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**An efficient local Chan-Vese model for image segmentation.**
*(English)*
Zbl 1185.68817

Summary: A new Local Chan-Vese (LCV) model is proposed for image segmentation, which is built based on the techniques of curve evolution, local statistical function and level set method. The energy functional for the proposed model consists of three terms, i.e., global term, local term and regularization term. By incorporating the local image information into the proposed model, the images with intensity inhomogeneity can be efficiently segmented. In addition, the time-consuming re-initialization step widely adopted in traditional level set methods can be avoided by introducing a new penalizing energy. To avoid the long iteration process for level set evolution, an efficient termination criterion is presented which is based on the length change of evolving curve. Particularly, we proposed constructing an Extended Structure Tensor (EST) by adding the intensity information into the classical structure tensor for texture image segmentation. It can be found that by combining the EST with our LCV model, the texture image can be efficiently segmented no matter whether it presents intensity inhomogeneity or not. Finally, experiments on some synthetic and real images have demonstrated the efficiency and robustness of our model. Moreover, comparisons with the well-known Chan-Vese model and recent popular local binary fitting model also show that our LCV model can segment images with few iteration times and be less sensitive to the location of initial contour and the selection of governing parameters.

### MSC:

68U10 | Computing methodologies for image processing |

### Keywords:

extended structure tensor; image segmentation; intensity inhomogeneity; level set method; local Chan-Vese model
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\textit{X.-F. Wang} et al., Pattern Recognition 43, No. 3, 603--618 (2010; Zbl 1185.68817)

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### References:

[1] | Linda, G. S.; George, C. S., Computer Vision (2001), Prentice-Hall: Prentice-Hall New Jersey |

[2] | Kass, M.; Witkin, A.; Terzopoulos, D., Snakes: active contour models, Int. J. Comput. Vision, 1, 4, 321-331 (1987) |

[3] | Osher, S.; Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79, 1, 12-49 (1988) · Zbl 0659.65132 |

[4] | Gelas, A.; Bernard, O.; Friboulet, D.; Prost, R., Compactly supported radial basis functions based collocation method for level-set evolution in image segmentation, IEEE Trans. Image Process., 16, 7, 1873-1887 (2007) |

[5] | Y.H. Tsai, S. Osher, Total variation and level set based methods in image science, Acta Numer. (2005) 1-61.; Y.H. Tsai, S. Osher, Total variation and level set based methods in image science, Acta Numer. (2005) 1-61. · Zbl 1119.65376 |

[6] | Caselles, V.; Catte, F.; Coll, T.; Dibos, F., A geometric model for active contours in image processing, Numer. Math., 66, 1, 1-31 (1993) · Zbl 0804.68159 |

[7] | Caselles, V.; Kimmel, R.; Sapiro, G., Geodesic active contours, Int. J. Comput. Vision, 22, 1, 61-79 (1997) · Zbl 0894.68131 |

[8] | Malladi, R.; Sethian, J. A.; Vemuri, B. C., Shape modeling with front propagation: a level set approach, IEEE Trans. Pattern Anal. Mach. Intell., 17, 2, 158-175 (1995) |

[9] | Mumford, D.; Shah, J., Optimal approximation by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math., 42, 577-685 (1989) · Zbl 0691.49036 |

[10] | Chan, T. F.; Vese, L. A., Active contours without edges, IEEE Trans. Image Process., 10, 2, 266-277 (2001) · Zbl 1039.68779 |

[11] | Tsai, A.; Yezzi, A.; Willsky, A. S., Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification, IEEE Trans. Image Process., 10, 8, 1169-1186 (2001) · Zbl 1062.68595 |

[12] | Paragios, N.; Deriche, R., Geodesic active regions and level set methods for supervised texture segmentation, Int. J. Comput. Vision, 46, 3, 223-247 (2002) · Zbl 1012.68726 |

[13] | Gao, S.; Bui, T. D., Image segmentation and selective smoothing by using Mumford-Shah model, IEEE Trans. Image Process., 14, 10, 1537-1549 (2005) |

[14] | Vese, L. A.; Chan, T. F., A multiphase level set framework for image segmentation using the Mumford and Shah model, Int. J. Comput. Vision, 50, 3, 271-293 (2002) · Zbl 1012.68782 |

