American Institute of Mathematical Sciences

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May  2010, 4(2): 257-271. doi: 10.3934/ipi.2010.4.257

Three-dimensional dental X-ray imaging by combination of panoramic and projection data

Nuutti Hyvönen 1, , Martti Kalke 2, , Matti Lassas 3, , Henri Setälä 2, and  Samuli Siltanen 4,

1. 

Aalto University, Institute of Mathematics, P.O.Box 1100, FI-00076 Aalto, Finland
2. 

PaloDex Group, P.O.Box 20, FI-04301 Tuusula, Finland, Finland
3. 

University of Helsinki, Department of Mathematics and Statistics, FI-00014 Helsinki, Finland
4. 

Department of Mathematics and Statistics, University of Helsinki

Received  February 2009 Revised  December 2009 Published  May 2010

A novel three-dimensional dental X-ray imaging method is introduced, based on hybrid data collected with a dental panoramic device. Such a device uses geometric movement of the X-ray source and detector around the head of a patient to produce a panoramic image, where all teeth are in sharp focus and details at a distance from the dental arc are blurred. A digital panoramic device is reprogrammed to collect two-dimensional projection radiographs. Two complementary types of data are measured from a region of interest: projection data with a limited angle of view, and a panoramic image. Tikhonov regularization is applied to these data in order to produce three-dimensional reconstructions. The algorithm is tested with simulated data and real-world in vitro measurements from a dry mandible. Reconstructions from limited-angle projection data alone do provide the dentist with three-dimensional information useful for dental implant planning. Furthermore, adding panoramic data to the process improves the reconstruction precision in the direction of the dental arc. The presented imaging modality can be seen as a cost-effective alternative to a full-angle CT scanner.
Keywords: limited angle data, three-dimensional reconstruction., panoramic image, X-ray imaging, hybrid data, Tikhonov regularization.
Mathematics Subject Classification: Primary: 92C55; Secondary: 65F2.
Citation: Nuutti Hyvönen, Martti Kalke, Matti Lassas, Henri Setälä, Samuli Siltanen. Three-dimensional dental X-ray imaging by combination of panoramic and projection data. Inverse Problems and Imaging, 2010, 4 (2) : 257-271. doi: 10.3934/ipi.2010.4.257
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