Abstract
Prior knowledge about shape may be quite important for image segmentation. In particular, a number of different methods have been proposed to compute the statistics on a set of training shapes, which are then used for a given image segmentation task to provide the shape prior. In this work, we perform a comparative analysis of shape learning techniques such as linear PCA, kernel PCA, locally linear embedding and propose a new method, kernelized locally linear embedding for doing shape analysis. The surfaces are represented as the zero level set of a signed distance function and shape learning is performed on the embeddings of these shapes. We carry out some experiments to see how well each of these methods can represent a shape, given the training set.
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
Terzopoulos, D., Szeliski, R.: Tracking with Kalman Snakes. In: Active Vision, pp. 3–20. MIT Press, Cambridge (1992)
Ayache, N., Cohen, I., Herlin, I.: Medical image tracking. In: Active Vision, pp. 3–20. MIT Press, Cambridge (1992)
Blake, A., Yuille, A. (eds.): Active Vision. MIT Press, Cambridge (1992)
Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging, Vision and Graphics. Springer, Heidelberg (2003)
Dambreville, S., Rathi, Y., Tannenbaum, A.: Shape-based approach to robust image segmentation using kernel pca. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2006)
Cootes, T., Taylor, C., Cooper, D., Graham, J.: Active shape models, their training and application. In: Computer Vision and Image Understanding, vol. 61, pp. 38–59 (1995)
Faugeras, O., Gomes, J.: Dynamic shapes of arbitrary dimension: the vector distance functions. In: Cipolla, R., Martin, R. (eds.) Proceedings of the Ninth IMA Conference on Mathematics of Surfaces. The Mathematics of Surfaces IX. Springer, Heidelberg (2000)
Cremers, D., Kohlberger, T., Schnörr, C.: Nonlinear shape statistics in mumford-shah based segmentation. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 93–108. Springer, Heidelberg (2002)
Leventon, M., Grimson, E., Faugeras, O.: Statistical shape influence in geodesic active contours. In: Proc. CVPR, pp. 1316–1324. IEEE, Los Alamitos (2000)
Tsai, A., Yezzi, A., Wells, W., Tempany, C., Tucker, D., Fan, A., Grimson, E., Willsky, A.: A shape-based approach to the sementation of medical imagery using level sets. IEEE Trans. on Medical Imaging 22, 137–153 (2003)
Gomes, J., Faugeras, O.: Shape representation as the intersection of n − k hypersurfaces. Technical Report 4011, INRIA (2000)
Osher, S.J., Sethian, J.A.: Fronts propagation with curvature dependent speed: Algorithms based on hamilton-jacobi formulations. Journal of Computational Physics 79, 12–49 (1988)
Wang, Y., Staib, L.: Boundary finding with correspondence using statistical shape models. In: Proc. CVPR, pp. 338–345 (1998)
Scholkopf, B., Smola, A., Muller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Technical report, Max-Planck-Institute fur biologische Kybernetik (1996)
Rathi, Y., Dambreville, S., Tannenbaum, A.: Statistical shape analysis using kernel pca. In: SPIE, Electronic Imaging (2006)
Mika, S., Scholkopf, B., Smola, A., Muller, K.R., Scholz, M., Ratsch, G.: Kernel pca and de-noising in feature spaces. Advances in Neural Information Processing Systems 11
Kwok, J., Tsang, I.: The pre-image problem in kernel methods. In: 20th Intl. Conference on Machine Learning (2003)
Funkhouser, T., Kazhdan, M., Shilane, P., Min, P., Kiefer, W., Tal, A., Rusinkiewicz, S., Dobkin, D.: Modeling by example. In: ACM Transactions on Graphics (SIGGRAPH 2004) (2004)
Saul, L.K., Roweis, S.: An introduction to locally linear embedding, http://www.cs.toronto.edu/~roweis/lle/papers/lleintro.pdf
Ridder, D., Duin, R.: Locally linear embedding for classification. Technical Report PH-2002-01, Pattern Recognition Group, Delft University of Technology (2002)
DeCoste, D.: Visualizing mercer kernel feature spaces via kernelized locally-linear embeddings. In: 8th Intl. Conf. on Neural Information Processing (2001)
Chan, T., Zhu, W.: Level set based shape prior segmentation. Technical report, Computational Applied Mathematics, UCLA (2003)
Srivastava, A., Joshi, S., Mio, W., Liu, X.: Statistical shape analysis: Clustering, learning and testing. Trans. PAMI (2005)
Yezzi, A., Mennucci, A.: Metrics in the space of curves (2004), http://arxiv.org/abs/math.DG/0412454
Michor, P., Mumford, D.: Riemannian geomtries of space of plane curves, http://front.math.ucdavis.edu/math.DG/0312384
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rathi, Y., Dambreville, S., Tannenbaum, A. (2006). Comparative Analysis of Kernel Methods for Statistical Shape Learning. In: Beichel, R.R., Sonka, M. (eds) Computer Vision Approaches to Medical Image Analysis. CVAMIA 2006. Lecture Notes in Computer Science, vol 4241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889762_9
Download citation
DOI: https://doi.org/10.1007/11889762_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46257-6
Online ISBN: 978-3-540-46258-3
eBook Packages: Computer ScienceComputer Science (R0)