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Hierarchical Statistical Modeling of Boundary Image Profiles

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. Geometric prior. Image match. Bayesian image segmentation.

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Hierarchical Statistical Modeling of Boundary Image Profiles

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

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

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

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

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

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

  8. Across-boundary model

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

  10. Along-boundary model • Gaussian profile pyramid arclength arclength out in out in

  11. Laplacian profile pyramid • /s - =

  12. Laplacian, local differences • /s /u

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

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

  15. Profiles around 1 hippocampus Inside Outside Inside Outside

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

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

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

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

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