Conference Proceeding

Curvature Based Biomarkers for Diabetic Retinopathy via Exponential Curve Fits in SE(2)

  • Erik J. Bekkers (Eindhoven University of Technology)
  • Jiong Zhang (Eindhoven University of Technology)
  • Remco Duits (Eindhoven University of Technology)
  • Bart M. ter Haar Romeny (Eindhoven University of Technology)


We propose a robust and fully automatic method for the analysis of vessel tortuosity. Our method does not rely on pre-segmentation of vessels, but instead acts directly on retinal image data. The method is based on theory of best-fit exponential curves in the roto-translation group SE(2). We lift 2D images to 3D functions called orientation scores by including an orientation dimension in the domain. In the extended domain of positions and orientations (identified with SE(2)) we study exponential curves, whose spatial projections have constant curvature. By locally fitting such curves to data in orientation scores, via our new iterative stabilizing refinement method, we are able to assign to each location a curvature and confidence value. These values are then used to define global tortuosity measures. The method is validated on synthetic and retinal images. We show that the tortuosity measures can serve as effective biomarkers for diabetes and different stages of diabetic retinopathy.

Keywords: Retina, vessel tortuosity, biomarkers, diabetes, curvature, orientation scores, roto-translation group

How to Cite:

Bekkers, E. J. & Zhang, J. & Duits, R. & ter Haar Romeny, B. M., (2015) “Curvature Based Biomarkers for Diabetic Retinopathy via Exponential Curve Fits in SE(2)”, Proceedings of the Ophthalmic Medical Image Analysis International Workshop 2(2015), 113-120. doi:

Rights: Copyright © 2015 Erik J. Bekkers, Jiong Zhang, Remco Duits, and Bart M. ter Haar Romeny

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Published on
09 Oct 2015
Peer Reviewed