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Medical Imaging

Medical Imaging. Dr. Mohammad Dawood Department of Computer Science University of Münster Germany. Recap. Sound waves Piezoelectric crystals Wave front formation. Inverse Radon transform Filtered back projection. Filtered back projection.

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Medical Imaging

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  1. Medical Imaging Dr. Mohammad Dawood Department of Computer Science University of Münster Germany

  2. Recap

  3. Sound waves Piezoelectric crystals Wave front formation

  4. Inverse Radon transformFiltered back projection Filtered back projection

  5. Fourier slice theorem Kaczmarz Method (=ART)

  6. Image Registration

  7. Registration T : Transformation In this lecture Floating image : The image to be registered Target image : The stationary image

  8. Registration Linear Transformations - Translation - Rotation - Scaling - Affine

  9. Registration 3D Translation

  10. Registration 3D Rotation

  11. Registration 3D Scaling

  12. Registration Rigid registration Angles are preserved Parallel lines remain parallel

  13. Registration Affine registration

  14. Registration Feature Points

  15. Registration Feature Points 1. De-mean 2. Compute SVD 3. Calculate the transform

  16. Registration Feature Points Iterative Closest Points Algorithm (ICP) 1. Associate points by the nearest neighbor criteria. 2. Estimate transformation parameters using a mean square cost function. 3. Apply registration and update parameters.

  17. Registration Feature Points

  18. Registration Feature Points Random Sample Consensus Algorithm (RNSAC) 1. Transformation is calculated from hypothetical inliers 2. All other data are then tested against the fitted model and, if a point fits well to the model, also considered as a hypothetical inlier 3. The estimated model is reasonably good if sufficiently many points have been classified as hypothetical inliers. 4. The model is re-estimated from all assumed inliers 5. Finally, the model is evaluated by estimating the error of the inliers relative to the model

  19. Registration Distance Measures - Sum of Squared Differences (SSD) - Root Mean Square Difference (RMSD) - Normalized Cross Correlation (NXCorr) - Mutual Information (MI)

  20. Registration Sum of Squared Differences SSD(f,t) SSD(20f,t)

  21. Registration Root Mean Squared Differences RMS(f,t) RMS(20f,t)

  22. Registration Normalized Cross Correlation NXCorr(f,t) NXCorr(20f,t)

  23. Registration Mutual Information MI(f,t) MI(20f,t)

  24. Define a joint probability distribution: Generate a 2-D histogram where each axis is the number of possible greyscale values in each image each histogram cell is incremented each time a pair (I1(x,y), I2(x,y)) occurs in the pair of images If the images are perfectly aligned then the histogram is highly focused. As the images mis-align the dispersion grows recall Entropy is a measure of histogram dispersion Entropy for Image Registration

  25. Optical Flow

  26. Optical flow Brightness consistency constraint With Taylor expansion V : Flow (Motion)

  27. Optical flow Lucas Kanade Algorithm: Assume locally constant flow =>

  28. Optical flow Horn Schunck Algorithm: Assume globally smooth flow

  29. Optical flow Bruhn’s Non-linear Algorithm

  30. PET no AC – gated PET no AC – gated, MC corrected

  31. Cardiacmotion Ungated data Large blur, low noise (Problem in plaque imaging) Onephase Small blur, highnoise

  32. Systole Diastole Continuity Equation:

  33. Visual result

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