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SCALESPACE
2015
Springer

Data-Driven Sub-Riemannian Geodesics in SE(2)

3 years 6 months ago
Data-Driven Sub-Riemannian Geodesics in SE(2)
We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group SE(2) = R2 S1 with a metric tensor depending on a smooth external cost C : SE(2) → [δ, 1], δ > 0, computed from image data. The method consists of a first step where geodesically equidistant surfaces are computed as a viscosity solution of a HamiltonJacobi-Bellman (HJB) system derived via Pontryagin’s Maximum Principle (PMP). Subsequent backward integration, again relying on PMP, gives the SR-geodesics. We show that our method produces geodesically equidistant surfaces. For C = 1 we show that our method produces the global minimizers, and comparison with exact solutions shows a remarkable accuracy of the SR-spheres/geodesics. Finally, trackings in synthetic and retinal images show the potential of including the SR-geometry.
Erik J. Bekkers, Remco Duits, Alexey Mashtakov, Go
Added 17 Apr 2016
Updated 17 Apr 2016
Type Journal
Year 2015
Where SCALESPACE
Authors Erik J. Bekkers, Remco Duits, Alexey Mashtakov, Gonzalo R. Sanguinetti
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