Fast and Automatic Vessel Centerline Detection for MRA

The extraction of vessel centerlines allows for better understanding of their topology, and can be used for further registration or quantification. We present a new method to extract the centerlines from Magnetic Resonance Angiographies. We use the gradient and the eigenvalues of the Hessian matrix to interpolate the zero-crossing of the gradient vector in the cross-sectional directions. Then, we connect the points belonging to the same cubes. A second connection step allows for the improvement the global connectivity. Our method is fast, extracts sub-voxel centerlines, and does not rely on a preliminary segmentation stage. Introduction Several methods can be considered in order to obtain the centerlines of vessels. A first class of methods derives a set of voxels that belong to the centerlines and then creates the lines as sets of points located at the center of voxels. These voxels can be obtained by simple thresholding of the image and then applying a skeletonization process, or by a linear multi-scale analysis [3]. A second class of methods tries to extract directly sub-voxel centerlines considering the line as an intersection of two iso-surfaces [2]. Sub-voxel Centerline Extraction Our method belongs to this second class of algorithms. It is based on the extraction of ridges as defined in [l]. Let I be the image as a function from B3 to B, VI be the gradient vector field, H ( I ) be the Hessian matrix with eigenvectors v l , v2, vs, and associated eigenvalues A1 5 XZ 5 X3. The derivatives of the intensity are computed by convolving the image with the derivatives of a Gaussian kernel of standard deviation n. We are interested in the automatic extraction of the points which satisfy the following properties: Improvement of the connectivity Although the algorithm is able to extract most of the centerlines, we post-process the detected lines using connectivity criteria which allows a better continuity of the vessels. We connect two extremities of distinct centerlines M I and Mz, with associated tangents t l and t2 (oriented outward), if and only if the distance between Mi and ,442 is lower than d,, and the two angles (tl , a) and (t2, MzMl) are lower than __f