Comparison of vesselness functions for multiscale analysis of the liver vasculature

The accurate segmentation of liver vessels is an important step for further computer assisted analysis in oncologic planning tools. Multiscale based vessel enhancement methods are very famous and many papers about this topic were published. Vesselness filters proposed by Sato et al., Frangi et al. and Erdt et al. are based on eigenvalue analysis of the Hessian matrix. They were developed using completely different approaches, namely experimental, geometrical and analytical. In this paper, their behavior at junctions and nearby vessels is systematically compared and evaluated for the enhancement of the liver vasculature. We found that the filter function proposed by Frangi et al. has problems at junctions, while the ones developed by Sato et al and Erdt et al. have problems with nearby vessels. The latter are preferred for the task of liver vessel enhancement.