1 stephen pizer, sarang joshi, guido gerig medical image display & analysis group (midag)...
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Stephen Pizer, Sarang Joshi, Guido GerigMedical Image Display & Analysis Group (MIDAG)
University of North Carolina, USA
with credit to P. T. Fletcher, C. Lu, M. Styner, A. Thall,
P. Yushkevich And others in MIDAG
This set of slides can be found at the website
midag.cs.unc.edu/pubs/presentations/SPIE_tut.htm
Tutorial:Tutorial: Anatomic Object Ensemble RepresentationsAnatomic Object Ensemble Representations forfor Segmentation & Statistical CharacterizationSegmentation & Statistical Characterization
Tutorial:Tutorial: Anatomic Object Ensemble RepresentationsAnatomic Object Ensemble Representations forfor Segmentation & Statistical CharacterizationSegmentation & Statistical Characterization
17 February 2003
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Segmentation Segmentation
Objective: Extract the most probable target object geometric conformation z given the image data I
Requires prior on object geometry p(z)
Requires a measure of match p(I|z) of the image to a particular object conformation, so the image must be represented in reference to the object geometric conformation
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Statistical Geometric Characterization
Statistical Geometric Characterization
Requires priors p(class) and likelihoods p(z|class) Uses
Medical science: determine geometric ways in which pathological and normal classes differ
Diagnostic: determine if a particular patient’s geometry is in the pathological or the healthy class
Educational: communicate anatomic variability in atlases Priors p(z) for segmentation Monte Carlo generation of images
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Part I
Multiscale Geometric Primitives,
Especially M-reps
Multiscale Deformable Model Segmentation
Stephen Pizer
Tutorial: Anatomic Object Ensemble Representations for Segmentation & Statistical Characterization
Tutorial: Anatomic Object Ensemble Representations for Segmentation & Statistical Characterization
17 February 2003
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Relation of this object instance to other instances Representing the real world Basic entities: object ensembles & single objects Deformation while staying in statistical entity class Discrimination by shape class and by locality Mechanical deformation within a patient: interior primitive
Relation to Euclidean space/projective Euclidean space Matching image data
Multiple object-oriented scale levels Yields efficiency in segmentation: coarse to fine Yields efficiency in number of training samples
for probabilities
Object Representation ObjectivesObject Representation Objectives
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Object Ensembles & Single ObjectsObject Ensembles & Single Objects
Object descriptionsIntuitive, related to anatomic understandingMathematically correct
Object interrelation descriptionsAbutment and non-interpenetration
Large scale Smaller scale
7 Multiple Object-oriented Scale Levels -- For Efficiency
Multiple Object-oriented Scale Levels -- For Efficiency
Scale based parents and neighborsIntuitive scale levels
Ensemble Object Main figure Subfigure
Slab through-section Boundary vertex
8 Multiple Object-oriented Scale Levels -- For Efficiency
Multiple Object-oriented Scale Levels -- For Efficiency
Scale based parents and neighbors Statistics via Markov random fields [Lu]
Residue from parent: zki = ith residue at scale
level k Difference from neighbors’ prediction p(zk
i relative to P(zki), zk
i relative to N(zki))
Efficiency of training from low dimension per probability
Features with position and level of locality (scale) Feature selection [Yushkevich]
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Discussion of ScaleDiscussion of Scale
Spatial aspects of a geometric feature Position Scale: 3 different types
Spatial extent Region summarized
Level of detail captured Residues from larger scales
Distances to neighbors with which it has a
statistical relationship
Markov random field Consider point distribution model,
landmarks, spherical harmonics, dense Euclidean positions, m-reps
Large scale Smaller scale
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Scale Situations in Various Statistical Geometric Analysis Approaches
Scale Situations in Various Statistical Geometric Analysis Approaches
