Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T05:50:11.920Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Variational Model with Dual Level Set Functions for Selective Segmentation

Published online by Cambridge University Press:  20 August 2015

Lavdie Rada  and
Ke Chen
Lavdie Rada*
Affiliation:
Centre for Mathematical Imaging Techniques (CMIT) and Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool L69 7ZL, United Kingdom
Ke Chen*
Affiliation:
Centre for Mathematical Imaging Techniques (CMIT) and Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool L69 7ZL, United Kingdom
*
Email:[email protected]
Corresponding author.Email:[email protected]
Get access

Abstract

In this paper we present a selective segmentation model using a dual level set variational formulation. Our variational model aims to segment all objects with one level set function (global) and the selected object, which is the closest to the geometric constraints (markers), with another level set (local). It is a combination of edge detection, markers distance function and active contour without edges. Experimental results show that our model is more robust than previous work.

Keywords

62H3565N2265N5574G6574G75Image selective segmentationlevel set functionEuler-Lagrange equation2D image segmentationre-initialization
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 1 , July 2012 , pp. 261 - 283
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Adalsteinsson, D. and Sethian, J. A., A fast level set method for propagating interfaces, J. Comput. Phys., 118(2) (1995), 1995–269.CrossRefGoogle Scholar
[2]Adams, R. and Bischof, L., Seeded region growing, IEEE T. Pattern Anal., 16(6) (1994), 1994–641.CrossRefGoogle Scholar
[3]Aubert, G. and Kornprobst, P., Mathematical Problems in Image Processing, Springer, New York, 2002.Google Scholar
[4]Badshah, N. and Chen, K., Image selective segmentation under geometrical constraints using an active contour approach, Commun. Comput. Phys., 7(4) (2009), 2009–759.Google Scholar
[5]Bresson, X., Esedoglu, S., Vandergheynst, P., Thiran, J. P. and Osher, S., Fast global minimization of the active contour/snake model, J. Math. Imag. Vision, 28(2) (2007), 2007–151.Google Scholar
[6]Caselles, V., Kimmel, R. and Sapiro, G., Geodesic active contours, Int. J. Comput. Vision, 22(1) (1997), 61–79.Google Scholar
[7]Chan, T. F., Sandberg, B. Y. and Vese, L. A., Active contours without edges for vector-valued images, J. Vis. Commun. Image Rep., 11(2) (2000), 2000–130.CrossRefGoogle Scholar
[8]Chan, T. F. and Shen, J. H., Image Processing and Analysis-Variational, PDE, Wavelet and Stochastic Methods, SIAM Publications, Philadelphia, USA, 2005.Google Scholar
[9]Chan, T. F. and Vese, L. A., Active contours without edges, CAM Report, UCLA (98-53), (1998).Google Scholar
[10]Chan, T. F. and Vese, L. A., An efficient variational multiphase motion for the Mumford-Shah segmentation model, Proc. 34th Asilomar Conf. Signals, Systems and Computers, 1 (2000), 490–494.Google Scholar
[11]Chan, T. F. and Vese, L. A., Active coutours without edges, IEEE Trans. Image Proc., 10(2) (2001), 2001–266.Google Scholar
[12]Forcadel, N., Guyader, C. Le and Gout, C., Image segmentation using a generalized fast marching method, Numer. Algor., 48(2) (2008), 2008–189.CrossRefGoogle Scholar
[13]Gout, C., Guyader, C. Le and Vese, L., Segmentation under geometrical conditions with geodesic active contour and interpolation using level set methods, Numer. Algor., 39 (2005), 155–173.Google Scholar
