Shape analysis of the cortex is becoming increasingly important in
neuroimaging studies to identify and quantify the progress of disease and
understand changes of the brain throughout aging. To date, most studies
have focused on extrinsic properties of the cortex with many results
focusing on cortical thickness or volume.
Mathematically, properties of the shape of curves and surfaces in 3D space
can be described by features such as their velocity fields, writhe,
extremal length, principal curvatures, and Gaussian curvatures. In
particular, we are interested in shape descriptors which are mathematical
invariants, meaning they are quantities which remain unchanged under a
given class of isometries. Invariants are extremely useful for classifying
mathematical objects because they usually reflect intrinsic properties of
the object of study.
We present a variety of geometric shape descriptors that have the property
that they are geometric invariants. We will discuss the invariants of
curvature, Gauss integrals and moments. We have applied these invariants
to sulcal curves obtained from neuroimaging data and our preliminary
results indicate that the selected feature vectors represent promising
characteristics for characterizing cortical shape.