National Alliance for Medical Image Computing Segmentation Foundations Easy Segmentation –Tissue/Air (except bone in MR) –Bone in CT Feasible Segmentation –White Matter/Gray Matter: MRI –M.S. White Matter Lesions: MRI

National Alliance for Medical Image Computing Statistical Classification Probabilistic model of intensity as a function of (tissue) class Intensity data Prior model Classification of voxels [Duda, Hart 78][MRI: MikeVannier late 80s]

National Alliance for Medical Image Computing Measurement Model Characterize sensor p(x|tissue class J) probability density intensity Tissue class conditional model of signal intensity mean for tissue J

National Alliance for Medical Image Computing A bit of notation… Estimate  by finding the one that maximizes the function f

National Alliance for Medical Image Computing Maximum Likelihood (ML) Estimation Estimate parameters to maximize probability of observed data conditioned on parameters. y o : observed data p(y|  ) : Measurement Model  Model Parameters

National Alliance for Medical Image Computing Example intensity p(x|gray matter) p(x|white matter)

National Alliance for Medical Image Computing Example - revisited white matter threshold gray matter

National Alliance for Medical Image Computing Multiple Sclerosis PDw T2w Provided by S Warfield

National Alliance for Medical Image Computing Dual Echo MRI Feature Space csf severe lesions gm wm air T2 Intensity PD Intensity

National Alliance for Medical Image Computing Detail MS Lesions are “graded phenomenon” in MRI, and can be anywhere on the curve gm wm lesions csf healthy mild severe

National Alliance for Medical Image Computing Multiple Sclerosis PDw T2w Segmentation Provided by S Warfield

National Alliance for Medical Image Computing Maximum A-Posteriori (MAP) Estimation Estimate parameters to maximize posterior probability model parameters conditioned on observed data Use Baye’s rule – ignore denominator p(  ) : Prior Model

National Alliance for Medical Image Computing Multiple Sclerosis PDw T2w kNNSVC Provided by S Warfield

National Alliance for Medical Image Computing Background: Intensity Inhomogeneities in MRI MRI signal derived from RF signals… Intra Scan Inhomogeneities –“Shading” … from coil imperfections –interaction with tissue? Inter Scan Inhomogeneities –Auto Tune –Equipment Upgrades

National Alliance for Medical Image Computing ML Estimation – with missing data x : missing data (true labeling) y 0 : observed intensities  : (parameters of) bias field

National Alliance for Medical Image Computing ML Estimation – EM Approach E []: Expected value under p(x|y o,  ) Take expectation of objective function with respect to the missing data, conditioned on everything we know x : missing data (true labeling) y 0 : observed intensities  : (parameters of) bias field

National Alliance for Medical Image Computing EM Algorithm General exponential family Iterate to convergence: E step: M step:

National Alliance for Medical Image Computing EM Algorithm: Example Measurement Model –Tissue intensity properties with bias correction Missing Data –Unknown true classification Prior Models –Tissue Frequencies –Intensity Correction is Low Frequency ML estimate of bias

National Alliance for Medical Image Computing Estimate intensity correction using residuals based on current posteriors. Compute tissue posteriors using current intensity correction. M-Step E-Step EM-Segmentation Provided by T Kapur

National Alliance for Medical Image Computing EM Segmentation… PD, T2 Data Seg Result w/o EM Seg Result With EM

National Alliance for Medical Image Computing EM Segmentation… External Surface of Brain

National Alliance for Medical Image Computing EM Segmentation… WM Surface with EMWM Surface w/o EM

National Alliance for Medical Image Computing EM Segmentation: MS Example Data provided by Charles Guttmann PDT2

National Alliance for Medical Image Computing EM Segmentation: MS Example Seg w/o EMSeg with EM

National Alliance for Medical Image Computing Prior Probability Models Simple: Frequency of Tissues More Interesting: –Powerful Mechanism for Incorporating Domain Knowledge into Segmentation Tissue properties Relative Location of Structures Atlases

National Alliance for Medical Image Computing Prior Model Example: EM-MF Segmentation Tina Kapur PhD thesis EM Segmentation, augmented with –Ising prior of tissue homogeneity Solved with Mean Field Approxomation –Prior on relative position of organs Spatially Conditioned Models

National Alliance for Medical Image Computing Prior Models: Ising Model Ising Model can capture the phenomenon of piecewise-homogeneity. Initially used in Statistical Physics to model the magnetic domains in Ferromagnetism. Used in Medical Image Processing to model the piecewise-homogeneity of Tissue.

National Alliance for Medical Image Computing Prior Models: Ising Model Ising Model relaxes spatial independence assumption Voxels depend conditionally on (only) their neighbors More probable to agree with neighbor

National Alliance for Medical Image Computing Define the Neighborhood 2 nd Order Lattice 26 Neighbors 1 st Order Lattice 6 Neighbors Reduce calculation cost => use 1 st order Lattice Neighbors = {East, South, West, North, Up, Down} Provided by K Pohl

National Alliance for Medical Image Computing Potts Model Potts model generalizes Ising model so that each lattice site takes on several values (more than two). Frequently used to model tissues (e.g. White Matter, Gray Matter, CSF, Fat, Air, etc.)

National Alliance for Medical Image Computing Some Results EM EM-MF Provided by T Kapur

National Alliance for Medical Image Computing More Results Noisy MRIEM Segmentation EM-MF Segmentation Provided by T Kapur

National Alliance for Medical Image Computing Posterior Probabilities (EM) White matter Gray matter Provided by T Kapur

National Alliance for Medical Image Computing Posterior Probabilities (EM- MF) White matter Gray matter Provided by T Kapur

National Alliance for Medical Image Computing Segmentation of 31 Structures Kilian Pohl PhD (defense several weeks ago)

National Alliance for Medical Image Computing Segmentation of 31 Structures Lower Front Provided by Kilian Pohl

National Alliance for Medical Image Computing Segmentation of 31 Structures Superior Temporal Gyrus Provided by Kilian Pohl

National Alliance for Medical Image Computing The End