A Texture Manifold for Curve-Based Morphometry of the Cerebral Cortex

The cortical surface of the human brain is composed of folds that are juxtaposed alongside one another. Several methods have been proposed to study the shape of these folds, e.g., by first segmenting them on the cortical surface or by analysis via a continuous deformation of a common template. A major disadvantage of these methods is that, while they can localize shape differences, they cannot easily identify the directions in which they occur. The type of deformation that causes a fold to change in length is quite different from that which causes it to change in width. Furthermore, these two deformations may have a completely different biological interpretation. In this article we propose a method to analyze such deformations using directional filters locally adapted to the geometry of the folding pattern. Motivated by the texture flow literature in computer vision we recover flow fields that maintain a fixed angle with the orientation of folds, over a significant spatial extent. We then trace the flow fields to determine which correspond to the shape changes that are the most salient. Using the OASIS database, we demonstrate that in addition to known regions of atrophy, our method can find subtle but statistically significant shape deformations.