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
w1 w8
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