A Comparison Study of Ellipsoid Fitting for Pose Normalization of Hippocampal Shapes

Pose normalization is an important step to establish shape correspondence for group comparison of anatomical structures. The most basic and widely used way is ellipsoid fitting, which provides three principal axes for shape alignment, and is often solved by least square fitting. In this paper, it is recognized that the deformation caused by neuro-degenerative diseases is usually locally irregular, behaving like the outliers to the majority of the anatomical surfaces. Therefore we hypothesize that the distance function in L1-norm may perform better than that in L2-norm for hippocampal surface fitting, and thus conduct a study to compare the influence of different distance functions. In particular, we show how to perform ellipsoid fitting via L1-norm based algebraic and geometric distances, and experimentally compare their performance together with the conventional L2-norm based distance functions. Our study demonstrates that L1-norm approach fits the majority of the surface, while L2-norm approach tends to fit the irregularity.