Hierarchical Statistical Modeling of Boundary Image Profiles
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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
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
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: 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)