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Three-Dimensional Shape Modeling and Analysis of Brain Structures
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Published on: November 14, 2019

Sparse Shape Representation using the Laplace-Beltrami Eigenfunctions and Its Application to Modeling Subcortical

Seung-Goo Kim1, Moo K Chung, Stacey M Schaefer

  • 1Department of Brain and Cognitive Sciences, Seoul National University, Korea.

Proceedings. Workshop on Mathematical Methods in Biomedical Image Analysis
|June 21, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a novel sparse shape modeling method using Laplace-Beltrami eigenfunctions. The approach effectively identifies significant eigenfunctions for accurate shape representation, aiding brain structure analysis.

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Area of Science:

  • Computational geometry
  • Neuroimaging analysis
  • Medical image processing

Background:

  • Laplace-Beltrami (LB) eigenfunctions are traditionally used for intrinsic surface shape representation via Fourier series.
  • Current methods often discard higher-frequency terms, potentially losing significant shape information.
  • Existing techniques may require additional surface-based smoothing to reduce noise.

Purpose of the Study:

  • To develop a sparse shape modeling framework using LB eigenfunctions.
  • To filter significant eigenfunctions adaptively by imposing an l1-penalty.
  • To investigate the influence of age and gender on amygdala and hippocampus shapes and their relation to emotional response.

Main Methods:

  • A novel sparse shape modeling framework is proposed, utilizing LB eigenfunctions.
  • An l1-penalty is imposed to selectively filter significant eigenfunctions, avoiding arbitrary truncation.
  • The method is applied to analyze shape variations in the amygdala and hippocampus in a healthy population.

Main Results:

  • The sparse framework effectively identifies and utilizes significant LB eigenfunctions for shape reconstruction.
  • The approach avoids the need for additional surface-based smoothing.
  • The study reveals age and gender-related shape differences in the amygdala and hippocampus.
  • A correlation between emotional response and subcortical structure anatomy is demonstrated.

Conclusions:

  • The proposed sparse LB eigenfunction framework offers a more robust and adaptive approach to shape modeling.
  • This method enhances the analysis of neuroanatomical variations and their functional correlates.
  • The findings contribute to understanding the neurobiological basis of emotional processing.