Abstract
This paper presents a new method for constructing compact statistical point-based models of ensembles of similar shapes that does not rely on any specific surface parameterization. The method requires very little preprocessing or parameter tuning, and is applicable to a wider range of problems than existing methods, including nonmanifold surfaces and objects of arbitrary topology. The proposed method is to construct a point-based sampling of the shape ensemble that simultaneously maximizes both the geometric accuracy and the statistical simplicity of the model. Surface point samples, which also define the shape-to-shape correspondences, are modeled as sets of dynamic particles that are constrained to lie on a set of implicit surfaces. Sample positions are optimized by gradient descent on an energy function that balances the negative entropy of the distribution on each shape with the positive entropy of the ensemble of shapes. We also extend the method with a curvature-adaptive sampling strategy in order to better approximate the geometry of the objects. This paper presents the formulation; several synthetic examples in two and three dimensions; and an application to the statistical shape analysis of the caudate and hippocampus brain structures from two clinical studies.
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
Brechbühler, C., Gerig, G., Kübler, O.: Parametrization of closed surfaces for 3-d shape description. Computer Vision Image Understanding 61, 154–170 (1995)
Davies, R.H., Twining, C.J., Cootes, T.F., Waterton, J.C., Taylor, C.J.: A minimum description length approach to statistical shape modeling. IEEE Trans. Med. Imaging 21(5), 525–537 (2002)
Audette, M., Ferrie, F., Peters, T.: An algorithmic overview of surface registration techniques for medical imaging. Medical Image Analysis 4, 201–217 (2000)
Frangi, A., Rueckert, D., Schnabel, J., Niessen, W.: Automatic construction of multiple-object three-dimensional statistical shape models: Application to cardiac modeling. IEEE Trans. Med. Imaging 21(9), 1151–1166 (2002)
Twining, C.J., Cootes, T.F., Marsland, S., Petrovic, V.S., Schestowitz, R., Taylor, C.J.: A unified information-theoretic approach to groupwise non-rigid registration and model building. In: Christensen, G.E., Sonka, M. (eds.) IPMI 2005. LNCS, vol. 3565, pp. 1–14. Springer, Heidelberg (2005)
Kotcheff, A., Taylor, C.: Automatic Construction of Eigenshape Models by Direct Optimization. Medical Image Analysis 2, 303–314 (1998)
Davies, R.H., Twining, C.J., Cootes, T.F., Waterton, J.C., Taylor, C.J.: 3d statistical shape models using direct optimisation of description length. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2352, pp. 3–20. Springer, Heidelberg (2002)
Thodberg, H.H.: Minimum description length shape and appearance models. In: Taylor, C.J., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 51–62. Springer, Heidelberg (2003)
Styner, M., Lieberman, J., Gerig, G.: Boundary and medial shape analysis of the hippocampus in schizophrenia. In: Ellis, R.E., Peters, T.M. (eds.) MICCAI 2003. LNCS, vol. 2879, pp. 464–471. Springer, Heidelberg (2003)
Cover, T., Thomas, J.: Elements of Information Theory. Wiley, Chichester (1991)
Boissonnat, J.D., Oudot, S.: Provably good sampling and meshing of surfaces. Graphical Models 67, 405–451 (2005)
Meyer, M.D., Georgel, P., Whitaker, R.T.: Robust particle systems for curvature dependent sampling of implicit surfaces. In: Proceedings of the International Conference on Shape Modeling and Applications 2005, pp. 124–133 (2005)
Meyer, M.D., Nelson, B., Kirby, R.M., Whitaker, R.: Particle systems for efficient and accurate high-order finite element visualization. IEEE Transactions on Visualization and Computer Graphics (Under Review)
Kindlmann, G., Whitaker, R., Tasdizen, T., Moller, T.: Curvature-based transfer functions for direct volume rendering. In: Proceedings of IEEE Visualization, pp. 512–520 (2003)
Sethian, J.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1996)
Goodall, C.: Procrustes methods in the statistical analysis of shape. J.R. Statistical Society B 53, 285–339 (1991)
Styner, M., Xu, S., El-SSayed, M., Gerig, G.: Correspondence evaluation in local shape analysis and structural subdivision. In: IEEE Symposium on Biomedical Imaging ISBI 2007, in print (2007)
Levitt, J., Westin, C.F., Nestor, P., Estepar, R., Dickey, C., Voglmaier, M., Seidman, L., Kikinis, R., Jolesz, F., McCarley, R., Shenton, M.: Shape of caudate nucleus and its cognitive correlates in neuroleptic-naive schizotypal personality disorder. Biol. Psychiatry 55, 177–184 (2004)
Styner, M., Oguz, I., Xu, S., Brechbühler, C., Pantazis, D., Levitt, J., Shenton, M., Gerig, G.: Framework for the statistical shape analysis of brain structures using SPHARM-PDM. The Insight Journal (2006)
Nain, D., Niethammer, M., Levitt, J., Shenton, M., Gerig, G., Bobick, A., Tannenbaum, A.: Statistical shape analysis of brain structures using spherical wavelets. In: IEEE Symposium on Biomedical Imaging ISBI 2007, in print
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Cates, J., Fletcher, P.T., Styner, M., Shenton, M., Whitaker, R. (2007). Shape Modeling and Analysis with Entropy-Based Particle Systems. 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_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-73273-0_28
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)