Level set estimation on the sphere

We investigate a technique for estimating level sets of functionals on the 2-sphere. The surface of the sphere is finely partitioned using a tree decomposition and a candidate level set is obtained by minimizing a regularized cost on the tree. A cycle spinning scheme, implemented as an ensemble classification method, is developed to decrease the variance of the tree-based estimate. Both constructions are compatible with many existing hierarchical discretizations of the 2-sphere, e.g. HEALPix and HTM. We present simulation results of a synthetic data set and an fMRI data set.