Heat Kernel Smoothing on Manifolds and Its Application to Hyoid Bone Growth Modeling

  • Moo K. ChungEmail author
  • Nagesh Adluru
  • Houri K. Vorperian
Part of the Emerging Topics in Statistics and Biostatistics book series (ETSB)


We present a unified heat kernel smoothing framework for modeling 3D anatomical surface data extracted from medical images. Due to image acquisition and preprocessing noises, it is expected the medical imaging data is noisy. The surface data of the anatomical structures is regressed using the weighted linear combination of Laplace-Beltrami (LB) eigenfunctions to smooth out noisy data and perform statistical analysis. The method is applied in characterizing the 3D growth pattern of human hyoid bone between ages 0 and 20 obtained from CT images. We detected a significant age effect on localized parts of the hyoid bone.


Heat kernel smoothing Hyoid bone growth Random field theory Laplace Beltrami eigenfunctions Diffusion on manifolds 



This work was supported by NIH Research Grants R01 DC6282, R01 EB022856, UL1TR000427 and P-30 HD03352 and U54 HD090256 to the Waisman Center. We thank Vikas Singh and Won Hwa Kim of University of Wisconsin-Madison for discussion on wavelets.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Moo K. Chung
    • 1
    Email author
  • Nagesh Adluru
    • 2
  • Houri K. Vorperian
    • 3
  1. 1.Department of Biostatistics and Medical InformaticsUniversity of WisconsinMadisonUSA
  2. 2.Waisman Laboratory for Brain Imaging and BehaviorUniversity of WisconsinMadisonUSA
  3. 3.Vocal Tract Development LaboratoryWaisman Center, University of WisconsinMadisonUSA

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