3D geometric invariant alignment of surfaces with application in brain mapping

This paper is concerned with the problem of full or partial alignment of surfaces in the presence of affine transformations, local deformation and noise. This work addresses many alignment problems in diverse areas such as face recognition, fusion of multi-modality (e.g., evoked potential and MRI) for in vivo alignment of metabolic with anatomical maps, and brain mapping. In this paper, we concentrate on brain mapping and consider the intra and inter-animal brain surface registration problems. Surface alignment is based on a set of local affine invariants derived from the set of ordered inflection point pairs that reside on the umbilical curves of the surface. These points are local intrinsic geometric surface landmarks that are sought after because they are preserved under the affine transformation. The method is illustrated for intra and inter-animal registration using 3D data sets obtained from a sequence of external contours of coronal sections.