Noisy image segmentation based on nonlinear diffusion equation model. (English) Zbl 1243.94006
Summary: We address the segmentation problem in noisy image based on nonlinear diffusion equation model and proposes a new adaptive segmentation model based on gray-level image segmentation model. This model also can be extended to the vector value image segmentation. By virtue of the prior information of regions and boundary of image, a framework is established to construct different segmentation models using different probability density functions. A segmentation model exploiting Gauss probability density function is given in this paper. An efficient and unconditional stable algorithm based on locally one-dimensional (LOD) scheme is developed and it is used to segment the gray image and the vector values image. Comparing with existing classical models, the proposed approach gives the best performance.
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 35Q94 | PDEs in connection with information and communication |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K55 | Nonlinear parabolic equations |
| 68U10 | Computing methodologies for image processing |
Keywords:
curve evolution; variation calculus technique; level set; locally one-dimensional; active contour model; nonlinear diffusion equationsReferences:
| [1] | Tammy Riklin-Raviv, Nir Sochen, Nahum Kiryati, Mutual segmentation with level sets, in: CVPR’06.; Tammy Riklin-Raviv, Nir Sochen, Nahum Kiryati, Mutual segmentation with level sets, in: CVPR’06. · Zbl 1098.68848 |
| [2] | Kass, M.; Witkin, A.; Terzopoulos, D., Snakes: active contour models, Int. J. Comput. Vision, 1, 4, 321-331 (1988) |
| [3] | Caselles, V.; Catte, F.; Coll, B.; Dibos, F., A geometric model for active contours in image processing, Numer. Math., 66, 1, 1-31 (1993) · Zbl 0804.68159 |
| [4] | Casselles, V.; Kimmel, R.; Sapiro, G., Geodesic active contours, Int. J. Comput. Vision, 22, 1, 61-79 (1997) · Zbl 0894.68131 |
| [5] | Goldenberg, Roman; Kimmel, Ron; Rivlin, Ehud; Rudzsky, Michael, Fast geodesic active contours, IEEE Trans. Image Process., 10, 10, 1467-1475 (2001) |
| [6] | Kühne, G.; Weickert, J., Fast Methods for Implicit Active Contour Models [M], (Osher, S.; Paragios, N., Geometric Level Set Methods in Imaging, Vision, and Graphics (2003), Springer Verlag) · Zbl 1027.68137 |
| [7] | Osher, S.; Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79, 12-49 (1988) · Zbl 0659.65132 |
| [8] | Paragion, N.; Deriche, R., Geodesic active contours and level sets for the detection and tracking of moving objects, IEEE Trans. Pattern Anal. Mach. Intell., 22, 3, 266-280 (2000) |
| [9] | Chan, T.; Vese, L., Active contours without edges, IEEE Trans. Image Process., 10, 2, 266-277 (2001) · Zbl 1039.68779 |
| [10] | 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 |
| [11] | Chen, Bo; Yuen, Pong-Chi; Lai, Jian-Huang; Chen, Wen-Sheng, Image segmentation and selective smoothing based on variational framework, J. Signal Process. Syst., 54, 145-158 (2009) |
| [12] | Kimmel, R., Fast Edge Integration [M], (Osher, S.; Paragios, N., Geometric Level Set Methods in Imaging Vision and Graphics (2003), Springer Verlag) · Zbl 1027.68137 |
| [13] | M. Russon, R. Deriche, A variational framework for active and adaptative segmentation of vector valued images [R], Technical Report 4515, INRIA, France, 2002.; M. Russon, R. Deriche, A variational framework for active and adaptative segmentation of vector valued images [R], Technical Report 4515, INRIA, France, 2002. |
| [14] | Li, C.; Xu, C.; Gui, C.; Fox, M. D., Distance regularized level set evolution and its application to image segmentation, IEEE Trans. Image Process., 19, 12, 3243-3254 (2010) · Zbl 1371.94226 |
| [15] | Dambreville, S., A geometric approach to joint 2D region-based segmentation and 3D pose estimation using a 3D shape prior, SIAM J. Imag. Sci., 3, 1, 110-132 (2010) · Zbl 1223.49048 |
| [16] | Leclerc, Y. G., Constructing simple stable description for image partitioning, Int. J. Comput. Vision, 3, 1, 73-102 (1989) |
| [17] | Zhu, S.; Yuille, A., Region competition: unifying snakes, region growing, and Bayes/MDL for multi-band image segmentation, IEEE Trans. Pattern Anal. Mach. Intell., 18, 9, 884-900 (1996) |
| [18] | Paragios, Nikos; Deriche, Rachid, Geodesic active regions: a new paradigm to deal with frame partition problems in computer vision, J. Vis. Commun. Image Represent. (2002) · Zbl 1012.68726 |
| [19] | Goldenberg, Roman; Kimmel, Ron; Rivlin, Ehud; Rudzsky, Michael, Fast geodesic active contours, IEEE Trans. Image Process., 10, 10, 1467-1475 (2001) |
| [20] | Malladi, R.; Sethian, J. A.; Vemuri, B. C., Shape modeling with front propagation: a level set approach, IEEE Trans. Pattern Anal. Machine Intell., 17, 2, 158-174 (1995) |
| [21] | Adalsteinsson, D.; Sethian, J. A., A fast level set method for propagating interfaces, J. Comput. Phys., 118, 269-277 (1995) · Zbl 0823.65137 |
| [22] | Chopp, D. L., Computing minimal surfaces via level set curvature flow, J. Comput. Phys., 106, 1, 77-91 (1993) · Zbl 0786.65015 |
| [23] | Sethian, J. A., Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics. Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Sciences (1996), Cambridge Univ. Press · Zbl 0859.76004 |
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