Robust and fast vessel segmentation via Gaussian derivatives in orientation scores

We propose a robust and fully automaticmatched filter-based method for retinal vessel segmentation. Different from conventional filters in 2D image domains, we construct a new matched filter based on secondorder Gaussian derivatives in so-called orientation scores, functions on the coupled space of position and orientations ℝ2 ⋊ S¹. We lift 2D images to 3D orientation scores by means of a wavelet-type transform using an anisotropic wavelet. In the domain ℝ2 ⋊ S¹, we set up rotation and translation invariant second-order Gaussian derivatives. By locally matching the multi-scale second order Gaussian derivative filters with data in orientation scores, we are able to enhance vessel-like structures located in different orientation planes accordingly. Both crossings and tiny vessels are well-preserved due to the proposed multi-scale and multi-orientation filtering method. The proposed method is validated on public databases DRIVE and STARE, and we show that the method is both fast and reliable. With respectively a sensitivity and specificity of 0.7744 and 0.9708 on DRIVE, and 0.7940 and 0.9707 on STARE, our method gives improved performance compared to state-of-the-art algorithms.