Cortical Surface Shape Analysis Based on Spherical

In vivo quantification of neuroanatomical shape vari- ations is possible due to recent advances in medical imaging and has proven useful in the study of neuropathology and neurodevel- opment. In this paper, we apply a spherical wavelet transformation to extract shape features of cortical surfaces reconstructed from magnetic resonance images (MRIs) of a set of subjects. The spher- ical wavelet transformation can characterize the underlying func- tions in a local fashion in both space and frequency, in contrast to spherical harmonics that have a global basis set. We perform principal component analysis (PCA) on these wavelet shape fea- tures to study patterns of shape variation within normal popula- tion from coarse to fine resolution. In addition, we study the devel- opment of cortical folding in newborns using the Gompertz model in the wavelet domain, which allows us to characterize the order of development of large-scale and finer folding patterns indepen- dently. Given a limited amount of training data, we use a regu- larization framework to estimate the parameters of the Gompertz model to improve the prediction performance on new data. We de- velop an efficient method to estimate this regularized Gompertz model based on the Broyden-Fletcher-Goldfarb-Shannon (BFGS)