Automated surface matching using mutual information applied to riemann surface structures

Yalin Wang, Ming Chang Chiang, Paul M. Thompson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

36 Scopus citations

Abstract

Many medical imaging applications require the computation of dense correspondence vector fields that match one surface with another. To avoid the need for a large set of manually-defined landmarks to constrain these surface correspondences, we developed an algorithm to automate the matching of surface features. It extends the mutual information method to automatically match general 3D surfaces (including surfaces with a branching topology). First, we use holomorphic 1-forms to induce consistent conformal grids on both surfaces. High genus surfaces are mapped to a set of rectangles in the Euclidean plane, and closed genus-zero surfaces are mapped to the sphere. Mutual information is used as a cost functional to drive a fluid flow in the parameter domain that optimally aligns stable geometric features (mean curvature and the conformal factor) in the 2D parameter domains. A diffeomorphic surface-to-surface mapping is then recovered that matches anatomy in 3D. We also present a spectral method that ensures that the grids induced on the target surface remain conformal when pulled through the correspondence field. Using the chain rule, we express the gradient of the mutual information between surfaces in the conformal basis of the source surface. This finite-dimensional linear space generates all conformal reparameterizations of the surface. We apply the method to hippocampal surface registration, a key step in subcortical shape analysis in Alzheimer's disease and schizophrenia.

Original languageEnglish (US)
Title of host publicationMedical Image Computing and Computer-Assisted Intervention - MICCAI 2005 - 8th International Conference, Proceedings
Pages666-674
Number of pages9
StatePublished - Dec 1 2005
Externally publishedYes
Event8th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005 - Palm Springs, CA, United States
Duration: Oct 26 2005Oct 29 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3750 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other8th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005
CountryUnited States
CityPalm Springs, CA
Period10/26/0510/29/05

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Wang, Y., Chiang, M. C., & Thompson, P. M. (2005). Automated surface matching using mutual information applied to riemann surface structures. In Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005 - 8th International Conference, Proceedings (pp. 666-674). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3750 LNCS).