denoising for medical images. Comput. Math. Methods Med. 2012, Article ID 438617 (2012). doi:10.​1155/​2012/​438617
23.
Zurück zum Zitat Wang, J., Lu, K., Wang, Q., Jia, J.: Kernel optimization for blind motion deblurring with image edge prior. Math Problems Eng. 2012, Article ID 639824 (2012). doi:10.1155/2012/639824 Wang, J., Lu, K., Wang, Q., Jia, J.: Kernel optimization for blind motion deblurring with image edge prior. Math Problems Eng. 2012, Article ID 639824 (2012). doi:10.​1155/​2012/​639824
24.
Zurück zum Zitat Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms with a new one. SIAM Mul. Model. Simul. 4(2), 490–530 (2005)CrossRefMATHMathSciNet Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms with a new one. SIAM Mul. Model. Simul. 4(2), 490–530 (2005)CrossRefMATHMathSciNet
25.
Zurück zum Zitat Peyré, G., Bougleux, S., Cohen, L.D.: Non-local regularization of inverse problems. ECCV Part III LNCS 5304(2008), 57–68 (2008) Peyré, G., Bougleux, S., Cohen, L.D.: Non-local regularization of inverse problems. ECCV Part III LNCS 5304(2008), 57–68 (2008)
26.
Zurück zum Zitat Miyoun, J., Gabriel, P., Lauren, D.C.: Non-local segmentation and in painting. 2011 18th IEEE Int. Conf. Image Process. 2011, 3373–3376 (2011) Miyoun, J., Gabriel, P., Lauren, D.C.: Non-local segmentation and in painting. 2011 18th IEEE Int. Conf. Image Process. 2011, 3373–3376 (2011)
27.
Zurück zum Zitat Yang, Y., Boying, W.: Convex image segmentation model based on local and global intensity fitting energy and Split Bregman method. J. Appl. Math. 2012 (2012). doi:10.1155/2012/692589 Yang, Y., Boying, W.: Convex image segmentation model based on local and global intensity fitting energy and Split Bregman method. J. Appl. Math. 2012 (2012). doi:10.​1155/​2012/​692589
28.
Zurück zum Zitat Bresson, X., Chan, T.: Non-local unsupervised variational image segmentation models. UCLA CAM Rep. 2008, 08–67 (2008) Bresson, X., Chan, T.: Non-local unsupervised variational image segmentation models. UCLA CAM Rep. 2008, 08–67 (2008)
29.
Zurück zum Zitat Hong, R., Tang, J., Tan, H.-K., Ngo, C.-W., Yan, S., Chua, T.-S.: Beyond search: event-driven summarization for web videos. TOMCCAP 7(4), 35 (2011)CrossRef Hong, R., Tang, J., Tan, H.-K., Ngo, C.-W., Yan, S., Chua, T.-S.: Beyond search: event-driven summarization for web videos. TOMCCAP 7(4), 35 (2011)CrossRef
30.
Zurück zum Zitat Wang, M., Hong, R., Li, G., Zha, Z.-J., Yan, S., Chua, T.-S.: Event driven web video summarization by tag localization and key-shot identification. IEEE Trans. Multimedia 14(4), 975–985 (2012)CrossRef Wang, M., Hong, R., Li, G., Zha, Z.-J., Yan, S., Chua, T.-S.: Event driven web video summarization by tag localization and key-shot identification. IEEE Trans. Multimedia 14(4), 975–985 (2012)CrossRef
31.
Zurück zum Zitat Gao, Y., Wang, M., Zha, Z., Shen, J., Li, X., Xindong, W.: Visual–textual joint relevance learning for tag-based social image search. IEEE Trans. Image Process. 22(1), 363–376 (2013)CrossRefMathSciNet Gao, Y., Wang, M., Zha, Z., Shen, J., Li, X., Xindong, W.: Visual–textual joint relevance learning for tag-based social image search. IEEE Trans. Image Process. 22(1), 363–376 (2013)CrossRefMathSciNet
32.
Zurück zum Zitat Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3D object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012)CrossRefMathSciNet Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3D object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012)CrossRefMathSciNet
33.
Zurück zum Zitat Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3D object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2012)CrossRefMathSciNet Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3D object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2012)CrossRefMathSciNet
34.
Zurück zum Zitat Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. SIAM Multiscale Model. Simul. (MMS) 7(3), 1005–1028 (2008)CrossRefMATHMathSciNet Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. SIAM Multiscale Model. Simul. (MMS) 7(3), 1005–1028 (2008)CrossRefMATHMathSciNet
35.
Zurück zum Zitat Boykov, Y., Kolmogorov, V., Cremers, D., Delong, A.: An integral solution to surface evolution PDEs via geo-cuts. Proc. ECCV LCNS 3953, 409–422 (2006) Boykov, Y., Kolmogorov, V., Cremers, D., Delong, A.: An integral solution to surface evolution PDEs via geo-cuts. Proc. ECCV LCNS 3953, 409–422 (2006)
36.
Zurück zum Zitat Zeng, X., Chen,W., Peng, Q.: Efficiently solving the piecewise constant Mumford-Shah model using graph cuts. Technical report, Zhejiang University (2006) Zeng, X., Chen,W., Peng, Q.: Efficiently solving the piecewise constant Mumford-Shah model using graph cuts. Technical report, Zhejiang University (2006)
37.
Zurück zum Zitat Grady, L.: The piecewise smooth Mumford-Shah functional on an arbitrary graph. IEEE Trans. Image Process. 18(11), 2547–2561 (2009)CrossRefMathSciNet Grady, L.: The piecewise smooth Mumford-Shah functional on an arbitrary graph. IEEE Trans. Image Process. 18(11), 2547–2561 (2009)CrossRefMathSciNet
38.
39.
Zurück zum Zitat Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)CrossRefMATH Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)CrossRefMATH
40.
Zurück zum Zitat Li, C., Xu, C., Gui, C., Fox, M. D.: Level set evolution without re-initialization: a new variational formulation. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05). 2005, 430–436 (2005) Li, C., Xu, C., Gui, C., Fox, M. D.: Level set evolution without re-initialization: a new variational formulation. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05). 2005, 430–436 (2005)
Metadaten
Titel
Nonlocal variational image segmentation models on graphs using the Split Bregman
verfasst von
Ke Lu
Qian Wang
Ning He
Daru Pan
Weiguo Pan
Publikationsdatum
01.06.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Multimedia Systems / Ausgabe 3/2015
Print ISSN: 0942-4962
Elektronische ISSN: 1432-1882
DOI
https://doi.org/10.1007/s00530-013-0351-z

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