Tracing of Curvilinear Structures in 3D Images with Single Scale Diameter Measurement

We introduce a 3D tracing method based on Differential geometry in Gaussian blurred images. The line point detection part of the tracing method starts with calculation of the line direction from the eigenvectors of the Hessian matrix. The sub-voxel center line position is estimated from a second order Taylor approximation of the 2D intensity profile perpendicular to the line. The line diameter is obtained at a single scale using the theoretical scale dependencies of the 0-th and 2nd order Gaussian derivatives at the line center. Experiments on synthetic images reveal that the localization of the centerline is mainly affected by line curvature. The diameter measurement is accurate for diameters as low as 4 voxels.