American Institute of Mathematical Sciences

Advanced
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 & Imaging, 2010, 4 (2) : 257-271. doi: 10.3934/ipi.2010.4.257
[1]

Arun K. Kulshreshth, Andreas Alpers, Gabor T. Herman, Erik Knudsen, Lajos Rodek, Henning F. Poulsen. A greedy method for reconstructing polycrystals from three-dimensional X-ray diffraction data. Inverse Problems & Imaging, 2009, 3 (1) : 69-85. doi: 10.3934/ipi.2009.3.69
[2]

Chengxiang Wang, Li Zeng, Yumeng Guo, Lingli Zhang. Wavelet tight frame and prior image-based image reconstruction from limited-angle projection data. Inverse Problems & Imaging, 2017, 11 (6) : 917-948. doi: 10.3934/ipi.2017043
[3]

Wenzhong Zhu, Huanlong Jiang, Erli Wang, Yani Hou, Lidong Xian, Joyati Debnath. X-ray image global enhancement algorithm in medical image classification. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1297-1309. doi: 10.3934/dcdss.2019089
[4]

Silvia Allavena, Michele Piana, Federico Benvenuto, Anna Maria Massone. An interpolation/extrapolation approach to X-ray imaging of solar flares. Inverse Problems & Imaging, 2012, 6 (2) : 147-162. doi: 10.3934/ipi.2012.6.147
[5]

Yuming Qin, Yang Wang, Xing Su, Jianlin Zhang. Global existence of solutions for the three-dimensional Boussinesq system with anisotropic data. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1563-1581. doi: 10.3934/dcds.2016.36.1563
[6]

Dan Jane, Gabriel P. Paternain. On the injectivity of the X-ray transform for Anosov thermostats. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 471-487. doi: 10.3934/dcds.2009.24.471
[7]

Victor Churchill, Rick Archibald, Anne Gelb. Edge-adaptive $ \ell_2 $ regularization image reconstruction from non-uniform Fourier data. Inverse Problems & Imaging, 2019, 13 (5) : 931-958. doi: 10.3934/ipi.2019042
[8]

Habib Ammari, Josselin Garnier, Vincent Jugnon. Detection, reconstruction, and characterization algorithms from noisy data in multistatic wave imaging. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 389-417. doi: 10.3934/dcdss.2015.8.389
[9]

François Rouvière. X-ray transform on Damek-Ricci spaces. Inverse Problems & Imaging, 2010, 4 (4) : 713-720. doi: 10.3934/ipi.2010.4.713
[10]

Chuanxin Zhao, Lin Jiang, Kok Lay Teo. A hybrid chaos firefly algorithm for three-dimensional irregular packing problem. Journal of Industrial & Management Optimization, 2020, 16 (1) : 409-429. doi: 10.3934/jimo.2018160
[11]

Masaru Ikehata, Mishio Kawashita. An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method. Inverse Problems & Imaging, 2014, 8 (4) : 1073-1116. doi: 10.3934/ipi.2014.8.1073
[12]

Zhenhua Zhao, Yining Zhu, Jiansheng Yang, Ming Jiang. Mumford-Shah-TV functional with application in X-ray interior tomography. Inverse Problems & Imaging, 2018, 12 (2) : 331-348. doi: 10.3934/ipi.2018015
[13]

Jakob S. Jørgensen, Emil Y. Sidky, Per Christian Hansen, Xiaochuan Pan. Empirical average-case relation between undersampling and sparsity in X-ray CT. Inverse Problems & Imaging, 2015, 9 (2) : 431-446. doi: 10.3934/ipi.2015.9.431
[14]

Adam Larios, E. S. Titi. On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 603-627. doi: 10.3934/dcdsb.2010.14.603
[15]

Yunmei Chen, Xiaojing Ye, Feng Huang. A novel method and fast algorithm for MR image reconstruction with significantly under-sampled data. Inverse Problems & Imaging, 2010, 4 (2) : 223-240. doi: 10.3934/ipi.2010.4.223
[16]

Masaru Ikehata, Esa Niemi, Samuli Siltanen. Inverse obstacle scattering with limited-aperture data. Inverse Problems & Imaging, 2012, 6 (1) : 77-94. doi: 10.3934/ipi.2012.6.77
[17]

Ryan Compton, Stanley Osher, Louis-S. Bouchard. Hybrid regularization for MRI reconstruction with static field inhomogeneity correction. Inverse Problems & Imaging, 2013, 7 (4) : 1215-1233. doi: 10.3934/ipi.2013.7.1215
[18]

Wenxiang Cong, Ge Wang, Qingsong Yang, Jia Li, Jiang Hsieh, Rongjie Lai. CT image reconstruction on a low dimensional manifold. Inverse Problems & Imaging, 2019, 13 (3) : 449-460. doi: 10.3934/ipi.2019022
[19]

Frank Natterer. Incomplete data problems in wave equation imaging. Inverse Problems & Imaging, 2010, 4 (4) : 685-691. doi: 10.3934/ipi.2010.4.685
[20]

Alfred K. Louis. Diffusion reconstruction from very noisy tomographic data. Inverse Problems & Imaging, 2010, 4 (4) : 675-683. doi: 10.3934/ipi.2010.4.675

2018 Impact Factor: 1.469

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences