Bayes Reconstruction of Missing Teeth
- 107 Downloads
We propose a method for restoring the surface of tooth crowns in a 3D model of a human denture, so that the pose and anatomical features of the tooth will work well for chewing. This is achieved by including information about the position and anatomy of the other teeth in the mouth. Our system contains two major parts: A statistical model of a selection of tooth shapes and a reconstruction of missing data.
We use a training set consisting of 3D scans of dental cast models obtained with a laser scanner, and we have build a model of the shape variability of the teeth, their neighbors, and their antagonists, using the eigenstructure of the covariance matrix, also known as Principle Component Analysis (PCA). PCA is equivalent to fitting a multivariate Gaussian distribution to the data and the principle directions constitute a linear model for stochastic data and is used both for a data reduction or equivalently noise elimination and for data analysis. However for small sets of high dimensional data, the log-likelihood estimator for the covariance matrix is often far from convergence, and therefore reliable models must be obtained by use of prior information. We propose a natural and intrinsic regularization of the log-likelihood estimate based on differential geometrical properties of teeth surfaces, and we show general conditions under which this may be considered a Bayes prior.
Finally we use Bayes method to propose the reconstruction of missing data, for e.g. finding the most probable shape of a missing tooth based on the best match with our shape model on the known data, and we superior improved reconstructions of our full system.
KeywordsPrinciple component analysis Bayes method Missing data Reconstruction of teeth
Unable to display preview. Download preview PDF.
- 2.Gürke, S.: Restoration of teeth by geometrically deformable models (1997). http://citeseer.comp.nus.edu.sg/gurke97restoration.html
- 3.Hayashi, T., Tsuchida, J., Kato, K.: Semi-automatic design of tooth crown using a 3-D dental CAD system, Vocs-1B. In: Proceedings of the 22nd Annual EMBS International Conference, Chicago IL, USA, July 2000, pp. 565–566 (2000) Google Scholar
- 4.Blanz, V., Mehl, A., Veter, T., Seidel, H.P.: A statistical method for robust 3D surface reconstruction from sparse data. In: Int. Symp. on 3D Data Processing, Visualization and Transmission, Thessaloniki, Greece (2004) Google Scholar
- 5.Hommelhoff Jensen, K., Sporring, J.: Reconstructing teeth with bite information. In: Ersbøll, B., Pedersen, K.S. (eds.) Proceedings of the Scandinavian Conference on Image Analysis (SCIA ’07). Lecture Notes in Computer Science, vol. 4522, pp. 102–111. Springer, Berlin (2007) Google Scholar
- 6.Pearson, K.: On lines and planes of closest fit to systems of points in space. Philos. Mag. 6(2), 559–572 (1901) Google Scholar
- 11.Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models—their training and application. Comput. Vis. Image Underst. 61(1) (1995) Google Scholar
- 12.Cootes, T.F., Taylor, C.J.: Statistical models of appearance for computer vision. Technical Report, University of Manchester to 1.8cm(March 2004). http://www.isbe.man.ac.uk/~bim/Models/app_models.pdf
- 13.de Bruijne, M., Lund, M.T., Tankó, L.B., Pettersen, P.C., Nielsen, M.: Quantitative vertebral morphometry using neighbor-conditional shape models. Med. Image Anal. (2007) Google Scholar
- 15.Pizer, S., Thall, A., Chen, D.: M-reps: A new object representation for graphics. Technical Report, University of North Carolina (1999) Google Scholar
- 16.Hutton, T.J., Buxton, B.F., Hammond, P.: Dense surface point distribution models of the human face. In: IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA), p. 153 (2001) Google Scholar
- 17.Blanz, V., Vetter, T.: A morphable model for the synthesis of 3d faces. In: Proc. of SIGGRAPH ’99, Los Angeles, August 1999, pp. 187–194 (1999) Google Scholar
- 18.Turk, G., O’Brien, J.F.: Variational implicit surfaces. Technical Report, Georgia Institute of Technology (May 1999). Tech Report GIT-GVU-99-15 Google Scholar
- 19.Wang, Y., Staib, L.H.: Boundary finding with correspondence using statistical shape models. Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pp. 338–345 (1998) Google Scholar
- 24.Gerschgorin, S.: Über die abgrenzung der eignewerte einer matrix. Izv. Akad. Nauk. USSR Otd. Fiz.-Mat. Nauk 7, 749–754 (1931) Google Scholar
- 25.Gershgorin circle theorem. http://en.wikipedia.org/wiki/Gershgorin_circle_theorem, September 8 2007
- 26.Blanz, V., Vetter, T.: Reconstructing the complete 3d shape of faces from partial information. Technical Report, University of Freiburg (2001). Computer Graphics Technical Report No. 1 Google Scholar