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Non-rigid Registration Methods for Medical Images

Non-rigid Registration Methods for Medical Images. Jan Kamenick ý Mariánská 2008. Registration. Registration. We deal with medical images Different viewpoints - multiview Different times - multitemporal Different sensors – multimodal Area-based methods (no features) Transformation model

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Non-rigid Registration Methods for Medical Images

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  1. Non-rigid Registration Methods for Medical Images Jan Kamenický Mariánská 2008

  2. Registration

  3. Registration • We deal with medical images • Different viewpoints - multiview • Different times - multitemporal • Different sensors – multimodal • Area-based methods (no features) • Transformation model • Cost function minimization

  4. Registration framework • Transformation model • Displacement field u(x)

  5. Registration framework • Transformation model • Displacement field u(x) • Cost function • Similarity measure (external forces) • Smoothing (penalization) term (internal forces) • Additional constraints (landmarks, volume preservation)

  6. Registration framework • Transformation model • Displacement field u(x) • Cost function • Similarity measure (external forces) • Smoothing (penalization) term (internal forces) • Additional constraints (landmarks, volume preservation) • Minimization

  7. Transformation models • Translation • Rigid (Euler) • Translation, rotation • Similarity • Translation, rotation, scaling • Affine • B-splines • Control points - regular grid on reference image

  8. Transformation models

  9. Similarity measure • Sum of Squared Differences • Normalized Correlation Coefficients • Mutual Information • Normalized Gradient Field

  10. Similarity measure • Sum of Squared Differences (SSD) • Equal intensity distribution (same modality) • Normalized Correlation Coefficients • Mutual Information • Normalized Gradient Field

  11. Similarity measure • Sum of Squared Differences • Normalized Correlation Coefficients (NCC) • Linear relation between intensity values (but still same modality) • Mutual Information • Normalized Gradient Field

  12. Similarity measure • Sum of Squared Differences • Normalized Correlation Coefficients • Mutual Information • Any statistical dependence • Normalized Gradient Field

  13. Similarity measure (MI) • Mutual Information (MI) • From entropy

  14. Similarity measure (MI) • Mutual Information (MI) • From Kullback-Leibler distance

  15. Similarity measure (MI) • Mutual Information (MI) • For images • p(x) … normalized image histogram • Normalized Mutual Information (NMI)

  16. Similarity measure (MI) • Mutual Information (MI) • Joint probability estimation • Using B-spline Parzen windows • and are defined by the histogram bins widths

  17. Similarity measure • Sum of Squared Differences • Normalized Correlation Coefficients • Mutual Information • Normalized Gradient Field (NGF) • Based on edges

  18. Smoothing term • Elastic • Elastic potential (motivated by material properties) • Fluid • Viscous fluid model (based on Navier-Stokes) • Diffusion • Much faster

  19. Smoothing term • Curvature • Doesn’t penalize affine transformation • Bending energy (Thin plate splines)

  20. Smoothing term curvature diffusion elastic fluid

  21. Additional constraints • Landmarks (fiducial markers) • “Hard” constraint • “Soft” constraint • Volume preservation

  22. Sampling • Full • Grid • Used with multi-resolution • Random • Random subset of voxels is selected • Improved speed

  23. Optimisation

  24. Optimisation methods • Gradient Descent (GD) • Linear rate of convergence • Quasi-Newton • Nonlinear Conjugate Gradient • Stochastic Gradient Descent • Evolution Strategy

  25. Optimisation methods • Gradient Descent • Quasi-Newton (QN) • Can be superlinearly convergent • Nonlinear Conjugate Gradient • Stochastic Gradient Descent • Evolution Strategy

  26. Optimisation methods • Gradient Descent • Quasi-Newton • Nonlinear Conjugate Gradient (NCG) • Superlinear rate of convergence can be achieved • Stochastic Gradient Descent • Evolution Strategy

  27. Optimisation methods • Gradient Descent • Quasi-Newton • Nonlinear Conjugate Gradient • Stochastic Gradient Descent (SGD) • Similar to GD, but uses approximation of the gradient (Kiefer-Wolfowitz, Simultaneous Perturbation, Robbins-Monro) • Evolution Strategy

  28. Optimisation methods • Gradient Descent • Quasi-Newton • Nonlinear Conjugate Gradient • Stochastic Gradient Descent • Evolution Strategy (ES) • Covariance matrix adaptation • Tries several possible directions (randomly according to the covariance matrix of the cost function), the best are chosen and their weighted average is used

  29. Multi-resolution • Data complexity • Gaussian pyramid • Laplacian pyramid • Wavelet pyramid • Transformation complexity • Transformation superposition • Different B-spline grid density

  30. Elastix • Registration toolkit based on ITK • Handles many methods • Similarity measures (SSD, NCC, MI, NMI) • Transformations (rigid, affine, B-splines) • Optimizers (GD, SGD-RM) • Samplers, Interpolators, Multi-resolution, … http://elastix.isi.uu.nl

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