1. Challenges

2. Challenge I : Improve adaptive diffusion on orientation score Iterate: 1. Estimate local shape (by exp-curve fit ) 2. Diffusion-step curvature orientation strength ?

3. Challenge II : Crossing Preserving Diffusion on HARDI Convolution (Precompute) : spherical surface measure : Green’s function diffusion : any rotation such that : Reflected Green’s function Left Invariant Finite Differences Goal : non-linear adaptive crossing preserving HARDI-diffusion (adaptive curvature & torsion)

4. 1. Angular erosion 2. Spatial erosion Challenge III : Left Invariant HJB-Equations on HARDI Combine the 2 evolution processes below to single erosion process on Goal: Improve fibertracking

5. Challenge IV : Contour completion Green’s functions diffusion on orientation scores of 2D-images Green’s functions diffusion on HARDI Contour enhancement

6. Left-invariant diffusion and erosion on Gabor trafo’s: 1. 2. Collagen fibres Muscle cells Extend to 2D texture analysis and recognition by evolutions on Gabor transforms and orientation scores. Challenge V: Applications

7. Challenge VI: EP-Catheter detection for bi-plane navigation in treatments of cardiac arrythmias Goal: Improve our final detection by : 1.Hamilton Jacobi Bellman equations on SE(2) 2.snakes on contact manifold Lagrangian: Internal energy (geodesics) + external energy (smoothed score)

8. Challenge VII: Towards a Graphical Eraser and the fundamental relation to diffusion Would like to get something in between Modes Mumford: “Modes are elastica curves”, since: ERASESKETCH