Geodesic Distances to Landmarks for Dense Correspondence on Ensembles of Complex Shapes
Establishing correspondence points across a set of biomedical shapes is an important technology for a variety of applications that rely on statistical analysis of individual subjects and populations. The inherent complexity (e.g. cortical surface shapes) and variability (e.g. cardiac chambers) evident in many biomedical shapes introduce significant challenges in finding a useful set of dense correspondences. Application specific strategies, such as registration of simplified (e.g. inflated or smoothed) surfaces or relying on manually placed landmarks, provide some improvement but suffer from limitations including increased computational complexity and ambiguity in landmark placement. This paper proposes a method for dense point correspondence on shape ensembles using geodesic distances to a priori landmarks as features. A novel set of numerical techniques for fast computation of geodesic distances to point sets is used to extract these features. The proposed method minimizes the ensemble entropy based on these features, resulting in isometry invariant correspondences in a very general, flexible framework.
KeywordsLeft Atrium Geodesic Distance Cortical Surface Eikonal Equation Automatic Correspondence
- 2.Styner, M., Oguz, I., Xu, S., Brechbühler, C., Pantazis, D., Levitt, J., Shenton, M., Gerig, G.: Framework for the statistical shape analysis of brain structures using SPHARM-PDM. The Insight Journal (2006)Google Scholar
- 3.Davies, R.H., Twining, C.J., Cootes, T.F., Waterton, J.C., Taylor, C.J.: 3D statistical shape models using direct optimisation of description length. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002, Part III. LNCS, vol. 2352, pp. 3–20. Springer, Heidelberg (2002)CrossRefGoogle Scholar
- 5.Thompson, P.M., et al.: Mapping cortical change in alzheimers disease, brain development, and schizophrenia (2004)Google Scholar
- 7.Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching. Proceedings of the National Academy of Science, 1168–1172 (2006)Google Scholar
- 10.Fu, Z., Kirby, M., Whitaker, R.: A fast iterative method for solving the eikonal equation on triangulated meshes. SIAM Journal on Scientific Computing (2011)Google Scholar