Registration - ISlide Number 2Formulation of problemDistance Measures?Slide Number 5Intensity BasedResultsMutual Information2-D HistogramSlide Number 11Histogram dispersion Registration criterionSlide Number 14Maximization of mutual informationSlide Number 16Slide Number 17GroupsSlide Number 19Slide Number 20Shashidhar Reddy Puchakayala (Shashi)Apr 15, 2010 What is registration? Why registration ?T ?Formulation of problemFind feasible transformations , , such thatDistance Measures? Uni Modality Intensity based. Correlation Multi Modality Mutual Information and joint Entropy Maximum Likelihood Kullback-Leibler DivergenceIntensity Based Minimisation of squared differencesResultsMutual InformationT ?2-D Histogram How does a 2-D histogram of two same images look like ?Image 1Image 2Registration compensates for different head position at acquisition.Difference imageunregisteredregisteredsagittal slices256 x 256 x 91.2 x 1.2 x 4mmHistogramHistogram dispersionp,aq,bTαA BRegistered Not registered2-D histogramCT intensityCT intensityMRintensityRegistration criterionthe statistical dependence of corresponding voxel intensities is maximal at registrationa abp(b|a)p(b|a)RegisteredNot registeredInterpretationHA(α), HB(α) marginal entropy of A and B, respectivelyHAB(α) joint entropy of A and BIAB(α) mutual information of A and BIAB(α) = HA(α) + HB(α) - HAB(α)“Find as much of the complexity in the separate datatsets (maximizing HAand HB) such that at the same timethey explain each other well (minimizing HAB).”IAB(α) = HA(α) - HA|B(α) “Find as much of the complexity in datatset A (maximizing HA) while minimizing the residual complexity of A knowing B (minimizing HA|B).”Maximization of mutual informationMaximization of mutual informationabTαABApplicationRadiotherapy treatment planning of the prostate from CT and MR images (Oyen et al.)
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