A mesh simplification strategy for a spatial regression analysis over the cortical surface of the brain
Tuesday 6th August 2013
Dassi, F.; Ettinger, B.; Perotto, S.; Sangalli, L.M.
We present a new mesh simplification technique developed for a statistical analysis of cortical surface data. The aim of this approach is to produce a simplified mesh which does not distort the original data distribution and such that the statistical estimates computed over the new mesh exhibit good inferential properties. To do this, we propose an iterative technique that, for each iteration, contracts the edge of the mesh with the lowest value of a cost function. This cost function takes into account both the geometry of the surface and the distribution of the data on it. After the data are associated with the simplified mesh, they are analyzed via a spatial regression model for non-planar domains. In particular, we resort to a penalized regression method that first conformally maps the simplified cortical surface mesh into a region in R2. Then, existing planar spatial smoothing techniques are extended to non-planar domains by suitably including the flattening phase. The effectiveness of the entire process is numerically demonstrated via a simulation study and an application to cortical surface thickness data.