Extract ridges and ravines using Hessian matrix of 3D image

Abstract

Edge detection in two and three-dimensional images is used to located points corresponding to surfaces of three dimension (3D) structures. The next stage is to characterize the local geometry of these surfaces in order to extract points or lines which may be used by registration and tracking procedures. Typically one must calculate second-order differential characteristics of the surfaces such as the maximum, mean, and Gaussian curvatures. Assuming that the surface is defined locally by a isointensity contour. One can calculate directly the curvatures and characterize the local curvature extrema (ridge points) from the first, second, and third derivatives of the vector valued function. These partial derivatives are computed using the operators of the edge detection.