Robust Shape Correspondence via Spherical Patch Matching for Atlases of Partial Skull Models

Abstract

Problems of dense partial correspondence for meshes of variable topology are ubiquitous in medical imaging. In particular, this problem arises when constructing average shapes and probabilistic atlases of partial skull models. We exploit the roughly spherical extrinsic geometry of the skull to first approximate skull models with shapes of spherical topology. The skulls are then matched parametrically via a non-local non-linear landmark search using normalized spherical cross-correlation of curvature features. A dense spherical registration algorithm is then applied for a final correspondence. We show that the non-local step is crucial for accurate mappings. We apply the entire pipeline to low SNR skull meshes extracted from conical CT images. Our results show that the approach is robust for creating averages for families of shapes that deviate significantly from local isometry.