Multiscale vessel enhancing diffusion in CT angiography noise filtering

Filtering of vessel structures in medical images by analyzing the second order information or the Hessian of the image, is a well known technique. In this work we incorporate Frangi's multiscale vessel filter, which is based on a geometrical analysis of the Hessian' eigenvectors, into a nonlinear, anisotropic diffusion scheme, such that diffusion mainly takes place along the vessel axis while diffusion perpendicular to this axis is inhibited. The multiscale character of the vesselness filter ensures an equally good response for varying vessel radii. The first, theoretical contribution of this paper is the modification of the original formulation of this vessel filter, such that it becomes a smooth function on its domain which is a necessary condition imposed by the diffusion process to ensure well-posedness. The second contribution concerns the application of noise filtering of 3D synthetic, phantom computed tomography (CT) and patient CT data. It is shown that the method is very effective in noise filtering, illustrating its potential as a preprocessing step in the analysis of low dose CT angiography.