A parameterization-based numerical method for isotropic and anisotropic diffusion smoothing on non-flat surfaces

Anand A. Joshi, David W. Shattuck, Paul M. Thompson, Richard M. Leahy

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

Neuroimaging data, such as 3-D maps of cortical thickness or neural activation, can often be analyzed more informatively with respect to the cortical surface rather than the entire volume of the brain. Any cortical surface-based analysis should be carried out using computations in the intrinsic geometry of the surface rather than using the metric of the ambient 3-D space. We present parameterization-based numerical methods for performing isotropic and anisotropic filtering on triangulated surface geometries. In contrast to existing FEM-based methods for triangulated geometries, our approach accounts for the metric of the surface. In order to discretize and numerically compute the isotropic and anisotropic geometric operators, we first parameterize the surface using a p-harmonic mapping. We then use this parameterization as our computational domain and account for the surface metric while carrying out isotropic and anisotropic filtering. To validate our method, we compare our numerical results to the analytical expression for isotropic diffusion on a spherical surface. We apply these methods to smoothing of mean curvature maps on the cortical surface, a step commonly required for analysis of gyrification or for registering surface-based maps across subjects.

Original languageEnglish
Pages (from-to)1358-1365
Number of pages8
JournalIEEE Transactions on Image Processing
Volume18
Issue number6
DOIs
StatePublished - 2009
Externally publishedYes

Keywords

  • Anisotropic diffusion smoothing
  • Isotropic
  • P-harmonic parameterization

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