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Image Registration: Demons Algorithm JOJO 2011.2.23

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Outline Background Demons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons Experiments Conclusions

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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

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Outline Background Demons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons Experiment Conclusion

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Demons: Maxwell’s Demons 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

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Outline Background Demons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons Experiment Conclusion

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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

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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’

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

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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

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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

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

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Outline Background Demons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons Application Conclusion

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

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Demons: Diffeomorphic Demons How to calculate exponential map 1)Let and choose N such that is close enough to 0, i.e. 2)Do N times recursive squaring of :

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Demons: Diffeomorphic Demons Diffeomorphic demons algorithm: 1)Initialize the transformation T, generally Identical transformation, then 2)Calculate the new, 3)Get the new T 4)If not convergence, go back to 2), otherwise, T is the optimal transformation

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Outline Background Demons Maxwell’s Demons Original Demons Diffeomorphic Demons Experiments Conclusions

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

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Experiment First experiments (results):

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

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Experiment Second experiments (results):

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

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Outline Background Demons Maxwell’s Demons Original Demons Diffeomorphic Demons Experiments Conclusions

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

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Thank you!

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