Hippocampal surface discrimination via invariant descriptors of spherical conformal maps

Weighted spherical harmonic shape descriptors are based on the subspaces of L ²(S ²) spanned by spherical harmonics of a single degree. Such shape descriptors incorporate both shape and scaling information, while preserving invariance with respect to other non-reflexive affine transformations. Thus, their application allows for direct comparison of shapes across subjects, resolutions and within-subject components. On the other hand, global conformal parametrization preserves intrinsic conformal structure and thus allows for vast differences in object scaling on the 2-sphere. As a result, surface energy is distributed more evenly across the spherical harmonic spectrum, with the higher resolution descriptors representing regions with higher conformal factor. We applied our morphometry to 96 hippocampal surfaces. The data used were 12 control and 12 Alzheimer (AD) T1 and T2 subjects. An independent-samples t-test revealed significant differences for the change in hemispheric shape difference in shape descriptors of degrees 3, 20, 22, 25 and 27, with the highest p-value of .001, t = 4.019, predicting 22 out of 24 subjects' diagnosis correctly.