We propose a nonlinear statistical shape model for level set segmentation that can be efficiently implemented. Given a set of training shapes, we perform a kernel density estimation in the low-dimensional subspace spanned by the training shapes. In this way, we are able to combine an accurate model of the statistical shape distribution with efficient optimization in a finite-dimensional subspace. In a Bayesian inference framework, we integrate the nonlinear shape model with a nonparametric intensity model and a set of pose parameters that are estimated in a more direct data-driven manner than in previously proposed level set methods. Quantitative results show superior performance (regarding runtime and segmentation accuracy) of the proposed nonparametric shape prior over existing approaches.
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.
9 References
Dervieux A, Thomasset F. 1979. A finite element method for the simulation of Rayleigh- Taylor instability. In Approximation methods for Navier-Stokes problems, pp. 145-158. Ed R Rautmann. Berlin: Springer.
Osher SJ, Sethian JA. 1988. Front propagation with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79:12-49.
Caselles V, Catt é F, Coll T, Dibos F. 1993. A geometric model for active contours in image processing. Num Math 66:1-31.
Malladi R, Sethian JA, Vemuri BC. 1994. A topology independent shape modeling scheme. In Proceedings of the SPIE conference on geometric methods in computer vision, Vol. 2031, pp. 246-258. Bellingham, WA: SPIE.
Kichenassamy S, Kumar A, Olver PJ, Tannenbaum A, Yezzi AJ. 1995. Gradient flows and geometric active contour models. In Proceedings of the fifth international conference computer vision (ICCV’95), pp. 810-815. Washington, DC: IEEE Computer Society.
Leventon M, Grimson W, Faugeras O. 2000. Statistical shape influence in geodesic active contours. In Proceedings of the IEEE international conference on computer vision and pattern recognition (CVPR), Vol. 1, pp. 316-323. Washington, DC: IEEE Computer Society.
Tsai A, Yezzi AJ, Willsky AS. 2003. A shape-based approach to the segmentation of medical imagery using level sets. IEEE Trans Med Imaging, 22(2):137-154.
Cremers D, Osher SJ, Soatto S. 2006. Kernel density estimation and intrinsic alignment for shape priors in level set segmentation. Int J Comput Vision. 69(3):335-351.
Rousson M, Paragios N, Deriche R. 2004. Implicit active shape models for 3d segmentation in MRI imaging. In Proceedings of the international conference on medical image computing and computer-assisted intervention (MICCAI 2000). Lecture notes in computer science, Vol. 2217, pp. 209-216. New York: Springer.
Dam EB, Fletcher PT, Pizer S, Tracton G, Rosenman J. 2004. Prostate shape modeling based on principal geodesic analysis bootstrapping. In Proceedings of the international conference on medical image computing and computer-assisted intervention (MICCAI 2003). Lecture notes in computer science, Vol. 2217, pp. 1008-1016. New York: Springer.
Freedman D, Radke RJ, Zhang T, Jeong Y, Lovelock DM, Chen GT. 2005. Model-based seg- mentation of medical imagery by matching distributions. IEEE Trans Med Imaging 24(3):281-292.
Rosenblatt F. 1956. Remarks on some nonparametric estimates of a density function. Ann Math Stat 27:832-837.
Silverman BW. 1992. Density estimation for statistics and data analysis. London: Chapman and Hall.
Paragios N, Deriche R. 2002. Geodesic active regions and level set methods for supervised texture segmentation. Int J Comput Vision 46(3):223-247.
Chan LA Vese TF. 2001. Active contours without edges. IEEE Trans Med Imaging, 10(2):266-277.
Rousson, M., Cremers, D., 2005. Efficient Kernel Density Estimation of Shape and Intensity Priors for Level Set Segmentation, International conference on medical image computing and computed-assisted intervention (MICCAI 2005), 2: 757-764.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Cremers, D., Rousson, M. (2007). Efficient Kernel Density Estimation Of Shape And Intensity Priors For Level Set Segmentation. In: Deformable Models. Topics in Biomedical Engineering. International Book Series. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68343-0_13
Download citation
DOI: https://doi.org/10.1007/978-0-387-68343-0_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-31204-0
Online ISBN: 978-0-387-68343-0
eBook Packages: EngineeringEngineering (R0)