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muscle cells

Enhancement, Completion and Detection of Elongated Structures in Medical Imaging via Evolutions on Lie Groups. Remco Duits. neural fibers in brain. bone-structure. catheters. muscle cells. hart. retinal bloodvessels. collagen fibres. DNA strains. Completion & Enhancement.

neil-stephenson
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muscle cells

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  1. Enhancement, Completion and Detection of Elongated Structures in Medical Imaging via Evolutions on Lie Groups Remco Duits neural fibers in brain bone-structure catheters muscle cells hart retinal bloodvessels collagen fibres DNA strains

  2. Completion & Enhancement Detection bone-structure muscle cells EP-catheters

  3. Completion & Enhancement Detection bone-structure muscle cells EP-catheters

  4. Invertible Orientation Scores image kernel orientation score invertible

  5. image kernel orientation score invertible orientation score image Invertible Orientation Scores orientations are disentangled in the orientation score

  6. Processing via Scores

  7. The Practical Advantage of Left Invariant Diffusions via Orientation Scores

  8. Extend to New Medical Image Modalities fibertracking fibertracking DTI HARDI Brownian motion of water molecules along fibers

  9. Challenges • Extension and analysis of non-linear diffusion on orientation scores. • 2. Diffusion on HARDI-images. • 3.Erosion on HARDI-images. • 4. Derivation Green’s functions of underlying stochastic processes for an automated graphical sketcher. • 5. Extension to other groups than SE(d) such as diffusion and erosion on • Gabor transforms of signals / images. • 6. Detection of elongated structures via Hamilton Jacobi equations on SE(2). Important for bi-plane navigation in treatments of cardiac arrhythmias. • 7. Isomorphism between diffusion and erosion on SE(d) ? • 8. Erosion towards optimal curves/modes. Compare different probabilistic • approaches to optimal paths: • contour completion elastica curves • contour enhancement geodesics

  10. : Left-invariant vector field on : Diffusion matrix Challenge II : Crossing Preserving Diffusion on HARDI

  11. Challenge II : Crossing Preserving Diffusion on HARDI

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

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

  14. Challenge V : Extension to other groups 14 • Goals : • Create a musical score from music • 2. Texture enhancement in medical imaging

  15. Strengths of the Proposal Ref. Evaluation: A+ / A+ • Mathematical Skills. Both theoretically & practically. • - “ The PI has undoubtly quite a range of theoretical knowledge (Lie groups, group representations, partial differential equations, wavelet transforms) ” (ref. 1) • “ The PI is widely regarded as an expert in the field in which he operates. ” (ref.2) • Generic Solution to Relevant Problem in Image Processing. • “ Detection, enhancement and completion of elongated structures is a very active field • of image processing. The proposal is very ambitious and covers a wide set of new investigations as well theoretically and practically oriented, which are extremely interesting in the whole. ” (ref.1) • “ General framework with numerous applications not only limited to biomedical imaging. ”(ref.2) • Realistic New Goals which build on cum laude Previous Work. • - “ Overall, the workplan is appropriate and realistic….The demand of two PhD students as well as a PostDoc fellow is justifed…. Excellent track record “ (ref.1 & 2 ) • Strong Multi-disciplinary Embedding. Both at W&I and BME. • - “Good "Embedding" environment and well-established collaborations both at the • national and international level. ” (ref.1)

  16. Strong Embedding. I have initiated (together with Luc Florack) a close and enthousiastic collaboration between W&I department and BME department at the TU/e. TU/e W&I :- Mathematical Image Processing (Florack) - LIME Imaging Applications (Matheij & Janssen). - Variational Methods and Probability Theory (Peletier & Wittich) TU/e BME : - Biomedical Applications (ter Haar Romeny & Platel) - Visualization (Vilanova). - Inviso b.v professional FPGA-design for real-time parallel computation. International: - Prof. Führ , Lehrstuhl A Für die Mathematik, RWTH Aachen, Germany. - Prof. Felsberg , Computer Vision Laboratory, Linköping University, Sweden. - Prof. Mumford , Dep. of Applied Mathematics, Brown University, Providence, USA.

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