[14]Le, C. Guyader and Gout, C., Geodesic active contour under geometrical conditions theory and 3D applications, Numer. Algor., 48 (2008), 105–133.Google Scholar
[15]Gout, C. and Guyader, C. Le, Segmentation of complex geophysical structures with well data, Comput. Geosci., 10(4) (2006), 2006–361.Google Scholar
[16]Kass, M., Witkin, A. and Terzopoulos, D., Snakes: active contour models, Int. J. Comput. Vis., 1 (1987), 321–331.Google Scholar
[17]Kichenassamy, S., Kumar, A., Olver, P. and Yezzi, A., Snake: conformal curvature flows: from phase transitions to active vision, Arch. Ration. Mech. An., 134(3) (1996), 1996–275.CrossRefGoogle Scholar
[18]Li, C., Xu, C., Gui, C. and Fox, M. D., Level set evolution without re-initialization: a new vari-ational formulation, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1 (2005), 430–436.Google Scholar
[19]Li, F., Ng, M. K., Zeng, T. Y. and Shen, C. L., A multiphase image segmentation method based on fuzzy region competition, SIAM J. Image Sci., 3(3) (2010), 2010–277.Google Scholar
[20]Lu, T., Neittaanmäki, P. and Tai, X.-C., A parallel splitting up method and its application to Navier-Stokes equationss, Appl. Math. Lett., 4(2) (1991), 1991–25.Google Scholar
[21]Malik, J., Leung, Th. and Shi, J., Contour and texture analysis for image segmentation, Int. J. Comput. Vision, 43(1) (2001), 7–27.Google Scholar
[22]Mitiche, A. and Ben-Ayed, I., Variational and Level Set Methods in Image Segmentation, Springer-Verlag, 2010.Google Scholar
[23]Malladi, R., Sethian, J. A., and Vermuri, B. C., A fast level set based algorithm for topology independent shape modeling, J. Math. Imag. Vision, 6 (1996), 269–289.Google Scholar
[24]Mumford, D. and Shah, J., Optimal approximation by piecewise smooth functions and associated variational problem, Commun. Pure Appl. Math., 42 (1989), 577–685.CrossRefGoogle Scholar
[25]Osher, S. and Fedkiw, R., Level Set Methods and Dynamic Implicit Surfaces, Springer, Berlin, 2003.Google Scholar
[26]Ronfard, R., Region-based strategies for active contour models, Int. J. Comput. Vis., 13 (1994), 229–251.CrossRefGoogle Scholar
[27]Sethian, J. A., Fast marching methods, SIAM Rev., 41(2) (1999), 1999–199.Google Scholar
[28]Sethian, J. A., Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Material Science (Cambridge Univ. Press, London, 1999).Google Scholar
[29]Sen, D. and Pal, S. K., Histogram thresholding using fuzzy and rough measures of association error, IEEE Trans. Image Pro., 18(4) (2009), 2009–879.Google ScholarPubMed
[30]Tao, W. B. and Tai, X.-C., Multiple piecewise constant active contours for image segmentation using graph cuts optimization, UCLA CAM report 09–13, (2009).Google Scholar
[31]Vese, L. A. and Chan, T. F., A multiphase level set framework for image segmentation using the mumford and shah model, Int. J. Comput. Vision, 50(3) (2002), 271–293.CrossRefGoogle Scholar
[32]Vincent, C. and Soille, P., Watersheds in digital spaces: an efficient algorithm based on immersion simulations, IEEE Trans. Patten Anal., 13 (1991), 583–598.Google Scholar
[33]Weickert, J. and Kuhne, G., Fast methods for implicit active conture models, Geometric Level Set Methodes in “Imaging, Vision and Graphics”, pp. 43–58, eds. Osher, S. and Paragios, N., Springer, 2003.Google Scholar
[34]Weickert, J., Haar Romeny, B. M. ter and Viergever, M. A., Efficient and reliable schemes for nonlinear diffusion filtering, IEEE Trans. Image Proc., 7(3) (1998), 1998–398.Google Scholar
[35]Zucker, S. W., Region growing: childhood and adolescence, Comput. Graph. Image Proc., 5 (1976), 382–399.Google Scholar