Abstract
Image segmentation is to segment images into subdomains with same intensity, texture or color. Texture is one of the most important features to images. Because of the complexity of texture, segmentation of texture image is especially difficult and it seriously restricts the development of image processing. In this paper, a nonlocal Mumford-Shah (NLMS) model is proposed to segment multiphase texture images. This proposed model uses nonlocal operators that are capable of handling texture information in the image. In order to segment different patterns of texture simultaneously, multiple region partition strategy which uses n label functions to segment n+1 texture regions is adopted. Furthermore, to improve computational efficiency, the proposed model avoids directly computing the resulting nonlinear partial differential equation (PDE) by using Split Bregman algorithm. Numerical experiments are conducted to validate the performance of proposed model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. In: AMS, vol. 147. Springer, Berlin (2002)
Chan, F.T., Shen, J.: Image processing and analysis: variational, PDE. Wavelet, and Stochastic Methods. SIAM (2005)
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42(5), 577–685 (1989)
Chan, T.F., Vese, L.A.: Active Contours Without Edges. IEEE. T. Image. Process. 10(2), 266–277 (2001)
Osher, S., Sethian, J.A.: Fronts propagation with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)
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)
Sandberg, B., Chan, T.F., Vese L.A.: A Level-set and Gabor Based Active Contour Algorithm for Segmenting Textured Images. UCLA CAM Report 02-39 (July 2002)
Buades, A., Coll, B., Morel, J.M.: A Review of Image Denoising Algorithms, with a New One. SIAM Multiscale Modeling Simulation 4(2), 490–530 (2005)
Gilboa, G., Osher, S.: Nonlocal Operators with Applications to Image Processing. SIAM Multiscale Modeling Simulation 7(3), 1005–1028 (2008)
Bresson, X., Chan, T.F.: Nonlocal Unsupervised Variational Image Segmentation Models. UCLA CAM Report 08-67 (October 2008)
Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2002)
Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, New York (2003)
Sapiro, G.: Geometric Partial Differential Equations and Image Processing. Cambridge University Press (2001)
Duan, J.M., Pan, Z.K.: Some fast projection methods based on Chan-Vese model for image segmentation. Eurasip. J. Image. Vide.. Process. (July 2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lu, W., Duan, J., Wei, W., Pan, Z., Wang, G. (2015). Nonlocal Mumford-Shah Model for Multiphase Texture Image Segmentation. In: Tan, T., Ruan, Q., Wang, S., Ma, H., Di, K. (eds) Advances in Image and Graphics Technologies. IGTA 2015. Communications in Computer and Information Science, vol 525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47791-5_43
Download citation
DOI: https://doi.org/10.1007/978-3-662-47791-5_43
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-47790-8
Online ISBN: 978-3-662-47791-5
eBook Packages: Computer ScienceComputer Science (R0)