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.

• Type: Journal
• Year: 2015
• Where: SCALESPACE
• Authors: Erik J. Bekkers, Remco Duits, Alexey Mashtakov, Gonzalo R. Sanguinetti
• Keywords: Computer Vision, SCALESPACE 2015