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Johns Hopkins EN 600 446 - MultiModality Registration Using Hilbert-Schmidt Estimators

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MultiModality Registration Using Hilbert-Schmidt EstimatorsOutlineThe ProjectOriginal Maximal DeliverablesWhat Has Been Achieved?RegistrationRegistering different modalitiesHow accurate is this method?What is the Hilbert-Schmidt bound?Maximization of Mutual InformationComparison of the two algorithmsPros and ConsPros and Cons Cont’dImprovements to be madeGradient Descent AlgorithmFuture DirectionsFeasibility of HS algorithm in real-life circumstancesWhat have I learned?What would I do differently?ConclusionsI’m DONE!!!MultiModality Registration MultiModality Registration Using Hilbert-Schmidt EstimatorsUsing Hilbert-Schmidt EstimatorsBy: Srinivas PeddiComputer Integrated Surgery IIApril 27th, 2001Final PresentationFinal PresentationOutlineOutline•Brief refresher of my project•Things accomplished in the project•Things left to improve upon•Future Directions•ConclusionsThe ProjectThe ProjectT1PDT2I want to be able to register different modalities of MR images accurately. This means coming up with a new registration algorithm and getting around the intensity difference problem.Original Maximal DeliverablesOriginal Maximal Deliverables•To register the three different modalities accurately by first using Bayesian Segmentation to circumvent the intensity-difference problem.•To compare this approach with other multimodality registration algorithms such as the Maximization of Mutual Information algorithm.•To examine the feasibility of using the Hilbert-Schmidt algorithm in real-life applications.What Has Been Achieved?What Has Been Achieved?T1PDT2Original imagesPD SegmentationPD SegmentationT1 SegmentationT1 SegmentationT2 SegmentationT2 SegmentationOriginal images  Bayesian SegmentationOriginal images  Bayesian Segmentation  Switching of IntensitiesPD Switched PD Switched SegmentationSegmentationT1 Switched T1 Switched SegmentationSegmentationT2 Switched T2 Switched SegmentationSegmentation•Once the segmentation process is done, and the intensities have been switched, we can actually do the registration.•We apply the Hilbert-Schmidt algorithm which uses a minimum mean-squared (MMSE) estimator. •Registration is achieved by finding the element of the special Euclidean group (SEn) that minimizes the error. RegistrationRegistrationRegistering different modalitiesRegistering different modalities•The maximum aim of the project has been achieved.•At this point, we are able to register PD with T1 (which you saw in the checkpoint presentation) but we can now also register PD with T2 and T1 with T2.•These registrations are possible at different noise levels as long as the segmentation is reasonable.How accurate is this method?How accurate is this method?•To examine how accurate something is, we must first define an error measure. The one that I will be using is called the Hilbert-Schmidt bound.•A second thing that can help in getting an intuitive feel about the accuracy of the algorithm, is having another algorithm to compare it to. In this presentation, I will be using the Maximization of Mutual Information Algorithm.What is the Hilbert-Schmidt bound?What is the Hilbert-Schmidt bound?•The Hilbert-Schmidt norm is defined as the norm of a matrix. Example:A = [2 -1 -4 -2]||A|| = [ 22 + (-1)2 + (-4)2 + (-2)2 ]1/2 = 5•The Hilbert-Schmidt bound (HSB) is defined as the matrix norm of the difference between the true matrix transformation and the calculated matrix transformation.Maximization of Mutual InformationMaximization of Mutual Information•This algorithm was implemented by Wells et al. at the SPL in 1996. Since then, it has become the registration tool of choice when doing multimodality registration.•The algorithm attempts to find the registration by maximizing the information that one volumetric image provides about the other.Comparison of the two algorithmsComparison of the two algorithmsAs one can see, the Hilbert-Schmidt algorithm outperforms the mutual information algorithm at high noise but at low noise, they both register the images accurately.HSB as a function of Signal Strength for registering T1 vs. T2 images00.10.20.30.40.50.60.70.80.91Signal StrengthHSBMutual InformationHilbert-SchmidtPros and ConsPros and Cons•Accuracy: As mentioned, it seems that the Hilbert-Schmidt algorithm outperforms the mutual information algorithm in this category, especially at high noise levels.•Speed: The Mutual Information algorithm runs much faster, at least for now, especially because it does not do much preprocessing.•Generality: The Mutual Information algorithm assumes no a priori relationship between the two modalities and hence all modalities can be registered using the same algorithm. The Hilbert-Schmidt algorithm is striving to do the same.Pros and Cons Cont’dPros and Cons Cont’d•Ease of use: Since the Mutual Information algorithm has less steps or at least is better integrated, it is easier to use. The hope is that later, the segmentation and the registration can be coupled in one program in which case, the Hilbert-Schmidt would also become easier to use.•Robustness: Since the Mutual Information algorithm is essentially a simpler algorithm with less steps, it is very robust. With time, I hope to make the Hilbert-Schmidt algorithm as robust.Improvements to be madeImprovements to be made•Gradient descent algorithm has been implemented but can be improved upon especially by using a ‘blurring’ algorithm and also by selecting random points more wisely.•The algorithm needs to be extended so that one can register 3D volumes rather than just 2D images which is what we have now.Gradient Descent AlgorithmGradient Descent AlgorithmProbability Density Function00.050.10.150.20.250.30.350.40.450.50 30 60 90 120 150 180 210 240 270 300 330 360Angle of RotationProbabilityWhat I presently do is pick a series of random points from 0 to What I presently do is pick a series of random points from 0 to 360, and then march in the direction of increasing probability. It 360, and then march in the direction of increasing probability. It would be nice to add two layers of random points so that there would be nice to add two layers of random points so that there


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Johns Hopkins EN 600 446 - MultiModality Registration Using Hilbert-Schmidt Estimators

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