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The 4D Hyperspherical Diffusion Wavelet: A New Method for the Detection of Localized Anatomical Variation

  • Ameer Pasha Hosseinbor
  • Won Hwa Kim
  • Nagesh Adluru
  • Amit Acharya
  • Houri K. Vorperian
  • Moo K. Chung
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8675)

Abstract

Recently, the HyperSPHARM algorithm was proposed to parameterize multiple disjoint objects in a holistic manner using the 4D hyperspherical harmonics. The HyperSPHARM coefficients are global; they cannot be used to directly infer localized variations in signal. In this paper, we present a unified wavelet framework that links HyperSPHARM to the diffusion wavelet transform. Specifically, we will show that the HyperSPHARM basis forms a subset of a wavelet-based multi-scale representation of surface-based signals. This wavelet, termed the hyperspherical diffusion wavelet, is a consequence of the equivalence of isotropic heat diffusion smoothing and the diffusion wavelet transform on the hypersphere. Our framework allows for the statistical inference of highly localized anatomical changes, which we demonstrate in the first-ever developmental study on the hyoid bone investigating gender and age effects. We also show that the hyperspherical wavelet successfully picks up group-wise differences that are barely detectable using SPHARM.

Keywords

Hyoid Bone Growth Spurt False Discovery Rate Correction Holistic Manner Mesh Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ameer Pasha Hosseinbor
    • 1
  • Won Hwa Kim
    • 1
  • Nagesh Adluru
    • 1
  • Amit Acharya
    • 2
  • Houri K. Vorperian
    • 1
  • Moo K. Chung
    • 1
  1. 1.University of Wisconsin-MadisonUSA
  2. 2.Marshfield ClinicUSA

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