[15] | J.E. Solem, N.C. Overgaard, A. Heyden, Initialization techniques for segmentation with the Chan-Vese model, in: Proceedings of the 18th International Conference on Pattern Recognition (ICPR’06), vol. 2, 2006, pp. 171-174.; J.E. Solem, N.C. Overgaard, A. Heyden, Initialization techniques for segmentation with the Chan-Vese model, in: Proceedings of the 18th International Conference on Pattern Recognition (ICPR’06), vol. 2, 2006, pp. 171-174. |

[16] | R.B. Xia, W.J. Liu, J.B. Zhao, L. Li, An optimal initialization technique for improving the segmentation performance of Chan-Vese model, in: Proceedings of the IEEE International Conference on Automation and Logistics, 2007, pp. 411-415.; R.B. Xia, W.J. Liu, J.B. Zhao, L. Li, An optimal initialization technique for improving the segmentation performance of Chan-Vese model, in: Proceedings of the IEEE International Conference on Automation and Logistics, 2007, pp. 411-415. |

[17] | Y. Shi, W. Karl, A fast level set method without solving PDES, in: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’05), vol. 2, 2005, pp. 97-100.; Y. Shi, W. Karl, A fast level set method without solving PDES, in: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’05), vol. 2, 2005, pp. 97-100. |

[18] | Y. Pan, J.D. Birdwell, S.M. Djouadi, Efficient implementation of the Chan-Vese models without solving PDEs, in: Proceedings of the International Workshop On Multimedia Signal Processing, 2006, pp. 350-354.; Y. Pan, J.D. Birdwell, S.M. Djouadi, Efficient implementation of the Chan-Vese models without solving PDEs, in: Proceedings of the International Workshop On Multimedia Signal Processing, 2006, pp. 350-354. |

[19] | C.M. Li, C.Y. Xu, C.F. Gui, M.D. Fox, Level set formulation without Re-initialization: a new variational formulation, in: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 2005, vol. 1, 2005, pp. 430-436.; C.M. Li, C.Y. Xu, C.F. Gui, M.D. Fox, Level set formulation without Re-initialization: a new variational formulation, in: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 2005, vol. 1, 2005, pp. 430-436. |

[20] | Pi, L.; Shen, C. M.; Li, F.; Fan, J. S., A variational formulation for segmenting desired objects in color images, Image Vision Comput., 25, 9, 1414-1421 (2007) |

[21] | Sum, K.; Cheung, P., Vessel extraction under non-uniform illumination: a level set approach, IEEE Trans. Biomed. Eng., 55, 1, 358-360 (2008) |

[22] | Brox, T.; Cremers, D., On the statistical interpretation of the piecewise smooth Mumford-Shah functional, Proc. Scale Space Var. Met. Comput. Vision, 4485, 203-213 (2007) |

[23] | Piovano, J.; Rousson, M.; Papadopoulo, T., Efficient segmentation of piecewise smooth images, Proc. Scale Space Var. Met. Comput. Vision, 4485, 709-720 (2007) |

[24] | An, J.; Rousson, M.; Xu, C., \(γ\)-Convergence approximation to piecewise smooth medical image segmentation, Proc. Med. Imag. Comput. Comp. Assist. Interven., 4792, 495-502 (2007) |

[25] | S. Lankton, D. Nain, A. Yezzi, . Tannenbaum, Hybrid geodesic region-based curve evolutions for image segmentation, in: Proceedings of the SPIE: Medical Imagining, vol. 6510, 2007, pp. 65104U.; S. Lankton, D. Nain, A. Yezzi, . Tannenbaum, Hybrid geodesic region-based curve evolutions for image segmentation, in: Proceedings of the SPIE: Medical Imagining, vol. 6510, 2007, pp. 65104U. |

[26] | Lankton, S.; Tannenbaum, A., Localizing region-based active contours, IEEE Trans. Image Process., 17, 11, 2029-2039 (2008) · Zbl 1371.94213 |

[27] | C.M. Li, C.Y. Kao, J.C. Gore, Z.H. Ding, Implicit active contours driven by local binary fitting energy, in: Proceedings of the CVPR’07, 2007, pp. 1-7.; C.M. Li, C.Y. Kao, J.C. Gore, Z.H. Ding, Implicit active contours driven by local binary fitting energy, in: Proceedings of the CVPR’07, 2007, pp. 1-7. |

[28] | G. Aubert, M. Barlaud, O. Faugeras, S. Jehan-Besson, Image segmentation using active contours: calculus of variations of shape gradients, Research Report, INRIA, July 2002.; G. Aubert, M. Barlaud, O. Faugeras, S. Jehan-Besson, Image segmentation using active contours: calculus of variations of shape gradients, Research Report, INRIA, July 2002. · Zbl 1053.94003 |