Coarse
Fine
Location
Leve
l of
Det
ail
Location Location
Global coef for Multidetail feature Detail residues each level of detail
Examples: boundary spherical boundary points, m-rep object harmonics, global dense position hierarchy, principal components displacements wavelets
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Atlas voxels with a displacement at each voxel: x(x), label(x)
Set of distinguished points {xi} with a displacement at each Landmarks Boundary points in a mesh
With normal b = (x,n)
Loci of medial atoms: m = (x,F,r,)
or end atom (x,F,r,)
(show on Pablo)
Object Representations: AtomsObject Representations: Atoms
u
v
t
Hub
Spoke Spoke
12Multiscale Object Representation via Interiors: M-reps
Multiscale Object Representation via Interiors: M-reps
Interiors (medial) at all but smallest scale levels Boundary displacement at smallest scale level
Allows fixed structure in medial part Residues from previous scale level
At each level recognizes invariances associated with shape
Provide correspondence Across population & Across comparable
structures Provides prediction by neighbors
Translation, rotation, magnification Structure trained from population [Styner] Basis for deformable model segmentation
Continuous vs. sampled rep’nsboundary trad’l medial medial atom
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M-rep Gives Multiscale Intrinsic Coord’s for Nonspherical & Nontubular Objects
M-rep Gives Multiscale Intrinsic Coord’s for Nonspherical & Nontubular Objects
Here single-figure On medial locus
(u,v) in r-proportional metric v along medial curve of
medial sheet u across medial sheet t around crest
Across narrow object dimension along medial spokes Proportion of medial width r
u
v
u
v
t
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Discrete M-rep Multifigure Objects and Multiobject Ensembles
Discrete M-rep Multifigure Objects and Multiobject Ensembles
Meshes of medial atoms Objects connected as host,
subfigures Hinge atoms of subfigure
on boundary of parent figure Blend in hinge regions Special coordinate system
(u,w,t) for blend region Multiple such objects, inter-
related via neighbor’s figural coords o
o
o o o
o
o o
o
o o
w
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M-rep Intrinsic Coordinates M-rep Intrinsic Coordinates
Within figure One medial atom provides a coordinate
system for its neighbor atoms Position, Orientation, Metric
Between subfigure and figure Host atoms’ coordinate systems provides
coordinate system for protrusion or indentation hinge
Between figures or between objects One object provides coordinate system for
neighbor object boundary
u
v
t
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Interpolating Boundaries in a FigureInterpolating Boundaries in a Figure
Interpolate x, r via B-splines [Yushkevich] Trimming curve via r<0 at outside control points
Avoids corner problems of quadmesh Yields continuous boundary
Via modified subdivision surface [Thall] Approximate orthogonality at spoke ends Interpolated atoms via boundary and distance
At ends elongation needs also to be interpolated
Need to use synthetic medial geometry [Damon]
Medial sheet
Implied boundary
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Sampled medial shape representation: M-rep tube figures
Sampled medial shape representation: M-rep tube figures
Same atoms as for slabs r is radius of tube spokes are rotated about b Chain rather than mesh
b
x n
x+
rRb,n()bx+rRb,n(-)b
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Segmentation by Deformable M-reps Segmentation by Deformable M-reps
w
For each scale level k, coarse to fineFor all residues i at scale level k: zk
iMaximize [log
p(zki relative to P(zk
i), zki relative to N(zk
i)) + log p(Image|{zj
i, j>=k, all i})]
i.e., maximize geometric typicality + geometry to image match
(show on Pablo)
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Intensity Profiles Template Used in Geometry to Image Match
Intensity Profiles Template Used in Geometry to Image Match
Mean profile image along red meridian line, from training or as analytic function of /r
Inside
Outside
Left Hippocampus
Template to target image correspondence via figural coordinates
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3-Scale Deformation of M-reps [Pizer, Joshi, Chaney, et al.]
Segmentation of Kidney from CT
3-Scale Deformation of M-reps [Pizer, Joshi, Chaney, et al.]
