Image Registration: Demons Algorithm

1. Image Registration: Demons Algorithm JOJO 2011.2.23

2. Outline • Background • Demons • Maxwell’s Demons • Thirion’s Demons • Diffeomorphic Demons • Experiments • Conclusions

3. Background • Definition: Register the pixels or voxels of the same anatomical structure in two medical images • Reasons: Different ways of obtaining images Different peoples’ different anatomical structures • Current non_rigid registration methods: Demons, LDDMM (Large Deformation Diffeomorphic Metric Mapping), Hammer

4. Outline • Background • Demons • Maxwell’s Demons • Thirion’s Demons • Diffeomorphic Demons • Experiment • Conclusion

5. A gas composed of a mix of two types of particles and • The semi-permeable membrane (半透膜) contains a set of ‘demons’ (distinguish the two types of particles) • Allow particles only to side A and particles only to side B Demons: Maxwell’s Demons

6. Outline • Background • Demons • Maxwell’s Demons • Thirion’s Demons • Diffeomorphic Demons • Experiment • Conclusion

7. Demons: Thirion’s Demons • Purpose: • Assumption membrane: the contour of an object O in S demons (P): scatter along the membrane particles: M is the deformable grid, vertices are particles

8. Demons: Thirion’s Demons • Process: Push the Model M inside O if the corresponding point of M is labelled ‘inside’, and outside O if it is labelled ‘outside’

9. Demons: Thirion’s Demons • Flow chart: The space of T The interpolation method to get the value Ti(M) The selection of the demons positions Ds The formula giving the force f of a demon Simple addition or composition mapping Different demons

10. Demons: Thirion’s Demons • Demons 0: Ds: sample points of the disc contour T: rigid transformation Ti(M): analytically defined f: constant magnitude forces from Ti to Ti+1: simple addition

11. Demons: Thirion’s Demons • Demons 1: Ds: All pixels (P) of s where T: free form transformation Ti(M): trilinear interpolation f: to get the displacement from Ti to Ti+1: simple addition

12. Demons: Thirion’s Demons • Disadvantage: The topology of the image may be changed (determined by Jacobian determinant) The transformation may be nonreversible

13. Outline • Background • Demons • Maxwell’s Demons • Thirion’s Demons • Diffeomorphic Demons • Application • Conclusion

14. Demons: Diffeomorphic Demons • Basic: The most obvious difference: composition mapping not simple addition New conceptions: Lie group, Lie algebra exponential map

15. Demons: Diffeomorphic Demons • How to calculate exponential map • Let and choose N such that is close enough to 0, i.e. • Do N times recursive squaring of :

16. Demons: Diffeomorphic Demons • Diffeomorphic demons algorithm: • Initialize the transformation T, generally Identical transformation, then • Calculate the new , • Get the new T • If not convergence, go back to 2), otherwise, T is the optimal transformation

17. Outline • Background • Demons • Maxwell’s Demons • Original Demons • Diffeomorphic Demons • Experiments • Conclusions

18. Experiment • First experiments (design): 100 experiments with random images to compare Thirion’s demons and diffeomorphic demons

19. Experiment • First experiments (results):

20. Experiment • Second experiment (design): Use synthetic T1 MR images from two different anatomies available from BrainWeb

21. Experiment • Second experiments (results):

22. Experiment • Third experiment: Try to apply the demons algorithm to automatic unsupervised classification of MR images in AD

23. Outline • Background • Demons • Maxwell’s Demons • Original Demons • Diffeomorphic Demons • Experiments • Conclusions

24. Conclusion • Advantages: Realize automation Good performance on non_rigid registration Relatively fast speed • Disadvantage: The segmentation accuracy based on demons need to be improved

25. Thank you!