To obtain precisely located features, Thirion introduced extremal points, which are points of locally maximal curvature in both principal directions of the surface. These points are specific points on the crest lines and can be seen as the generalization of corner points for smooth surfaces in 3D.
Modeling an extremal point by a frame and example of crest lines and "extremal frames" on a closeup on the occipital foramen from a CT image.
To the position of the point, we can add the normal vector n and the two principal directions t1 and t2 of the surface to constitute a local coordinate system or a frame. In this context, a 3D medical image is modeled as a set of frames:
The matching problem is to find correspondences between a subset of these frame sets in different images.