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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 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 Analysis:

  • 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 Analysis:

  • Surface & Parameterization

  • Fit coefficients of parameterized basis functions to surface

  • Sample parameterization and reconstruct object

  • Hierarchical description

1

3

6

10


Correspondence spharm

Surface Analysis:

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 Analysis:

  • 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 Analysis:

  • Optimization using parameterization

  • Initialization with SPHARM parameterization


Population based
Population Based Analysis:

  • 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 Analysis:

  • 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 Analysis:

  • 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 Analysis:

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 Analysis:

  • 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 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 Analysis:

  • 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… Analysis:

  • 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 Analysis:

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 Analysis:

  • 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 Analysis:

  • Questions?


Permutation hypothesis tests

S Analysis: 0

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