Robust Retinal Vessel Segmentation via Locally Adaptive Derivative Frames in Orientation Scores

This paper presents a robust and fully automatic filter-based approach for retinal vessel segmentation. We propose new filters based on 3D rotating frames in so-called orientation scores, which are functions on the Lie-group domain of positions and orientations Formula: see text. By means of a wavelet-type transform, a 2D image is lifted to a 3D orientation score, where elongated structures are disentangled into their corresponding orientation planes. In the lifted domain Formula: see text, vessels are enhanced by means of multi-scale second-order Gaussian derivatives perpendicular to the line structures. More precisely, we use a left-invariant rotating derivative (LID) frame, and a locally adaptive derivative (LAD) frame. The LAD is adaptive to the local line structures and is found by eigensystem analysis of the left-invariant Hessian matrix (computed with the LID). After multi-scale filtering via the LID or LAD in the orientation score domain, the results are projected back to the 2D image plane giving us the enhanced vessels. Then a binary segmentation is obtained through thresholding. The proposed methods are validated on six retinal image datasets with different image types, on which competitive segmentation performances are achieved. In particular, the proposed algorithm of applying the LAD filter on orientation scores (LAD-OS) outperforms most of the state-of-the-art methods. The LAD-OS is capable of dealing with typically difficult cases like crossings, central arterial reflex, closely parallel and tiny vessels. The high computational speed of the proposed methods allows processing of large datasets in a screening setting.