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• W3106127140 abstract "In order to detect salient lines in spherical images, we consider the problem of minimizing the functional $$int limits _0^l mathfrak {C}(gamma (s)) sqrt{xi ^2 + k_g^2(s)} , mathrm{d}s$$ for a curve $$gamma $$ on a sphere with fixed boundary points and directions. The total length l is free, s denotes the spherical arclength, and $$k_g$$ denotes the geodesic curvature of $$gamma $$ . Here the smooth external cost $$mathfrak {C}ge delta >0$$ is obtained from spherical data. We lift this problem to the sub-Riemannian (SR) problem in Lie group $${text {SO(3)}}$$ and show that the spherical projection of certain SR geodesics provides a solution to our curve optimization problem. In fact, this holds only for the geodesics whose spherical projection does not exhibit a cusp. The problem is a spherical extension of a well-known contour perception model, where we extend the model by Boscain and Rossi to the general case $$xi > 0, mathfrak {C} ne 1$$ . For $$mathfrak {C}=1$$ , we derive SR geodesics and evaluate the first cusp time. We show that these curves have a simpler expression when they are parameterized by spherical arclength rather than by sub-Riemannian arclength. For case $$mathfrak {C} ne 1$$ (data-driven SR geodesics), we solve via a SR Fast Marching method. Finally, we show an experiment of vessel tracking in a spherical image of the retina and study the effect of including the spherical geometry in analysis of vessels curvature." @default.
• W3106127140 created "2020-11-23" @default.
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• W3106127140 date "2017-02-17" @default.
• W3106127140 modified "2023-09-30" @default.
• W3106127140 title "Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in $${text {SO(3)}}$$ SO(3)" @default.
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• W3106127140 doi "https://doi.org/10.1007/s10851-017-0705-9" @default.
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