Journal Title
Title of Journal: J Math Imaging Vis
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Abbravation: Journal of Mathematical Imaging and Vision
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Authors: Erik Bekkers Remco Duits Tos Berendschot Bart ter Haar Romeny
Publish Date: 2014/01/23
Volume: 49, Issue: 3, Pages: 583-610
Abstract
This paper presents a method for retinal vasculature extraction based on biologically inspired multiorientation analysis We apply multiorientation analysis via socalled 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 SE2 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 applicationsTo this end we recall Fig 7 where one can observe that each tangent vector to the lifted curve s↦xsysθs with thetas=argdotxs+i dotys eg the curve following the right edge of a blood vessel in SE2 is pointing orthogonal to a plane mathcalV plotted in yellow Within mathcalV we see that the maximum values of the absolute value of the imaginary part of the score is located at the origin of the yellow plane in the tangent spaceIn general the real part imaginary part or absolute value of an orientation score is a complicated function on SE2 Therefore we will consider the case where C mathitSE2 tomathbbR+ is a socalled “completion field” 5 6 59 60 67 This corresponds to collision probability densities of a source particle g 1∈SE2 and a sink particle g 2∈SE2
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