An Analysis of Vessel Enhancement Filters Based on the Hessian Matrix for Intracranial MRA
Brian E. Chapman, Dennis L. Parker · 2001
0.5, 0.5 and 0.5max(S) respectively. The HessDiff filter is a generalization of Du and Parker's filter that uses the continuous directionality properties of the Hessian matrix. As with Frangi's filter, we solve for the eignevalues of the Hessian matrix and sort them according to magnitude. For the filter response to be nonzero we again require that both l2 and l3 be less than zero (for bright blood) otherwise we take the filter response (V )t o be simplyV=|l3|-|l1|. This is a natural extension toDu and Parker's filter. For both Frangi's filter and the HessDiff filter an identical multiscale implementation was used. Successfully larger Gaussian functions for the filter kernels were used. Scales were grown linearly. The maximum response over all the scales was selected at each voxel. The filters were tested using three images acquired on volunteers participating in a familial aneurysm study. Each patient provided informed consent. A single slab 3D TOF pulse sequence on a 1.5 T Signa scanner was used for each acquisition. Images were acquired on a 512x192x64 grid and reconstructed on a 1024x768x128 grid. Magnetization transfer was used to suppress background signal. The filters were applied to a 512x512x120 subregion centered on the circle of Willis. We sampled voxels from randomly selected slices within the images and classified them as vessel (large, medium, small and very small) or background. A total of 15648 points were sampled and classified as follows: large vessel (2701), small vessel (635) and background (12312). The filter performance was analyzed in terms of how well the vessel voxels were separated from the background voxels. Separation was measured with the trapezoidal ROC curve (AUC). The mean and 10% confidence intervals (two tailed) for these curves were calculated by performing 2000 bootstraps. The ROC areas were calculated for the HessDiff filter, Frangi's filter and its three components, Ra, Rb ,a ndS. A digital phantom was also used to test the relationship between the filters and the MIP algorithm.