Abstract
In this paper, we propose an Expectation-Maximization (EM) approach to separate a shape database into different shape classes, while simultaneously estimating the shape contours that best exemplify each of the different shape classes. We begin our formulation by employing the level set function as the shape descriptor. Next, for each shape class we assume that there exists an unknown underlying level set function whose zero level set describes the contour that best represents the shapes within that shape class. The level set function for each example shape is modeled as a noisy measurement of the appropriate shape class’s unknown underlying level set function. Based on this measurement model and the judicious introduction of the class labels as hidden data, our EM formulation calculates the labels for shape classification and estimates the shape contours that best typify the different shape classes. This resulting iterative algorithm is computationally efficient, simple, and accurate. We demonstrate the utility and performance of this algorithm by applying it to two medical applications.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Basri, R., Costa, L., Geiger, D., Jacobs, D.: Determining the similarity of deformable shapes. IEEE Workshop: Phys. Based Modeling in Comput. Vis. 135–143 (1995)
Cohen, I., Ayache, N., Sulger, P.: Tracking points on deformable objects using curvature information. In: ECCV, pp. 458–466 (1992)
Del Bimbo, A., Pala, P.: Visual image retrieval by elastic matching of user sketches. IEEE Trans. PAMI 19, 121–132 (1997)
Dempster, A., Laird, N., Rubin, D.: Maximum-likelihood from incomplete data via the EM algorithm. J. of Royal Statist. Soc. Ser B 39, 1–38 (1977)
Dionisio, C., Kim, H.: A supervised shape classification technique invariant under rotation and scaling. In: Int’l Telecommunications Symposium (2002)
Gdalyahu, Y., Weinshal, D.: Flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes. IEEE Trans. on PAMI 21, 1312–1328 (1999)
Golland, P., Grimson, E., Kikinis, R.: Statistical shape analysis using fixed topology skeletons: corpus callosum study. In: IPMI, pp. 382–387 (1999)
Kawata, Y., Niki, N., Ohmatsu, H., Kakinuma, R., Eguchi, K., Kaneko, M., Moriyama, N.: Classification of pulmonary nodules in thin-section CT images based on shape characteristics. IEEE Trans. on Nucl. Sci. 45, 3075–3082 (1998)
Osher, S., Sethian, J.: Fronts propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. of Comput. Phys. 79, 12–49 (1988)
Paragios, N., Rousson, M.: Shape priors for level set representations. In: ECCV, Copenhagen, Denmark (June 2002)
Tsai, A., Yezzi, A., Wells, W., Tempany, C., Tucker, D., Fan, A., Grimson, E., Willsky, A.: A shaped-based approach to segmentation of medical imagery using level sets. IEEE Trans. on Medical Imaging 22, 137–154 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tsai, A., Wells, W., Warfield, S.K., Willsky, A. (2004). Level Set Methods in an EM Framework for Shape Classification and Estimation. In: Barillot, C., Haynor, D.R., Hellier, P. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2004. MICCAI 2004. Lecture Notes in Computer Science, vol 3216. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30135-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-30135-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22976-6
Online ISBN: 978-3-540-30135-6
eBook Packages: Springer Book Archive