Abstract
We introduce Localized Components Analysis (LoCA) for describing surface shape variation in an ensemble of biomedical objects using a linear subspace of spatially localized shape components. In contrast to earlier methods, LoCA optimizes explicitly for localized components and allows a flexible trade-off between localized and concise representations. Experiments comparing LoCA to a variety of competing shape representation methods on 2D and 3D shape ensembles establish the superior ability of LoCA to modulate the locality-conciseness tradeoff and generate shape components corresponding to intuitive modes of shape variation. Our formulation of locality in terms of compatibility between pairs of surface points is shown to be flexible enough to enable spatially-localized shape descriptions with attractive higher-order properties such as spatial symmetry.
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
Carmichael, O.T., Thompson, P.M., Dutton, R.A., Lu, A., Lee, S.E., Lee, J.Y., Kuller, L.H., Lopez, O.L., Aizenstein, H.J., Meltzer, C.C., Liu, Y., Toga, A.W., Becker, J.T.: Mapping ventricular changes related to dementia and mild cognitive impairment in a large community-based cohort. In: IEEE International Symposium on Biomedical Imaging (ISBI), IEEE Computer Society Press, Los Alamitos (2006)
Curran-Everett, D.: Multiple comparisons: philosophies and illustrations. Am. J. Physiol. Regul. Integr. Comp. Physiol. 279(1), 1–8 (2000)
Thompson, P., Dutton, R., Hayashi, K., Lu, A., Lee, S., Lee, J., Lopez, O., Aizenstein, H., Toga, A., Becker, J.: 3d mapping of ventricular and corpus callosum abnormalities in hiv/aids. NeuroImage 31(1), 12–23 (2006)
Cootes, T.F., Hill, A., Taylor, C.J., Haslam, J.: The use of active shape models for locating structures in medical images. Image and Vision Computing 12(6), 355–366 (1994)
Bookstein, F.L.: Morphometric tools for landmark data: Geometry and Biology. Cambridge Univ. Press, New York (1991)
Allen, B., Curless, B., Popovic, Z.: The space of human body shapes: reconstruction and parameterization from range scans. In: Proceedings of ACM SIGGRAPH, pp. 587–594. ACM Press, New York (2003)
Chennubhotla, C., Jepson, A.: Sparse PCA: Extracting multi-scale structure from data. In: Proc. ICCV, Vancouver, pp. 641–647. IEEE, Washington, DC, USA (2001)
Zou, H., Hastie, T., Tibshirani, R.: Sparse principal component analysis. Journal of Computational and Graphical Statistics 15(2), 265–286 (2006)
Sjöstrand, K., Stegmann, M.B., Larsen, R.: Sparse principal component analysis in medical shape modeling. In: Reinhardt, J.M., Pluim, J.P.W. (eds.) Proc. SPIE Medical Imaging: Image Processing. vol. 6144 (2006)
Johnstone, I.M., Lu, A.Y.: Sparse principal components analysis. In: Proceedings, IMS Mini-Meeting on Functional Data Analysis (2003), http://www.stat.ufl.edu/symposium/2003/fundat/Archive/
Stegmann, M.B., Sjöstrand, K., Larsen, R.: Sparse modeling of landmark and texture variability using the orthomax criterion. In: Reinhardt, J.M., Pluim, J.P.W., eds.: Proc. SPIE Medical Imaging: Image Processing. vol. 6144 (2006)
Üzümcü, M., Frangi, A., Sonka, M., Reiber, J., Lelieveldt, B.: ICA vs. In: Ellis, R.E., Peters, T.M. (eds.) MICCAI 2003. LNCS, vol. 2878, pp. 451–458. Springer, Heidelberg (2003)
Ballester, M.A.G., Linguraru, M.G., Aguirre, M.R., Ayache, N.: On the adequacy of principal factor analysis for the study of shape variability. In: Fitzpatrick, J.M., Reinhardt, J.M., eds.: In: Proc. SPIE Medical Imaging: Image Processing. vol. 5747 (2005)
Vermaak, J., Perez, P.: Constrained subspace modeling. In: Conf. Computer Vision and Pattern Recog, CVPR’03, Madison, Wisconsin (June 2003)
Pizer, S., Fritsch, D., Yushkevich, P., Johnson, V., Chaney, E., Gerig, G.: Segmentation, registration, and measurement of shape variation via image object shape. IEEE Trans. Med. Imaging 18(10), 851–865 (1999)
Press, W., Teukolsky, S., Vetterling, F.B.: Numerical Recipes In C, 2nd edn. Cambridge University Press, Cambridge (1992)
Witelson, S.: Hand and sex differences in the isthmus and body of the corpus callosum: a postmortem morphological study. Brain 112, 799–835 (1989)
Ghosh, D., Amenta, N.: Landmark transfer using deformable models. Technical Report CSE-2007-6, Department of Computer Science, University of California, Davis (2007)
Frost, S.R., Marcus, L.F., Bookstein, F.L., Reddy, D.P., Delson, E.: Cranial allometry, phylogeography, and systematics of large-bodied papionins (primates: Cercopitihecinae) inferred from geometric morphometric analysis of landmark data. The Antatomical Record Part A 275A, pp. 1048–1072 (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Alcantara, D. et al. (2007). Localized Components Analysis. In: Karssemeijer, N., Lelieveldt, B. (eds) Information Processing in Medical Imaging. IPMI 2007. Lecture Notes in Computer Science, vol 4584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73273-0_43
Download citation
DOI: https://doi.org/10.1007/978-3-540-73273-0_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73272-3
Online ISBN: 978-3-540-73273-0
eBook Packages: Computer ScienceComputer Science (R0)