Jeroen Hermans, Frederik Maes, Dirk Vandermeulen, Paul Suetens Unified Framework for Automatic Segmentation, Probabilistic Atlas Construction, Registration and Clustering of Brain MR Images Annemie Ribbens Jeroen Hermans, Frederik Maes, Dirk Vandermeulen, Paul Suetens

Introduction Computer–aided diagnosis

Introduction Segmentation

Introduction Atlas & Atlas-to-image registration Φ

Introduction Population Specific Atlases

Introduction Atlas Construction Images I Registrations Atlas previous iteration Registrations

Images I Deformed images New Atlas Averaging

Introduction Computer aided-diagnosis Registration Segmentation Prob. Atlases Registration

Framework Aspects: Advantages: Segmentation Clustering (i.e. computer-aided diagnosis) (+ Localization of cluster specific morphological differences) Groupwise registration (nonrigid probabilistic atlases per cluster) Atlas-to-image registration Advantages: Less prior information necessary Cooperation Statistical framework  convergence

Framework Segmentation Atlas-to-image registration Atlas formation & Clustering

Framework: model K = tissue classes  number of Gaussians Y = intensities Image i

Framework: model Atlas t (Gray matter map) Image i (Gray matter map)

Framework: model Uniform prior for all voxels in an image

Framework: model G1 G2 Deformations

Framework: MAP MAP: Jensen’s inequality Expectation maximization framework

Framework: EM algorithm: E-step i = images j = voxels k = tissue classes t = clusters Per cluster: atlas deformed towards image Gaussian prior on the deformations of each cluster Uniform prior on the cluster memberships Gaussian mixture model

Framework: EM Posterior Posterior = (clustering) * (segmentation using the atlas of the same cluster) Clustering = probability that voxel j of image i belongs to cluster t = sum over all tissue classes of the posterior = (prior of clustering) * (atlas is sharp & close to intensity model) * (subject specific registration close to groupwise) Segmentation = probability that a voxel belongs to a certain tissue class = sum over all clusters of the posterior = weighted sum of the segmentations using a specific atlas

Framework: EM algorithm: M-step Maximum likelihood Q-function  parameters All solutions close form (except registration) Solutions (e.g. atlas) ~ literature

Framework: EM algorithm: M-step Gaussian mixture parameters: Atlas Prior cluster memberships Groupwise registration Atlas-to-image registration No closed form solution Spatial regularization  Viscous fluid model on derivative  Weighting terms per voxel

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Experiments Brainweb data: 20 simulated normal images One cluster  Segmentation & Atlas: Dice =

Experiments 8 brain MR images of healthy persons (normals) 8 brain MR images of Huntington disease patients (HD)  Cluster memberships: all correctly classified

Conclusion Statistical framework combining: Segmentation Clustering Atlas construction per cluster (weighted) Registration  Convergence & cooperation & less prior information needed Validation  promising Cluster specific morphological differences are found Easily extendable to incorporate clinical/spatial prior knowledge