Abstract
We propose a fast and robust segmentation model for piecewise smooth images. Rather than modeling each region with global statistics, we introduce local statistics in an energy formulation. The shape gradient of this new functional gives a contour evolution controlled by local averaging of image intensities inside and outside the contour. To avoid the computational burden of a direct estimation, we express these terms as the result of convolutions. This makes an efficient implementation via recursive filters possible, and gives a complexity of the same order as methods based on global statistics. This approach leads to results similar to the general Mumford-Shah model but in a faster way, without solving a Poisson partial differential equation at each iteration. We apply it to synthetic and real data, and compare the results with the piecewise smooth and piecewise constant Mumford-Shah models.
This is a preview of subscription content, log in via an institution to check access.
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., et al.: Image segmentation using active contours: Calculus of variations or shape gradients? SIAM Journal of Applied Mathematics 63(6), 2128–2154 (2003)
Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. International Journal of Computer Vision 22, 61–79 (1997)
Cremers, D., Rousson, M., Deriche, R.: A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape. International Journal of Computer Vision (2006)
Deriche, R.: Using Canny’s criteria to derive a recursively implemented optimal edge detector. The International Journal of Computer Vision 1(2), 167–187 (1987)
Dervieux, A., Thomasset, F.: A finite element method for the simulation of Raleigh-Taylor instability. Lecture Notes in Mathematics, vol. 771. Springer, Heidelberg (1979)
Juan, O., Keriven, R., Postelnicu, G.: Stochastic motion and the level set method in computer vision: Stochastic active contours. The International Journal of Computer Vision 69(1), 7–25 (2006)
Kichenassamy, S., et al.: Gradient flows and geometric active contour models. In: Proceedings of the 5th International Conference on Computer Vision, Boston, MA, June 1995, pp. 810–815. IEEE Computer Society Press, Los Alamitos (1995)
Kim, J., et al.: Nonparametric methods for image segmentation using information theory and curve evolution. In: IEEE International Conference on Image Processing, September 2002, pp. 797–800 (2002)
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–685 (1989)
Osher, S., Sethian, J.: Fronts propagation with curvature dependent speed: Algorithms based on Hamilton–Jacobi formulations. J. of Comp. Phys. 79, 12–49 (1988)
Paragios, N., Deriche, R.: Geodesic active regions and level set methods for supervised texture segmentation. The International Journal of Computer Vision 46(3), 223–247 (2002)
Rousson, M., Deriche, R.: A variational framework for active and adaptative segmentation of vector valued images. In: Proc. IEEE Workshop on Motion and Video Computing, Orlando, Florida, December 2002, pp. 56–62. IEEE Computer Society Press, Los Alamitos (2002)
Sethian, J.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Sciences. Cambridge Monograph on Applied and Computational Mathematics. Cambridge University Press, Cambridge (1999)
Tsai, A., Yezzi Jr., A., Willsky, A.S.: Curve evolution implementation of the mumford-shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Transactions on Image Processing 10(8), 1169–1186 (2001)
Vese, L.: Multiphase object detection and image segmentation. In: Osher, S., Paragios, N. (eds.) Geometric Level Set Methods in Imaging, Vision and Graphics, pp. 175–194. Springer, Heidelberg (2003)
Vese, L., Chan, T.: A multiphase level set framework for image segmentation using the mumford and shah model. International Journal of Computer Vision 50, 271–293 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Piovano, J., Rousson, M., Papadopoulo, T. (2007). Efficient Segmentation of Piecewise Smooth Images. In: Sgallari, F., Murli, A., Paragios, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72823-8_61
Download citation
DOI: https://doi.org/10.1007/978-3-540-72823-8_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72822-1
Online ISBN: 978-3-540-72823-8
eBook Packages: Computer ScienceComputer Science (R0)