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Updated: Jun 8, 2026

Three-Dimensional Shape Modeling and Analysis of Brain Structures
05:33

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

Shape-based diffeomorphic registration on hippocampal surfaces using Beltrami holomorphic flow.

Lok Ming Lui1, Tsz Wai Wong, Paul Thompson

  • 1Department of Mathematics, Harvard University, Cambridge, MA, USA.

Medical Image Computing and Computer-Assisted Intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
|October 1, 2010
PubMed
Summary

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We developed a novel algorithm for automatic hippocampal surface registration, achieving complete geometric matching without manual landmarks. This method accurately captures subtle shape differences, aiding in disease analysis.

Area of Science:

  • Medical imaging
  • Computational anatomy
  • Neuroscience

Background:

  • Accurate registration of hippocampal surfaces is crucial for understanding brain structure and function.
  • Current methods often require manual landmarking, which is time-consuming and subjective.
  • Developing automated, geometrically complete registration methods is essential for large-scale neuroimaging studies.

Purpose of the Study:

  • To introduce a new algorithm for automatic registration of hippocampal surfaces with complete geometric matching.
  • To propose a novel shape energy metric based on Beltrami coefficients and curvatures for accurate surface comparison.
  • To evaluate the algorithm's effectiveness in registering hippocampal surfaces from normal and Alzheimer's disease subjects.

Main Methods:

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Last Updated: Jun 8, 2026

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  • Developed a novel shape index using Beltrami coefficients and curvatures to measure local shape dissimilarity.
  • Defined a shape energy function that is zero if and only if two surfaces are identical up to rigid motion.
  • Proposed a simplified representation of surface diffeomorphisms using Beltrami coefficients.
  • Implemented an iterative optimization process using the Beltrami Holomorphic flow (BHF) method to minimize shape energy.

    • Main Results:

    • The algorithm successfully achieved complete geometric matching for hippocampal surfaces.
    • Experimental results on 212 subjects (normal and Alzheimer's disease) demonstrated the algorithm's effectiveness.
    • The proposed shape energy metric effectively captured local shape differences relevant for disease analysis.

    Conclusions:

    • The developed algorithm provides an effective automated solution for hippocampal surface registration.
    • The novel shape energy metric and BHF method offer a robust approach for geometric matching.
    • This method has potential applications in neurodegenerative disease research, particularly for Alzheimer's disease analysis.