Gr Gonzalo Sanguinetti

A PDE Approach to Data-Driven Sub-Riemannian Geodesics in

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group

SE

SE(2) = \mathbb{R}^2 \rtimes S^1

(2)

with a metric tensor depending on a smooth external cost

Locally Adaptive Frames in the Roto-Translation Group and Their Applications in Medical Imaging

\mathcal{C}:SE(2) \to [\delta,1]

Numerical approaches for linear left-invariant diffusions on SE(2), their comparison to exact solutions, and their applications in retinal imaging

,

Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution.

\delta>0

Sub-Riemannian fast marching in SE(2)

, computed from image data. The method consists of a first step where an SR-distance map is computed as a viscosity solution of a Hamilton--Jacobi--Bellman system derived via Pontryagins maximum principle (PMP). Subsequent backward integration, again relying on PMP, gives the SR-geodesics. For

Laplacian-regularized MAP-MRI: Improving axonal caliber estimation

\mathcal{C}=1

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

we show that our method produces the global minimizers. Comparison with exact solutions shows a remarkable accuracy of the SR-spheres and the SR-geodesics. We present numerical computations of Maxwell points and cusp points, which we again verify for the uniform cost case

New Approximation of a Scale Space Kernel on SE(3) and Applications in Neuroimaging

\mathcal{C}=1