Abstract
A framework for optimisation of specific criteria across the shape variability found in a population is proposed. The method is based on level set segmentation in the parametric space defined by Principal Component Analysis (PCA). The efficient narrow band evolution of the level set allows to search for the instances only in the neighborhood of the zero level set and not in the whole shape space. We are able to optimise any given criterion not to provide a single best fitting instance in the shape space, but rather to provide a group of instances that meet the criterion. This effectively defines a partition in the shape space, which can have any topology. The method works for data of any dimension, determined by the number of principal components retained. Results are shown on the application to shape analysis of human femora.
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
Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models - their training and applications. Comp. Vis. Image Underst. 61(2) (1995)
Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)
Rajamani, K.T., Styner, M.A., Talib, H., Zheng, G., Nolte, L.P., González, M.A.: Statistical deformable bone models for robust 3d surface extrapolation from sparse data. Medical Image Analysis 11(2), 99–109 (2007)
Sierra, R., Zsemlye, G., Szekely, G., Bajka, M.: Generation of variable anatomical models for surgical training simulators. Medical Image Analysis 10(2), 275–285 (2006)
Leventon, M., Grimson, W.E.L., Faugeras, O., Wells, W.M.: Level set based segmentation with intensity and curvature priors. In: Procedings of IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (2000)
Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Visualisation 1, 321–331 (1980)
McInerney, T., Terzopoulos, D.: Deformable models in medical images analysis: a survey. Medical Image Analysis 1(2), 91–108 (1996)
Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42, 577–685 (1989)
Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Transactions on Image Processing 10, 266–277 (2001)
Chen, X.F., Guan, Z.C.: Image segmentation based on Mumford-Shah functional. Journal of Zhejiang University SCIENCE 5, 123–128 (2004)
Tsai, A., Yezzi, A., Willsky, A.S.: Curve evolution implementation of the Mumford-Shah functional for image segmentation - denoising, interpolation, and magnification. IEEE Trans. on Image Processing 10, 1169–1186 (2001)
Zhao, H.-K., Chan, T., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. of Computational Physics 127, 179–195 (1996)
Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation. Journal of Computational Physics 79, 12–49 (1988)
Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton (1992)
Adalsteinsson, D., Sethian, J.A.: A fast level set method for propagating interfaces. Journal of Computational Physics 118, 269–277 (1995)
Li, C., Xu, C., Konwar, K.M., Fox, M.D.: Fast distance preserving level set evolution for medical image segmentation. In: Proceedings of ICARCV (2006)
Brechbühler, C., Gerig, G., Kübler, O.: Parametrization of closed surfaces for 3-d shape description. Comp. Vis. Image Underst. 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 modelling. IEEE Transactions on Medical Imaging 21(5), 525–537 (2002)
Platzer, W., Kahle, W., Frotscher, M.: Color Atlas and Textbook of Human Anatomy: Locomotor System. Thieme Medical Publishers (2004)
Tannast, M., Kubiak-Langer, M., Langlotz, F., Puls, M., Murphy, S.B., Siebenrock, K.: Noninvasive three-dimensional assessment of femoroacetabular impingement. Journal of Orthopaedic Research 25, 122–131 (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kozic, N., González Ballester, M.Á., Tannast, M., Nolte, L.P., Reyes, M. (2008). Statistical Shape Space Analysis Based on Level Sets. In: Dohi, T., Sakuma, I., Liao, H. (eds) Medical Imaging and Augmented Reality. MIAR 2008. Lecture Notes in Computer Science, vol 5128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79982-5_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-79982-5_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79981-8
Online ISBN: 978-3-540-79982-5
eBook Packages: Computer ScienceComputer Science (R0)