A 3D thin nets extraction method for medical imaging

This paper presents a powerful tool designed to extract characteristic lines, called 3D thin nets, from 3D volumetric images. 3D thin nets are the lines where the 3D grey level function is focally extremum in a given plane. Recently, we have shown that it is possible to characterize 2D thin nets as the crest lines of the image surface. This paper generalizes this approach to 3D data having three principal curvatures of the hypersurface defined by the 3D volumetric image. Using differential properties of image hypersurfaces, we explain that 3D thin nets can be extracted by intersecting of two surfaces, one corresponding to the maximization of maximum curvature in its associated direction, and the other one to the maximization of medium curvature in its associated direction. We apply this approach to the extraction of blood vessels in 3D medical images