Segmentation of Kidney from CT
Optimal movement
Optimal warp
Refined boundary
Hand-placed
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Three Stage - Single Figure Segmentation of Kidney from CT
Three Stage - Single Figure Segmentation of Kidney from CT
Axial, sagittal, and coronal target image slicesAxial, sagittal, and coronal target image slices
Grey curve: before step. White curve: after stepGrey curve: before step. White curve: after step
Optimal movement Optimal warp
Refined boundary
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Segmentation by Deformable M-repsControlled Validations
Segmentation by Deformable M-repsControlled Validations
w
KidneysHuman segmented
Robust over all 12 kidney pairsAvg distance to human segn’s boundary: <1.7mm
Clinically acceptable agreement with humansMonte Carlo produced
Robust against initialization Other anecdotal validations
Liver, male pelvis ensemble, caudate, hippocampus
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For a copy of the slides in this talk see website: midag.cs.unc.edu/pubs/presentations/SPIE_tut.htm
For background to this talk see tutorial at website: midag.cs.unc.edu/projects/object-shape/tutorial/index.htm
or papers at midag.cs.unc.edu
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References: Non-M-repsReferences: Non-M-reps Voxel displacements and labels: Grenander, U and M Miller
(1998). Computational anatomy: an emerging discipline. Quarterly of Applied Mathematics, 56: 617-694. Christensen, G, S Joshi, and M Miller (1997). Volumetric transformation of brain anatomy. IEEE Transactions on Medical Imaging, 16(6): 864-877.
Landmarks: Dryden, I & K Mardia, (1998). Statistical Shape Analysis. John Wiley and Sons (Chichester).
Point distribution models: T Cootes, A Hill, CJ Taylor (1994). Use of active shape models for locating structures in medical images. Image & Vision Computing 12: 355-366.
Spherical harmonic models: Kelemen, A, G Székely, G Gerig (1999). Elastic model-based segmentation of 3D neuroradiological data sets. IEEE Transactions of Medical Imaging, 18: 828-839.
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References: M-repsReferences: M-reps Overview: Pizer, S, G Gerig, S Joshi, S Aylward (2002). Multiscale
medial shape-based analysis of image objects. Proc. IEEE, to appear. http://midag.cs.unc.edu/pubs/papers/IEEEproc03_Pizer_multimed.pdf
Deformable m-reps segmentation: Pizer, S, et al. (2002). Deformable m-reps for 3D medical image segmentation. Subm. for IJCV special UNC-MIDAG issue. http://midag.cs.unc.edu/pubs/papers/IJCV01-Pizer-mreps.pdf
Figural coordinates: Pizer S, et al. (2002). Object models in multiscale intrinsic coordinates via m-reps. Image & Vision Computing special issue on generative model-based vision, to appear. http://midag.cs.unc.edu/pubs/papers/GMBV02_Pizer.pdf
Forming m-rep models: Styner, M et al., Statistical shape analysis of neuroanatomical structures based on medial models. Medical Image Analysis, to appear spring 2003. http://midag.cs.unc.edu/pubs/papers/MEDIA01-styner-submit.pdf
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References: M-repsReferences: M-reps Continuous m-reps: Yushkevich, P et al. (2002). Continuous Medial
Representations for Geometric Object Modeling in 2D and 3D. Image & Vision Computing special issue on generative model-based vision, to appear. http://midag.cs.unc.edu/pubs/papers/IVC02-Yushkevich
Implied boundaries via subdivision surfaces: Thall, A (2002). Fast C2 interpolating subdivision surfaces using iterative inversion of stationary subdivision rules. UNC Comp. Sci. Tech. Rep. TR02-001. http://midag.cs.unc.edu/pubs/papers/Thall_TR02-001.pdf
Markov random fields: Lu, C, S Pizer, S Joshi (2003). A Markov Random Field approach to multi-scale shape analysis. Subm. to Scale Space. http://midag.cs.unc.edu/pubs/papers/ScaleSpace03_Conglin_shape.pdf
Math of m-reps --> boundaries: Damon, J (2002), Determining the geometry of boundaries of objects from medial data. UNC Math. Dept. http://midag.cs.unc.edu/pubs/papers/Damon_SkelStr_III.pdf
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