Hierarchical Statistical Modeling of Boundary Image Profiles Sean

Hierarchical Statistical Modeling of Boundary Image Profiles Sean Ho Department of Computer Science University of North Carolina, Chapel Hill, NC, USA Supported by NIH-NCI P 01 CA 47982.

Bayesian image segmentation log p(m | I) = log p(m) + log [p(I | m) / p(I)] Geometric prior Image match

Model-based segmentation Shape typicality (“prior”) n Shape representation n PDM, SPHARM, Mrep, level-set, etc. Probabilistic model n Model-to-image match Likelihood of a given shape Image representation Global (no corresp. ) n Local (req. corresp. ) n n Probabilistic model n Fit of a given shape in a given image

Example: corpus callosum n Automatic segmentation n Shape rep: 2 D Fourier (Staib et al) n Image rep: 1 D profiles normal to boundary (Cootes et al) Each profile independent of its neighbors n 100 profiles => 100 separate PCAs n n (movie)

Some examples of related work n Snakes: gradient magnitude n Also region-based inside/outside snakes n Template matching, correlation n ASM/SPHARM: independent profiles n AAM: hierarchical over whole image

Object-intrinsic coordinates n Use SPHARM parameterization to sample image in collar around object boundary

Across-bdy Profiles in normalized coords Along-boundary direction

Across-boundary model

Driving Questions n fine sampling necessary? pyramid n object specific n n how do we deal with noise? n would like to blur along boundary n local statistical model

Along-boundary model arclength n Gaussian profile pyramid out in

Laplacian profile pyramid - = n / s

Laplacian, local differences n / s / u

Profiles in 3 D n Use SPHARM parameter space of unit sphere n Recursive subdivision with icosahedron 0 th level: 20 profiles n 1 st level: 20*4 profiles n n 1 -way Markov chain

Profiles along 1 object in 3 D All profiles Left Hippocampus Inside Outside Profiles along red meridian line

Profiles around 1 hippocampus Inside Outside

Profiles: at 1 point on boundary n 1 corresponding point on population of case numbers 10 hippocampi n Step-edge visible n More variability outside

At another point on boundary n Large variability across subjects case numbers n Mean profile nearly flat: low confidence

Current / ongoing work n SPHARM segmentation framework: Standard ASM-like independent profiles n New hierarchical along-boundary model n New statistical model (local PCA, MRF) n n Testbed in 2 D with 71 corpora callosa n Testbed in 3 D with: 90 caudates (L/R) n 90 hippocampi (L/R) n

Profile Pyramid Average of 20 n multiscale along boundary n Image match model for segmentation n