Three-Materials Image Recover from Value Range Projection Data

  • Chuanlin LiuEmail author
  • Amit Yadav
  • Asif Khan
  • Jing Zou
  • Weizhen Hu
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 940)


In order to figure out the number of the tooth’s roots and subroots, only the bone, air and blood to be separated is enough. This paper proposed a new algorithm denoted Value Range Transform which inherits the idea of the Mojette transform to recover the value range of each pixel, instead of the exact value. According to the Hounsfield scale of the bone, air and blood, the value range of each pixel can easily tell the exact material of the pixel belong to. The Value Range Transform included the direct transform and the inverse transform. The value range projection data produced from the direct value range transform. From the value range projection data, the inverse transform can recover the three different materials of the scene. After examied by the experiments, the materials can be recovered from the projection data sets which Katz’s criterion are far to be checked.


Mojette transform Value range transform Three materials Projection data 


  1. 1.
    Liu, C., Yadav, A., Khan, A.: Limited number materials scene reconstructions. In: 3rd International Conference on Emerging Research in Electronics, Computer Science and Technology, August 2018Google Scholar
  2. 2.
    Liu, C., Yadav, A., Khan, A.: 4 materials scene reconstruction from line Mojette projections. In: 8th International Conference on Advances in Computing and Communication, July 2018CrossRefGoogle Scholar
  3. 3.
    Liu, C., Guedon, J.: Finding all solutions of three-material image reconstruction problem. J. South China Univ. Technol. (Nat. Sci. Ed.) 41(7), 114–119 (2013)Google Scholar
  4. 4.
    Guedon, J. (ed.): The Mojette Transform: Theory and Applications. ISTE Wiley, London and Hoboken (2009)Google Scholar
  5. 5.
    Guedon, J., Normand, N.: Chapter 4: reconstructability with the Mojette transform. In: The Mojette Transform: Theory and Applications, pp. 67–83. ISTE Wiley, London and Hoboken (2009)Google Scholar
  6. 6.
    Guedon, J., Liu, C.: The 2 and 3 materials scene reconstructed from some line Mojette projections. In: Image Processing Theory Tools and Applications (IPTA), Paris, pp. 189–194 (2010)Google Scholar
  7. 7.
    Liu, C., Guedon, J., Svalbe, I. Amouriq, Y.: Line Mojette ternary reconstructions and ghosts. In: IWCIA, Madrid, May 2011Google Scholar
  8. 8.
    Svalbe, I., Guedon, J.: Chapter 2: Discrete Verions of the Radon Transform. In: Guedon, J. (ed.) The Mojette Transform: Theory and Applications, pp. 21–38. ISTE Wiley, London and Hoboken (2009)Google Scholar
  9. 9.
    Kalender, W.A. (ed.): Computed Tomography: Fundamentals, System Technology Image Quality, Applications. ISTE Wiley, London and Hoboken (2011)zbMATHGoogle Scholar
  10. 10.
    Katz, M.: Questions of Uniqueness and Resolution in Reconstruction from Projections. Lecture Notes in Biomathematics, vol. 26. Springer, Heidelberg (1979). Scholar
  11. 11.
    Bruckheimer, M., Arcavi, A.: Farey series and Pick’s area theorem. Math. Intell. 17(4), 64–67 (1995)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Niqui, M.: Exact arithmetic on the Stern-Brocot tree. Discrete Algorithm 5, 356–379 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Jaffar, J., Maher, M.J.: Constraint logic programming: a survey. J. Logic Program. 19(20), 503–581 (1994)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kumar, V.: Algorithms for constraint-satisfaction problems: a survey. Artif. Intell. 13(1), 32–44 (1992)MathSciNetGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Chuanlin Liu
    • 1
    Email author
  • Amit Yadav
    • 1
  • Asif Khan
    • 2
  • Jing Zou
    • 3
  • Weizhen Hu
    • 1
  1. 1.Chengdu Neusoft UniversityChengduPeople’s Republic of China
  2. 2.Crescent Institute of Science and TechnologyChennaiIndia
  3. 3.Kyland Technology Co., Ltd.BeijingPeople’s Republic of China

Personalised recommendations