Hierarchical Statistical Modeling of Hierarchical Statistical Modeling of Boundary Image ProfilesBoundary Image Profiles

Sean Ho

Department of Computer Science

University of North Carolina, Chapel Hill, NC, USA

Supported by NIH-NCI P01 CA47982.

Bayesian image segmentationBayesian image segmentation

Geometric priorGeometric prior Image matchImage match

log p(m | I) = log p(m) + log [p(I | m) / p(I)]log p(m | I) = log p(m) + log [p(I | m) / p(I)]

Model-based segmentationModel-based segmentation

Shape Shape representationrepresentation PDM, SPHARM, M-PDM, SPHARM, M-

rep, level-set, etc.rep, level-set, etc.

Probabilistic Probabilistic modelmodel Likelihood of a given Likelihood of a given

shapeshape

Shape typicality Shape typicality (“prior”)(“prior”)

Image Image representationrepresentation Global (no corresp.)Global (no corresp.) Local (req. corresp.)Local (req. corresp.)

Probabilistic Probabilistic modelmodel Fit of a given shape Fit of a given shape

in a given imagein a given image

Model-to-image Model-to-image matchmatch

Example: corpus callosumExample: corpus callosum

Automatic segmentationAutomatic segmentation Shape rep: 2D Fourier (Staib et al)Shape rep: 2D Fourier (Staib et al) Image rep: 1D profiles normal to Image rep: 1D profiles normal to

boundary (Cootes et al)boundary (Cootes et al) Each profile independent of its neighborsEach profile independent of its neighbors 100 profiles => 100 separate PCAs100 profiles => 100 separate PCAs

((moviemovie))

Some examples of related workSome examples of related work

Snakes: gradient magnitudeSnakes: gradient magnitude Also region-based inside/outside snakesAlso region-based inside/outside snakes

Template matching, correlationTemplate matching, correlation ASM/SPHARM: independent profilesASM/SPHARM: independent profiles AAM: hierarchical over whole imageAAM: hierarchical over whole image

Object-intrinsic coordinatesObject-intrinsic coordinates

Use SPHARM parameterization to sample Use SPHARM parameterization to sample image in collar around object boundaryimage in collar around object boundary

Profiles in normalized coordsProfiles in normalized coords

Along-boundary directionAlong-boundary direction

Acr

oss-

bdy

Across-boundary modelAcross-boundary model

Driving QuestionsDriving Questions

fine sampling necessary?fine sampling necessary? pyramidpyramid object specificobject specific

how do we deal with noise? how do we deal with noise? would like to blur along boundarywould like to blur along boundary

local statistical modellocal statistical model

Along-boundary modelAlong-boundary model

Gaussian profile pyramidGaussian profile pyramid

out in out in

arcl

engt

h

arcl

engt

h

Laplacian profile pyramidLaplacian profile pyramid

--

==

Laplacian, local differencesLaplacian, local differences

uu

Profiles in 3DProfiles in 3D

Use SPHARM parameter space of unit Use SPHARM parameter space of unit spheresphere

Recursive subdivision with icosahedronRecursive subdivision with icosahedron 00thth level: 20 profiles level: 20 profiles 11stst level: 20*4 profiles level: 20*4 profiles

1-way Markov chain1-way Markov chain

Profiles along 1 object in 3DProfiles along 1 object in 3D

Profiles along red meridian line

Inside Outside

Inside

Outside

All profiles

Left Hippocampus

Profiles around 1 hippocampusProfiles around 1 hippocampus

Inside Outside Inside Outside

Profiles: at 1 point on boundaryProfiles: at 1 point on boundary

1 1 corresponding point on population of corresponding point on population of 10 hippocampi10 hippocampi

Step-edge visibleStep-edge visible More variability outsideMore variability outside

case

nu

mb

ers

At another point on boundaryAt another point on boundary

Large variability across subjectsLarge variability across subjects Mean profile nearly flat: low confidenceMean profile nearly flat: low confidence

case

nu

mb

ers

Current / ongoing workCurrent / ongoing work

SPHARM segmentation framework:SPHARM segmentation framework: Standard ASM-like independent profilesStandard ASM-like independent profiles New hierarchical along-boundary modelNew hierarchical along-boundary model New statistical model (local PCA, MRF)New statistical model (local PCA, MRF)

Testbed in 2D with 71 corpora callosaTestbed 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)

Average of 20Average of 20 multiscale along multiscale along

boundaryboundary Image match model for Image match model for

segmentationsegmentation

Profile PyramidProfile Pyramid