Ej Erik Bekkers

A Multi-Orientation Analysis Approach to Retinal Vessel Tracking

This paper presents a method for retinal vasculature extraction based on biologically inspired multi-orientation analysis. We apply multi-orientation analysis via so-called invertible orientation scores, modeling the cortical columns in the visual system of higher mammals. This allows us to generically deal with many hitherto complex problems inherent to vessel tracking, such as crossings, bifurcations, parallel vessels, vessels of varying widths and vessels with high curvature. Our approach applies tracking in invertible orientation scores via a novel geometrical principle for curve optimization in the Euclidean motion group SE(2). The method runs fully automatically and provides a detailed model of the retinal vasculature, which is crucial as a sound basis for further quantitative analysis of the retina, especially in screening applications.

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 ℝ2 × S1. 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 ℝ2 × S1, 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.

A PDE Approach to Data-Driven Sub-Riemannian Geodesics in

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group

SE

SE(2) = \mathbb{R}^2 \rtimes S^1

(2)

with a metric tensor depending on a smooth external cost

Robust and fast vessel segmentation via Gaussian derivatives in orientation scores

\mathcal{C}:SE(2) \to [\delta,1]

Crossing-Preserving Multi-scale Vesselness

,

Retinal vessel delineation using a brain-inspired wavelet transform and random forest

\delta>0

Brain-inspired algorithms for retinal image analysis

, computed from image data. The method consists of a first step where an SR-distance map is computed as a viscosity solution of a Hamilton--Jacobi--Bellman system derived via Pontryagins maximum principle (PMP). Subsequent backward integration, again relying on PMP, gives the SR-geodesics. For

Sub-Riemannian fast marching in SE(2)

\mathcal{C}=1