1. 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 P01 CA47982.

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

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

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

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

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

7. Profiles in normalized coords Along-boundary direction Across-bdy

8. Across-boundary model

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

10. Along-boundary model Gaussian profile pyramid Gaussian profile pyramid outinoutin arclength

11. Laplacian profile pyramid   - =

12. Laplacian, local differences  u  u

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

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

15. Profiles around 1 hippocampus InsideOutside

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

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

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

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