Cortical thickness is an important biomarker for image-based studies of the brain. A diffeomorphic registration based cortical thickness (DiReCT) measure is introduced where a continuous one-to-one correspondence between the gray matter-white matter interface and the estimated gray matter-cerebrospinal fluid interface is given by a diffeomorphic mapping in the image space. Thickness is then defined in terms of a distance measure between the interfaces of this sheet like structure. This technique also provides a natural way to compute continuous estimates of thickness within buried sulci by preventing opposing gray matter banks from intersecting. In addition, the proposed method incorporates neuroanatomical constraints on thickness values as part of the mapping process. Evaluation of this method is presented on synthetic images. As an application to brain images, a longitudinal study of thickness change in frontotemporal dementia (FTD) spectrum disorder is reported.