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Non-Rigid Registration

Non-Rigid Registration. Why Non-Rigid Registration. In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject: tissue deformation Inter-subject: anatomical variability across individuals Fast-Moving area: Non-rigid.

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Non-Rigid Registration

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  1. Non-Rigid Registration

  2. Why Non-Rigid Registration • In many applications a rigid transformation is sufficient. (Brain) • Other applications: Intra-subject: tissue deformation Inter-subject: anatomical variability across individuals • Fast-Moving area: Non-rigid

  3. Registration Framework • In terms of L.Brown.(1992) • Feature Space • Transformation • Similarity Measure • Search Strategy (Optimization) • Rigid vs. Non-rigid in the framework

  4. Feature Space • Geometric landmarks: Points Edges Contours Surfaces, etc. • Intensities: Raw pixel values • 35 • 56

  5. Transformation

  6. Transformation • Rigid transformation: 3DOF (2D) 6 DOF (3D) • Affine transformation: 12 DOF

  7. Transformation • Additional DOF. • Second order polynomial-30 DOF • Higher order: third-60, fourth-105,fifth-168 • Model only global shape changes

  8. Transformation • For each pixel (voxel), one 2d(3d) vector to describe local deformation. • Parameters of non-rigid >> that of rigid

  9. Similarity Measure • Point based ---The distance between features, such as points,curves,or surfaces of corresponding anatomical structure. --- Feature extraction. • Voxel based ---Absolute Difference, Sum of squared differences, Cross correlation, or Mutual information

  10. Search Strategy • Registration can be formulated as an optimization problem whose goal is to minimize an associated energy or cost function. • General form of cost function: C = -Csimilarity+Cdeformation

  11. Search Strategy • Powell’s direction set method • Downhill simplex method • Dynamic programming • Relaxation matching Combined with • Multi-resolution techniques

  12. Registration Scheme

  13. Non-rigid Registration • Feature-based • Control Points: TPS • Curve/Edge/Contour • Surface • Intensity-based • Elastic model • Viscous fluid model • Others

  14. Thin-plate splines (TPS) • Come from Physics: TPS has the property of minimizing the bending energy.

  15. TPS (cont.) • Splines based on radial basis functions • Surface interpolation of scattered data

  16. Description of the Approach • Select the control points in the images. • Calculate the coefficients for the TPS. • Apply the TPS transformation on the whole image.

  17. Synthetic Images T2 T1

  18. TPS-Results(1)

  19. TPS-Results(2)

  20. Rigid and non-rigid registration • Rigid Registration as pre-processing (global alignment) • Non-rigid registration for local alignment

  21. Next time • Affine-mapping technique

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