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Enhanced Correspondence and Statistics for Structural Shape Analysis: Current Research. Martin Styner Department of Computer Science and Psychiatry. Concept: Shape Analysis. Traditional analysis: Regional volume Our view: Analysis of local shape. Volumetric analysis: Size, Growth.

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enhanced correspondence and statistics for structural shape analysis current research

Enhanced Correspondence and Statistics for Structural Shape Analysis: Current Research

Martin Styner

Department of Computer Science and Psychiatry

concept shape analysis
Concept: Shape Analysis
  • Traditional analysis: Regional volume
  • Our view: Analysis of local shape

Volumetric analysis: Size, Growth

Statistical analysis

Shape Representation

Binary Segmentation

geometric correspondence
Geometric Correspondence
  • Template/Model fit
    • Fit a model to the data, model bias
    • m-rep, deformation fields
  • Pair-wise optimization
    • Template/Model bias
    • Many PDM based analysis methods
  • Object inherent
    • No bias, fully independent
    • SPHARM
  • Population-wise optimization
    • No template, population vs. single object
    • MDL, DetCovar
spharm spherical harmonics
SPHARM: Spherical Harmonics
  • Surface & Parameterization
  • Fit coefficients of parameterized basis functions to surface
  • Sample parameterization and reconstruct object
  • Hierarchical description

1

3

6

10

correspondence spharm

Surface

SPHARM

Parametrization

Correspondence: SPHARM
  • Correspondence by same parameterization
    • Area ratio preserving through optimization
    • Location of meridian and equator ill-defined
  • Poles and Axis of first order ellipsoid
  • Object specific, independent, good initial correspondence
parameterization based correspondence
Parameterization based Correspondence
  • SPHARM
    • Can also be used as initialization of other methods
  • Optimization of spherical parametrization
    • Optimize over (,), evaluate on surface
    • Template matching
      • Surface geometry: Curvature + Location
      • Meier, Medical Image Analysis 02
    • Population based:
      • Optimization of location/coordinate distribution
      • Davies, TMI 02
      • Our current research (Ipek Oguz)
        • Fusion with SPHARM and surface geometry, fusion of all 3 methods
population based davies
Population Based – Davies
  • Optimization using parameterization
  • Initialization with SPHARM parameterization
population based
Population Based
  • Population Criterions: MDL & DetCov
  • MDL = Minimum Description Length
    • In terms of shape modeling: Cost of transmitting the coded point location model (in number of bits)
  • DetCov = log determinant of covariance matrix
    • Compactness of model
  • Criterions very similar
  • MDL expensive computation
correspondence evaluation
Correspondence Evaluation
  • How can we evaluate correspondence?
    • Comparison to manual landmarks
      • Selection variability quite large
      • Experts disagree on landmark placement
    • Correspondence quality measurements
  • Best metric for evaluation => best metric for correspondence definition
  • Evaluation in Styner et al, IPMI 2003
    • Widely cited
    • Shows need for evaluation and validation
  • 2 structures: Lateral ventricle, Femoral head

Styner, Rajamani, Nolte, Zsemlye, Szekely, Taylor, Davies: Evaluation of 3D Correspondence Methods for Model Building, IPMI 2003, p 63-75

correspondence evaluation1
Correspondence Evaluation
  • Evaluation based on derived shape space
    • Principal Component Analysis (PCA) model
  • Generalization
    • Does the model describe new cases well?
    • Leave-one-out tests (Jack-knife)
      • Select a case, remove from training, build model
      • Check approximation error of removed case
  • Specificity
    • Does the model only represent valid objects?
    • Create new objects in shape space with Gaussian sampling
      • Approximation error to closest sample in training set
correspondence evaluation2
Correspondence Evaluation

M: number of modes in model

MDL and DetCov are performing the best

MDL has strong statistical bias for shape analysis

For shape analysis: optimization and analysis on same features

Femur

Lateral

Ventricle

Styner, Rajamani, Nolte, Zsemlye, Szekely, Taylor, Davies: Evaluation of 3D Correspondence Methods for Model Building, IPMI 2003, p 63-75

population based curvature
Population Based Curvature
  • Current project in correspondence
  • Population based  better modeling
  • Surface Geometry  no statistical bias
  • Use of SPHARM  efficiency, noise stability
  • Curvature
    • Shape Index S and Curvedness C
    • SPHARM derivatives

SPHARM first derivatives

statistical analysis
Statistical Analysis
  • Surfaces with
    • Correspondence
    • Pose normalized
  • Analyze shape feature
    • Features per surface point
    • Univariate
      • Distance to template
        • Template bias
      • Thickness
    • Multivariate
      • Point locations (x,y,z)
      • m-rep parameters
      • Spherical wavelets
hypothesis testing
Hypothesis Testing
  • At each location: Hypothesis test
    • P-value of group mean difference
      • Schizophrenia group vs Control group
    • Significance map
    • Threshold α = 5%, 1%, 0.1%
  • Parametric: Model of distribution (Gaussian)
  • Non-parametric: model free
    • P-value directly from observed distribution
    • Distribution estimation via permutation tests
many many too many
Many, Many, Too Many…
  • Many local features computed independently
    • 1000 - 5000 features
  • Even if features are pure noise, still many locations are significant
  • Overly optimistic  Raw p-values
  • Multiple comparison problem
    • P-value correction
      • False-Positive Error control
      • False Detection Rate
    • General Linear Mixed Modeling
      • Model covariance structure
      • Dimensionality reduction
      • Work with Biostatistics
        • MICCAI 2003, M-rep
p value correction

Correction

P-value Correction
  • Corrected significance map
    • As if only one test performed
  • Bonferroni correction
    • Global, simple, very pessimistic
    • pcorr = p/n = 0.05/1000 = 0.00005
  • Non-parametric permutation tests
    • Minimum statistic of raw p-values
    • Global, still pessimistic

Pantazis, Leahy, Nichols, Styner: Statistical Surface Based Morphometry Using a Non-Parametric Approach, ISBI 2004,1283-1286

Styner, Gerig: Correction scheme for multiple correlated statistical tests in local shape analysis, SPIE Medical Imaging 2004, p. 233-240,2004

ongoing research
Ongoing Research
  • False Detection Rate (FDR): more relaxed, fMRI, VBM
    • Currently being added to software
  • Program design: Software not based on ITK statistics framework
  • Next:
    • Covariates: No account of covariates
    • Age, Medication, Gender
    • General Linear Model, per feature at each location
    • multivariate analysis of fitted parameters
the end
The End
  • Questions?
permutation hypothesis tests

S0

Permutation Hypothesis Tests
  • Estimate distribution
    • Permute group labels
      • Na , Nb in Group A and B
      • Create M permutations
      • Compute feature Sj for each perm
      • Histogram  Distribution
  • p-value:

#Perms larger / #Perms total

Sj

#

perm

Sj

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