Geometric Shape Descriptors for Shape Analysis and Sulcal Classification of MRI Data

Monica Hurdal
Florida State University
Mathematics

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.