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Online Statistical Inference for Large-Scale Binary Images

  • Moo K. ChungEmail author
  • Ying Ji Chuang
  • Houri K. Vorperian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10434)

Abstract

We present a unified online statistical framework for quantifying a collection of binary images. Since medical image segmentation is often done semi-automatically, the resulting binary images may be available in a sequential manner. Further, modern medical imaging datasets are too large to fit into a computer’s memory. Thus, there is a need to develop an iterative analysis framework where the final statistical maps are updated sequentially each time a new image is added to the analysis. We propose a new algorithm for online statistical inference and apply to characterize mandible growth during the first two decades of life.

Notes

Acknowledgements

This work was supported by NIH Research Grants R01 DC6282, P-30 HD03352, UL1TR000427 and R01 EB022856.

References

  1. 1.
    Ashburner, J., Friston, K.: Why voxel-based morphometry should be used. NeuroImage 14, 1238–1243 (2001)CrossRefGoogle Scholar
  2. 2.
    Bagarinao, E., Nakai, T., Tanaka, Y.: Real-time functional MRI: development and emerging applications. Magn. Reson. Med. Sci. 5, 157–165 (2006)CrossRefGoogle Scholar
  3. 3.
    Blum, A.: On-line algorithms in machine learning. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms. LNCS, vol. 1442, pp. 306–325. Springer, Heidelberg (1998). doi: 10.1007/BFb0029575CrossRefGoogle Scholar
  4. 4.
    Chan, T.F., Golub, G.H., LeVeque, R.J.: Algorithms for computing the sample variance: analysis and recommendations. Am. Stat. 37, 242–247 (1983)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Chung, M.K., Qiu, A., Seo, S., Vorperian, H.K.: Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images. Med. Image Anal. 22, 63–76 (2015)CrossRefGoogle Scholar
  6. 6.
    Deng, C.Y.: A generalization of the Sherman-Morrison-Woodbury formula. Appl. Math. Lett. 24, 1561–1564 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Finch, T.: Incremental calculation of weighted mean and variance. University of Cambridge, 4:11–4:15 (2009)Google Scholar
  8. 8.
    Jaakkola, T., Jordan, M.: A variational approach to bayesian logistic regression models and their extensions. In: Sixth International Workshop on Artificial Intelligence and Statistics, vol. 82 (1997)Google Scholar
  9. 9.
    Karp, R.M.: On-line algorithms versus off-line algorithms: how much is it worth to know the future? In: IFIP Congress, vol. 12, pp. 416–429 (1992)Google Scholar
  10. 10.
    Kelly, M.P., Vorperian, H.K., Wang, Y., Tillman, K.K., Werner, H.M., Chung, M.K., Gentry, L.R.: Characterizing mandibular growth using three-dimensional imaging techniques and anatomic landmarks. Arch. Oral Biol. 77, 27–38 (2017)CrossRefGoogle Scholar
  11. 11.
    Knuth, D.: The Art of Computing, Volume 2: Seminumerical Algorithms. Addison-Wesley, Boston (1981)zbMATHGoogle Scholar
  12. 12.
    Worsley, K.J., Cao, J., Paus, T., Petrides, M., Evans, A.C.: Applications of random field theory to functional connectivity. Hum. Brain Mapp. 6, 364–367 (1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Moo K. Chung
    • 1
    • 2
    Email author
  • Ying Ji Chuang
    • 2
  • Houri K. Vorperian
    • 2
  1. 1.Department of Biostatistics and Medical InformaticsUniversity of WisconsinMadisonUSA
  2. 2.Vocal Tract Development Laboratory, Waisman CenterUniversity of WisconsinMadisonUSA

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