International Journal of Computer Vision

, Volume 105, Issue 2, pp 155-170

First online:

Teichmüller Shape Descriptor and Its Application to Alzheimer’s Disease Study

  • Wei ZengAffiliated withFlorida International University Email author 
  • , Rui ShiAffiliated withState University of New York at Stony Brook
  • , Yalin WangAffiliated withArizona State University
  • , Shing-Tung YauAffiliated withHarvard University
  • , Xianfeng GuAffiliated withState University of New York at Stony Brook
  • , Alzheimer’s Disease Neuroimaging Initiative

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We propose a novel method to apply Teichmüller space theory to study the signature of a family of nonintersecting closed 3D curves on a general genus zero closed surface. Our algorithm provides an efficient method to encode both global surface and local contour shape information. The signature—Teichmüller shape descriptor—is computed by surface Ricci flow method, which is equivalent to solving an elliptic partial differential equation on surfaces and is numerically stable. We propose to apply the new signature to analyze abnormalities in brain cortical morphometry. Experimental results with 3D MRI data from Alzheimer’s disease neuroimaging initiative (ADNI) dataset [152 healthy control subjects versus 169 Alzheimer’s disease (AD) patients] demonstrate the effectiveness of our method and illustrate its potential as a novel surface-based cortical morphometry measurement in AD research.


Teichmüller space Conformal welding Shape analysis