Vesselness filters aim at enhancing tubular structures in medical images. The most popular vesselness filters are based on eigenanalyses of the Hessian matrix computed at different scales. However, Hessian-based methods have well-known limitations, most of them related to the use of second order derivatives. In this paper, we propose an alternative strategy in which ring-like patterns are sought in the local orientation distribution of the gradient. The method takes advantage of symmetry properties of ring-like patterns in the spherical harmonics domain. For bright vessels, gradients not pointing towards the center are filtered out from every local neighborhood in a first step. The opposite criterion is used for dark vessels. Afterwards, structuredness, evenness and uniformness measurements are computed from the power spectrum in spherical harmonics of both the original and the half-zeroed orientation distribution of the gradient. Finally, the features are combined into a single vesselness measurement. Alternatively, a structure tensor that is suitable for vesselness can be estimated before the analysis in spherical harmonics. The two proposed methods are called Ring Pattern Detector (RPD) and Filtered Structure Tensor (FST) respectively. Experimental results with computed tomography angiography data show that the proposed filters perform better compared to the state-of-the-art.
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