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Bayes Reconstruction of Missing Teeth

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Abstract

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.

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Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, Universitetsparken 1, 2100, Copenhagen, Denmark

    Jon Sporring & Katrine Hommelhoff Jensen

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  1. Jon Sporring
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  2. Katrine Hommelhoff Jensen
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Correspondence to Jon Sporring.

Additional information

J. Sporring gratefully acknowledges Technical University of Denmark, Department of Informatics and Mathematical Modelling, Richard Petersens Plads DTU-Building 321, 2800 Lyngby, Denmark for making research facilities available during part of this work.

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Sporring, J., Hommelhoff Jensen, K. Bayes Reconstruction of Missing Teeth. J Math Imaging Vis 31, 245–254 (2008). https://doi.org/10.1007/s10851-008-0081-6

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  • DOI: https://doi.org/10.1007/s10851-008-0081-6

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