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( Adaptive ) enhancement of HARDI images

( Adaptive ) enhancement of HARDI images. Eric Creusen Supervisor: Remco Duits. Diffusion of Water. Diffusion is dependent on orientation. * Graphic borrowed from Thomas Schultz. Diffusion of water: Modelling. Domain.

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( Adaptive ) enhancement of HARDI images

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  1. (Adaptive) enhancement of HARDI images Eric Creusen Supervisor: Remco Duits

  2. Diffusion of Water Diffusion is dependent on orientation *Graphicborrowedfrom Thomas Schultz / BIOMIM

  3. Diffusion of water: Modelling BIOMIM

  4. Domain Diffusionweighted images are functionsonposition and orientation Both HARDI and DTI! / Communicatie Expertise Centrum

  5. Embed in group Embedposition and orientationintotranslations and rotationgroup / BIOMIM

  6. Parametrization of Sphere Euler Angles / Communicatie Expertise Centrum

  7. Embeddingproblem SE(3) has 3 angles(α,β,γ) Positions and orientationonly 2 (β,γ) Orientations are independent of α Introduceequivalence classes on SE(3) Processesshould preserve α-invariance! / BIOMIM

  8. Convection-diffusionprocesses Seefunction as distribution of orientedparticles Particlescan translate and rotate / BIOMIM

  9. Rotatedcoordinate system A1 z A3 n n Rn (α) y A2 x / Communicatie Expertise Centrum

  10. Now that we have a basis: derivatives! In the same direction as normal Angular derivatives Should be zero Perpendicular (make random choice here) Derivativescanbecalculated Directionsdependantonorientationn 3 spatialdirections 2 angulardirections (+1 dummy direction) For n=ez / Communicatie Expertise Centrum

  11. Smoothing processes Withderivatives, we cansimulatediffusionprocessesbysimulatingPDE’s General diffusionprocesses are givenby the PDE: (with parameter D and simulation time t) / Communicatie Expertise Centrum

  12. Some simple examples Notinteresting, onlyspatial OR onlyangulardiffusion • IsotropicSpatialGaussian smoothing: • Angulardiffusion: / Communicatie Expertise Centrum

  13. More examples “Contour enhancement” Spatial diffusion Angular diffusion “Contour completion” Convection term / Communicatie Expertise Centrum

  14. Simulation of PDEs • Convolutions with kernels • Finite difference methods / Communicatie Expertise Centrum

  15. Creating convolution kernels Getapproximationswithcomplicatedmath……. OR Start withoriented delta peak Simulate PDE withfinitedifferencemethods / Communicatie Expertise Centrum

  16. Finite difference methods: enhancement enhancement Directly use finite difference methods to simulate PDE / Communicatie Expertise Centrum

  17. Finite difference: contour completion completion / Communicatie Expertise Centrum

  18. Adaptive filtering Makesmoothingdependanton data Finitedifferencemethodsneccesary / Communicatie Expertise Centrum

  19. Perona-Malik type diffusion “Contour enhancement” Goal: Edge preserving smoothing Contour enhancement, but stop diffusionacrossedges / BIOMIM

  20. / BIOMIM

  21. / BIOMIM

  22. Future work • Adaptivediffusionprocesses • Usecurvature and torsionforadaptiveprocesses • Combine diffusion and erosionprocesses • Start lookinginto practical applications / Communicatie Expertise Centrum

  23. Questions? / Communicatie Expertise Centrum

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