3D surface matching with mutual information and Riemann surface structures

Yalin Wang, Ming Chang Chiang, Paul M. Thompson

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

4 Scopus citations

Abstract

Many medical imaging applications require the computation of dense correspondence vector fields that match one surface with another. Surface-based registration is useful for tracking brain change, registering functional imaging data from multiple subjects, and for creating statistical shape models of anatomy. 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). We use diffeomorphic flows to optimally align the Riemann surface structures of two surfaces. 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. Next, we compute stable geometric features (mean curvature and the conformal factor) and pull them back as scalar fields onto the 2D parameter domains. Mutual information is used as a cost functional to drive a fluid flow in the parameter domain that optimally aligns these surface features. A diffeomorphic surface-to-surface mapping is then recovered that matches anatomy in 3D. Lastly, we 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. Illustrative experiments show the method applied to hippocampal surface registration, a key step in subcortical shape analysis in Alzheimer's disease and schizophrenia.

Original languageEnglish (US)
Title of host publicationProceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005
EditorsM.H. Hamza
Pages94-99
Number of pages6
StatePublished - Dec 1 2005
Externally publishedYes
EventEighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005 - Honolulu, HI, United States
Duration: Aug 15 2005Aug 17 2005

Publication series

NameProceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005

Other

OtherEighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005
CountryUnited States
CityHonolulu, HI
Period8/15/058/17/05

Keywords

  • Brain Mapping
  • Mutual Information
  • Riemann Surface Structure
  • Surface Matching

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Wang, Y., Chiang, M. C., & Thompson, P. M. (2005). 3D surface matching with mutual information and Riemann surface structures. In M. H. Hamza (Ed.), Proceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005 (pp. 94-99). (Proceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005).