Quantitative Neuro-Anatomic and Functional Image Assessment Recent progress on image registration and its applications Applications of image registration in neuroimagingMotivation: A Natural QuestionPopulation VariabilityAverage after linear alignment (affine)Motivation: A Natural QuestionMotivation: A Natural QuestionMotivation: A Natural QuestionMotivation: A Natural QuestionMathematical Foundations of Computational AnatomyUnbiased Diffeomorphic Atlas Construction for Computational Anatomy (Joshi, Davis, Lorenzen)Slide Number 12Averaging Anatomies’Group-wise Atlas BuildingMore than Pairs: Sample of 16 Bull’s eye ImagesGroup-wise Image AveragingAveraging of 16 Bull’s eye imagesAverages in Metric SpacesLarge deformation diffeomorphisms.Atlas Building – Population Average (Infant 2 yr)Atlas Builder – Atlas with 14 imagesAveraging Brain ImagesMotivation Atlas Building: Statistics of embedded ShapesEmbedded Objects: Voxel RepresentationVoxel-based Representation: Linear vs. Nonlinear AtlasAtlas-based segmentation: Atlas BuildingPipelineSlide Number 29Automatic segmentation (N=130)DTI: Population-based analysis of fiber tractsAtlas Building for DTI Tensor FieldsSlide Number 33Unbiased atlas-building by deformable registrationCo-registration: From linear to nonlinearAtlas Building: FA of average tensor fieldQuantitative Fibertracking: Example Uncinate FasciculusConcept: Group statistics of fiber tracts Pediatric Example: Genu Tract 1-2yrs Towards 4D Atlases: Study of Healthy AgingManifold Kernel Regression (B. Davis)Manifold Kernel Regression (B. Davis)Aging Brain via Population Shape: Manifold Kernel RegressionBibliographyConclusionsSlide Number 46Quantitative Neuro-Anatomic and Functional Image Assessment Recent progress on image registration and its applicationsGuido GerigSarang JoshiTom FletcherApplications of image registration in neuroimaging• Atlas construction– Probabilistic atlases– Statistical atlases– Unbiased atlases• Atlas-based segmentation– Atlases are used as prior knowledge– Tissue and/or anatomical segmentation• Quantification of anatomical and functional differences– across time ⇒ longitudinal studies– across groups ⇒ cross-sectional studiesMotivation: A Natural Question• Given a collection of Anatomical Images what is the Image of the “Average Anatomy”.Courtesy S. JoshiPopulation Variability• How to compare and measure structures across different subjects?Courtesy S. JoshiAverage after linear alignment (affine)Adult brain MRI atlas (Montreal Neurological Institute):• 152 adult subjects• Affine registration• Superposition• Serves as probabilistic template for brain mapping• Blurry, does not look like a real imageMotivation: A Natural QuestionWhat is the Average?Consider two simple images of circles:Courtesy S. JoshiMotivation: A Natural QuestionWhat is the Average?Consider two simple images of circles:Courtesy S. JoshiMotivation: A Natural QuestionWhat is the Average?Courtesy S. JoshiMotivation: A Natural QuestionAverage considering “Geometric Structure” A circle with “average radius”Courtesy S. JoshiMathematical Foundations of Computational Anatomy• Structural variation with in a population represented by transformation groups:– For circles simple multiplicative group of positive reals (R+)– Scale and Orientation: Finite dimensional Lie Groups such as Rotations, Similarity and Affine Transforms.– High dimensional anatomical structural variation: Infinite dimensional Group of Diffeomorphisms.Courtesy S. JoshiUnbiased Diffeomorphic Atlas Constructionfor Computational Anatomy (Joshi, Davis, Lorenzen)Image 1 Image 2Meanh1(x) h2(x)Mean by WarpingAtlas Formation: Symmetric RegistrationAveraging Anatomies’Group-wise Atlas BuildingMinimize total distance beetween population and template(Gee & Avants, Joshi&Fletcher)More than Pairs: Sample of 16 Bull’s eye ImagesCourtesy S. JoshiGroup-wise Image AveragingCourtesy S. JoshiAveraging of 16 Bull’s eye imagesVoxel Averaging LDMM AveragingNumerical geometric average of the radii of the individual circles forming the bulls eye sample.Courtesy S. JoshiAverages in Metric SpacesLarge deformation diffeomorphisms.• infinite dimensional “Lie Group”. • Tangent space: The space of smooth vector valued velocity fields on .• Construct deformations by integrating flows of velocity fields.• Induce a metric via a differential norm on velocity fields.)(ΩDiffΩddth (x; t)=v(h(x; t); t) h(x; 0)=x:Atlas Building – Population Average (Infant 2 yr)Atlas Builder – Atlas with 14 imagesAveraging Brain ImagesMotivation Atlas Building: Statistics of embedded Shapes• Brain atlases is central to the understanding of the variability of brain anatomy.• How to study statistical shape properties from nonlinear deformation fields of atlases?h1h2h3h4hnEmbedded Objects: Voxel RepresentationTo evaluate shape variability • reliable user-supervised voxel segmentations by geodesic snakes• probability map in atlas spaceh1h2h3h4hnVoxel-based Representation: Linear vs. Nonlinear Atlas• Single population• Linear averaging of voxel objects — blurry probability maps• Nonlinear average appears sharper• Notion of probabilistic label atlas: centered & population-basedLinearNonlinearAtlas-based segmentation: Atlas BuildingT1T2T3T4T5T6T1T2T3T4T5T6Template image created from several casesProbabilistic maps of the 12 ROIsStep 1 Step 2PipelineAtlas with segmented structuresCase iTransformationTFrom the atlas to the case iAmygdalaPutamenPallidusCaudateHyppocampusLat VentricleAmygdalaPutamenPallidusCaudateHyppocampusLat Ventricle12transformation TSagittal ViewCoronal ViewAxial ViewSegmented ROIsSegmented caseWithout ROIs With ROIsAutomatic segmentation (N=130)UNC Chapel Hill pediatric autism study (J. Piven, H. Cody, G. Gerig et al.)DTI: Population-based analysis of fiber tractsExample: 150 neonate DTI mapped to unbiased atlasCasey Goodlett, Sarang Joshi, Sylvain Gouttard, Guido Gerig, (MICCAI’06, MICCAI’08, NeuroImage 2009Atlas Building for DTI Tensor FieldsI1I5I2I3I4Î1Atlas[Joshi et al 2004] [Goodlett et al 2006, 2009]Backdrop: FAColor: RGB(e1)G. KindlmannUnbiased atlas-building by deformable registrationStructuralAverageDeformation Fields(1:N) StructuralOperatorTransformation(Affine, Fluid) H-1-fields(1:N) [Goodlett et al MICCAI 06, ISMRM 06][Goodlett et al., NeuroImage, in print]Co-registration: From linear to nonlinearLinear registration (affine)