From partial derivatives of 3-D density images to ridge lines

摘要

Abstract: imensional edge detection in voxel images is used to locate points corresponding to surfaces of 3-D 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. The classical approach is to use local surface fitting, thereby confronting the problem of establishing links between 3-D edge detection and local surface approximation. To avoid this problem, we propose to compute the curvatures at locations designated as edge points using directly the partial derivatives of the image. By assuming that the surface is defined locally by an iso- intensity-contour (i.e., the 3-D gradient at an edge point corresponds to the normal to the surface) one can calculate directly the curvatures and characterize the local curvature extrema (ridge points) from the first, second, and third derivatives of the grey level function. These partial derivatives can be computed using the operators of the edge detection. We present experimental results obtained using real data (x-ray scanner data) applying these two methods. As an example of the stability, we extract ridge lines in two 3-D x-ray scanner data of a skull taken in different positions. !16