[29] | B. Sandberg, T. Chan, L. Vese, A level-set and gabor-based active contour algorithm for segmenting textured images, Technical Report 39, Mathematical Department, UCLA, Los Angeles, USA, July 2002.; B. Sandberg, T. Chan, L. Vese, A level-set and gabor-based active contour algorithm for segmenting textured images, Technical Report 39, Mathematical Department, UCLA, Los Angeles, USA, July 2002. |

[30] | M. Rousson, T. Brox, R. Deriche, Active unsupervised texture segmentation on a diffusion based feature space, in: Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’03), vol. 2, 2003, pp. 699-7-4.; M. Rousson, T. Brox, R. Deriche, Active unsupervised texture segmentation on a diffusion based feature space, in: Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’03), vol. 2, 2003, pp. 699-7-4. |

[31] | J. Bigun, G.H. Grandlund, Optimal orientation detection of linear symmetry, in: Proceedings of the IEEE First International Conference on Computer Vision (ICCV), 1987, pp. 433-438.; J. Bigun, G.H. Grandlund, Optimal orientation detection of linear symmetry, in: Proceedings of the IEEE First International Conference on Computer Vision (ICCV), 1987, pp. 433-438. |

[32] | Bigun, J.; Grandlund, G. H.; Wiklund, J., Multidimensional orientation estimation with applications to texture analysis and optical flow, IEEE Trans. Pattern Anal. Mach. Intell., 13, 8, 775-790 (1991) |

[33] | C. Feddern, J. Weickert, B. Burgeth, Level-set methods for tensor-valued images, in: Proceedings of the Second IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, 2003, pp. 65-72.; C. Feddern, J. Weickert, B. Burgeth, Level-set methods for tensor-valued images, in: Proceedings of the Second IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, 2003, pp. 65-72. |

[34] | Z. Wang, B. Vemuri, Tensor field segmentation using region based active contour model, in: Proceedings of the Eighth European Conference on Computer Vision (ECCV’04), Springer Lecture Notes in Computer Science, vol. 3024, 2004, pp. 304-315.; Z. Wang, B. Vemuri, Tensor field segmentation using region based active contour model, in: Proceedings of the Eighth European Conference on Computer Vision (ECCV’04), Springer Lecture Notes in Computer Science, vol. 3024, 2004, pp. 304-315. · Zbl 1098.68884 |

[35] | S.M. Lee, A.L. Abott, N.A. Clark, P.A. Araman, Active contours on statistical manifolds and texture segmentation, in: Proceedings of the IEEE International Conference on Image Processing (ICIP), vol. 3, 2005, pp. 828-831.; S.M. Lee, A.L. Abott, N.A. Clark, P.A. Araman, Active contours on statistical manifolds and texture segmentation, in: Proceedings of the IEEE International Conference on Image Processing (ICIP), vol. 3, 2005, pp. 828-831. |

[36] | Maroulis, D. E.; Savelonas, M. A.; Iakovidis, D. K.; Karkanis, S. A.; Dimitropoulos, N., Variable background active contour model for computer-aided delineation of nodules in thyroid ultrasound images, IEEE Trans. Inf. Technol. Biomed., 11, 5, 537-543 (2007) |

[37] | Vovk, U.; Pernuš, F.; Likar, B., A review of methods for correction of intensity inhomogeneity in MRI, IEEE Trans. Med. Imaging, 26, 3, 405-421 (2007) |

[38] | Hou, Z. J., A review on MR image intensity inhomogeneity correction, Int. J. Biomed. Imaging, 2006, 1-11 (2006) |

[39] | Sussman, M.; Fatemi, E., An efficient, interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow, SIAM J. Sci. Comput., 20, 1165-1191 (1999) · Zbl 0958.76070 |

[40] | Gomes, J.; Faugeras, O., Reconciling distance functions and level sets, J. Visual Commun. Imaging Representation, 1, 11, 209-222 (2000) |

[41] | Adalsteinsson, D.; Sethian, J. A., A fast level set method for propagating interface, J. Comput. Phys., 118, 269-277 (1995) · Zbl 0823.65137 |

[42] | Sethian, J. A., Level Set Methods and Fast Marching Methods (1999), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0929.65066 |

[43] | Brox, T.; Weickert, J.; Burgeth, B.; Mrázek, P., Nonlinear structure tensors, Image Vis. Comput., 24, 1, 41-55 (2006) |

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