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Updated: Sep 30, 2025

How to Measure Cortical Folding from MR Images: a Step-by-Step Tutorial to Compute Local Gyrification Index
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Cortical Surface Shape Analysis Based on Alexandrov Polyhedra.

Min Zhang1, Yang Guo2, Na Lei3

  • 1Brigham and Women's Hospital, Harvard Medical School.

Proceedings. IEEE International Conference on Computer Vision
|March 16, 2022
PubMed
Summary
This summary is machine-generated.

Alexandrov polyhedra offer novel shape signatures for analyzing brain cortical surfaces. This method effectively distinguishes between Alzheimer's disease (AD) and healthy individuals, pinpointing structural changes.

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Area of Science:

  • Neuroimaging
  • Computational anatomy
  • Medical image analysis

Background:

  • Shape analysis is crucial for diagnosing neurodegenerative diseases like Alzheimer's disease (AD).
  • Effective shape representation for cortical surfaces remains a significant challenge in neuroimaging.
  • Current methods may not fully capture the intrinsic geometric information of brain structures.

Purpose of the Study:

  • To introduce Alexandrov polyhedra as surface-based shape signatures for cortical morphometry.
  • To develop a novel method for computing these polyhedra using spherical optimal transport (OT).
  • To evaluate the effectiveness of Alexandrov polyhedra in identifying AD-related structural changes.

Main Methods:

  • Utilized Alexandrov polyhedra as convex shape representations for closed genus-0 cortical surfaces.
  • Employed a novel spherical optimal transport (OT) computation to derive these polyhedra.
  • Developed a visualization technique to compare local geometry differences across cortical surfaces.

Main Results:

  • Observed significant differences in Alexandrov polyhedra between Alzheimer's disease (AD) and cognitively unimpaired individuals.
  • Demonstrated the method's efficacy in pinpointing regional cortical structural changes associated with AD.
  • The proposed shape signatures effectively capture AD-impacted morphometric variations.

Conclusions:

  • Alexandrov polyhedra provide a robust intrinsic geometric representation for cortical surfaces.
  • The novel OT-based computation enables effective shape analysis for neurodegenerative disease research.
  • This approach shows promise for early AD diagnosis and understanding disease progression.