Abstract
A method for building statistical point distribution models is proposed. The novelty in this paper is the adaption of Markov random field regularization of the correspondence field over the set of shapes. The new approach leads to a generative model that produces highly homogeneous polygonized shapes and improves the capability of reconstruction of the training data. Furthermore, the method leads to an overall reduction in the total variance of the point distribution model. Thus, it finds correspondence between semi-landmarks that are highly correlated in the shape tangent space. The method is demonstrated on a set of human ear canals extracted from 3D-laser scans.
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, G.J., Cooper, D.H., Graham, J.: Training models of shape from sets of examples. In: British Machine Vision Conference: Selected Papers 1992, Springer, Berlin (1992)
Cootes, T., Cooper, D., Taylor, C., Graham, J.: Active shape models - their training and application. Comp. Vision and Image Understanding 61, 38–59 (1995)
Gower, J.: Generalized Procrustes analysis. Psychometrika 40, 33–51 (1975)
Larsen, R., Hilger, K.B.: Statistical 2D and 3D shape analysis using non-euclidean metrics. Medical Image Analysis (2003) (to appear)
Paulsen, R.R., Larsen, R., Laugesen, S., Nielsen, C., Ersbøll, B.K.: Building and testing a statistical shape model of the human ear canal. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2489, pp. 373–380. Springer, Heidelberg (2002)
Andresen, P.R., Nielsen, M.: Non-rigid registration by geometry-constrained diffusion. In: Taylor, C., Colchester, A. (eds.) MICCAI 1999. LNCS, vol. 1679, pp. 533–543. Springer, Heidelberg (1999)
Andresen, P.R., Bookstein, F.L., Conradsen, K., Ersbøll, B.K., Marsh, J., Kreiborg, S.: Surface-bounded growth modeling applied to human mandibles. IEEE Transactions on Medical Imaging 19, 1053–1063 (2000)
Nielsen, M., Johansen, P., Jackson, A., Lautrup, B.: Brownian warps: A least committed prior for non-rigid registration. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2489, pp. 557–564. Springer, Heidelberg (2002)
Davies, R., Cootes, T., Twining, C., Taylor, C.: An information theoretic approach to statistical shape modelling. In: British Machine Vision Conference, pp. 3–11 (2001)
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)
Bookstein, F.L.: Shape and the information in medical images: A decade of the morphometric synthesis. Comp. Vision and Image Understanding 66, 97–118 (1997)
Lorenz, C., Krahnstöver, N.: Generation of point-based 3D statistical shape models for anatomical objects. Comp. Vision and Image Understanding 77, 175–191 (2000)
Besag, J.: Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B 36, 192–236 (1974)
Geman, D.: Random fields and inverse problems in imaging. In: Saint-Flour lectures 1988. Lecture Notes in Mathematics, pp. 113–193. Springer, Heidelberg (1990)
Besag, J.: Towards Bayesian image analysis. Journal of Applied Statistics 16, 395–407 (1989)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721–741 (1984)
Vidal, R.V.V.: Applied simulated annealing. Lect. Notes in Econom. And Math. Syst., vol. 396. Springer, Berlin (1993)
Cohn, H., Fielding, M.: Simulated annealing: searching for an optimal temperature schedule. SIAM Journal of Optimization 9, 779–802 (1999)
Hilger, K.B.: Exploratory Analysis of Multivariate Data. PhD thesis, Informatics and Mathematical Modelling, Technical University of Denmark, DTU, Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby (2001)
Dryden, I., Mardia, K.: Statistical Shape Analysis. Wiley, Chichester (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Paulsen, R.R., Hilger, K.B. (2003). Shape Modelling Using Markov Random Field Restoration of Point Correspondences. In: Taylor, C., Noble, J.A. (eds) Information Processing in Medical Imaging. IPMI 2003. Lecture Notes in Computer Science, vol 2732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45087-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-45087-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40560-3
Online ISBN: 978-3-540-45087-0
eBook Packages: Springer Book Archive