Anisotropic Distributions on Manifolds: Template Estimation and Most Probable Paths

@article{Sommer2015AnisotropicDO,
  title={Anisotropic Distributions on Manifolds: Template Estimation and Most Probable Paths},
  author={Stefan Sommer},
  journal={Information processing in medical imaging : proceedings of the ... conference},
  year={2015},
  volume={24},
  pages={193-204}
}
We use anisotropic diffusion processes to generalize normal distributions to manifolds and to construct a framework for likelihood estimation of template and covariance structure from manifold valued data. The procedure avoids the linearization that arise when first estimating a mean or template before performing PCA in the tangent space of the mean. We derive flow equations for the most probable paths reaching sampled data points, and we use the paths that are generally not geodesics for… CONTINUE READING