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

Three-dimensional edge detection in voxel images is used to locate points corresponding to surfaces of 3-D structures, and the local geometry of these surfaces is characterized in order to extract points or lines which may be used by registration and tracking procedures. Typically, second-order differential characteristics of the surfaces must be calculated. To avoid the problem of establishing links between 3-D edge detection and local surface approximation it is proposed to compute the curvatures at locations designated as edge points, using the partial derivatives of the image directly. By assuming that the surface is defined locally by an iso-intensity-contour, it is possible to calculate directly the curvatures and characterize the local curvature extrema (ridge points) from the first, second, and third derivatives of the gray-level function. These partial derivatives can be computed using the operators of the edge detection. Experimental results obtained using real X-ray scanner data are presented