A primal sketch of the cortex mean curvature: a morphogenesis based approach to study the variability of the folding patterns

In this paper, we propose a new representation of the cortical surface that may be used to study the cortex folding process and to recover some putative stable anatomical landmarks called sulcal roots usually buried in the depth of adult brains. This representation is a primal sketch derived from a scale space computed for the mean curvature of the cortical surface. This scale-space stems from a diffusion equation geodesic to the cortical surface. The primal sketch is made up of objects defined from mean curvature minima and saddle points. The resulting sketch aims first at highlighting significant elementary cortical folds, second at representing the fold merging process during brain growth. The relevance of the framework is illustrated by the study of central sulcus sulcal roots from antenatal to adult age. Some results are proposed for ten different brains. Some preliminary results are also provided for superior temporal sulcus.