×

A novel method for image segmentation using reaction-diffusion model. (English) Zbl 1386.94017

Summary: We propose an image segmentation model that is derived from reaction-diffusion equations and level set methods. In our model, a diffusion term is used for regularization of a level set function, and a reaction term has the desired sign property to force the level set function to move up or down and finally identify an object and its background. Our level set function can be initialized to any bounded function (e.g., a constant function). The proposed model can be applied to a wider range of images with promising results, especially for real images that have high noise and blurred boundaries. This study gives a new method for the further investigations of reaction-diffusion equations directly for segmentation.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
35K57 Reaction-diffusion equations
Full Text: DOI

References:

[1] Aldo, M., Philippe, C., Bertrand, A., & Christine, F. M. (2008). Cooperation of the partial differential equation methods and the wavelet transform for the segmentation of multivalued images. Signal Processing: Image Communication, 23(1), 14-30.
[2] Bini, A. A., & Bhat, M. S. (2014). Despeckling low SNR, low contrast ultrasound images via anisotropic level set diffusion. Multidimensional Systems and Signal Processing, 25, 41-65. doi:10.1007/s11045-012-0184-5. · Zbl 1282.93229 · doi:10.1007/s11045-012-0184-5
[3] Catte, F., Lions, P., Morel, J., & Coll, T. (1992). Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis, 29, 182-193. · Zbl 0746.65091 · doi:10.1137/0729012
[4] Chan, T., & Vese, L. (2001). Active contours without edges. IEEE Transactions on Image Processing, 10(2), 266-277. · Zbl 1039.68779 · doi:10.1109/83.902291
[5] Chen, Y., Vemuri, B., & Wang, L. (2000). Image denoising and segmentation via nonlinear diffusion. Computers and Mathematics Applications, 39, 131-149. · Zbl 0951.68556 · doi:10.1016/S0898-1221(00)00050-X
[6] Chuang, K. S., Hzeng, H. L., Chen, S., Wu, J., & Chen, T. J. (2006). Fuzzy c-means clustering with spatial information for image segmentation. Computerized Medical Imaging and Graphics, 30, 9-15. · doi:10.1016/j.compmedimag.2005.10.001
[7] Crandall, R. (2009). Image segmentation using the Chan-Vese algorithm. ECE 532 Project, Fall. · Zbl 0951.68556
[8] Gao, G., Zhao, L., Zhang, J., Zhou, D., & Huang, J. (2008). A segmentation algorithm for SAR images based on the anisotropic heat diffusion equation. Pattern Recognition, 41, 3035-3043. · Zbl 1161.68765 · doi:10.1016/j.patcog.2008.01.029
[9] Hsu, R. C., Chan, D. Y., Liu, C.-T., & Lai, W.-C. (2012). Contour extraction in medical images using initial boundary pixel selection and segmental contour following. Multidimensional Systems and Signal Processing, 23, 469-498. doi:10.1007/s11045-012-0176-5. · Zbl 1298.92057 · doi:10.1007/s11045-012-0176-5
[10] Kanungo, T., Mount, D. M., Netanyahu, N. S., Piatko, C. D., Silverman, R., & Wu, A. Y. (2002). An efficient k-means clustering algorithm: Analysis and implementation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(7), 881-892. · Zbl 1077.68109 · doi:10.1109/TPAMI.2002.1017616
[11] Kimia, B. B., Tannenbaum, A., & Zucker, S. (1995). Shapes, shocks, and deformations I: The components of two-dimensional shape and the reaction-diffusion space. International Journal of Computer Vision, 15, 189-224. · doi:10.1007/BF01451741
[12] Li, C., Xu, C., Gui, C., & Fox, M. D. (2005) Level set formulation without re-initialization: A new variational formulation. In Proceedings of IEEE conference on computer vision and pattern recognition, San Diego (Vol. 1, pp. 430-436). · Zbl 1161.68765
[13] Liu, B., Cheng, H. D., Huang, J., Tian, J., Tang, X., & Liu, J. (2010). Probability density difference-based active contour for ultrasound image segmentation. Pattern Recognition, 43, 2028-2042. · Zbl 1191.68588 · doi:10.1016/j.patcog.2010.01.002
[14] Li, C., Xu, C., Gui, C., & Fox, M. D. (2010). Distance regularized level set evolution and its application to image segmentation. IEEE Transactions on Image Processing, 19(12), 3243-3254. · Zbl 1371.94226 · doi:10.1109/TIP.2010.2069690
[15] Morfu, S. (2009). On some applications of diffusion processes for image processing. Physics Letters A, 373, 2438-2444. · Zbl 1231.68270 · doi:10.1016/j.physleta.2009.04.076
[16] Morfu, S., Nofiele, B., & Marquie, P. (2007). On the use of multistability for image processing. Physics Letters A, 367, 192-198. · Zbl 1209.94012 · doi:10.1016/j.physleta.2007.02.086
[17] Nie, F., Wang, Y., Pan, M., Peng, G., & Zhang, P. (2013). Two-dimensional extension of variance-based thresholding for image segmentation. Multidimensional Systems and Signal Processing, 24, 485-501. doi:10.1007/s11045-012-0174-7. · Zbl 1328.94014 · doi:10.1007/s11045-012-0174-7
[18] Osher, S., & Sethian, J. A. (1988). Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79, 12-49. · Zbl 0659.65132 · doi:10.1016/0021-9991(88)90002-2
[19] Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7), 629-639. · doi:10.1109/34.56205
[20] Pun, T. (1980). A new method for gray-level picture thresholding using the entropy of the histogram. Signal Processing, 2, 223-237. · doi:10.1016/0165-1684(80)90020-1
[21] Shattuck, D. W., Sandor-Leahy, S. R., Schaper, K. A., Rottenberg, D. A., & Leahy, R. M. (2001). Magnetic resonance image tissue classification using a partial volume model. Neuroimage, 13, 856-876. · doi:10.1006/nimg.2000.0730
[22] Tsai, Y. H., & Osher, S. (2005). Total variation and level set based methods in image science. Acta Numerica, 14, 1-61. · Zbl 1119.65376 · doi:10.1017/S0962492904000273
[23] Wang, Y., & He, C. (2011). Adaptive level set evolution starting with a constant function. Applied Mathematical Modelling, 36, 3217-3228. · Zbl 1252.65050 · doi:10.1016/j.apm.2011.10.023
[24] Weickert, J. (1997). A review of anisotropic diffusion filtering. Scale-Space Theory in Computer Science, 1252, 3-28.
[25] Wu, Y., & He, C. (2015). A convex variational level set model for image segmentation. Signal Processing, 106, 123-133. · doi:10.1016/j.sigpro.2014.07.013
[26] Wu, Z., Zhao, J., Yin, J., & Li, H. (2001). Nonlinear diffusion equations. Singapore: World Scientific. · Zbl 0997.35001 · doi:10.1142/4782
[27] Yan, C., Sang, N., & Zhang, T. (2003). Local entropy-based transition region extraction and thresholding. Pattern Recognition Letters, 24(16), 2935-2941. · doi:10.1016/S0167-8655(03)00154-5
[28] Zhang, K., Zhang, L., Song, H., & Zhou, W. (2010). Active contours with selective local or global segmentation: A new formulation and level set method. Image and Vision Computing, 28, 668-676. · doi:10.1016/j.imavis.2009.10.009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.