1. Enhanced Correspondence and Statistics for Structural Shape Analysis: Current Research Martin Styner Department of Computer Science and Psychiatry

2. 2 Concept: Shape Analysis Traditional analysis: Regional volume Our view: Analysis of local shape Binary Segmentation Volumetric analysis: Size, Growth Shape Representation Statistical analysis

3. 3 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

4. 4 SPHARM: Spherical Harmonics 1 10 3 6 1.Surface & Parameterization 2.Fit coefficients of parameterized basis functions to surface 3.Sample parameterization and reconstruct object Hierarchical description

5. 5 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 Surface Parametrization SPHARM

6. 6 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

7. 7 Population Based – Davies Optimization using parameterization Initialization with SPHARM parameterization

8. 8 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 Population Based

9. 9 Correspondence Evaluation How can we evaluate correspondence? 1.Comparison to manual landmarks Selection variability quite large Experts disagree on landmark placement 2.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

10. 10 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

11. 11 Correspondence Evaluation Femur Lateral Ventricle 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 Styner, Rajamani, Nolte, Zsemlye, Szekely, Taylor, Davies: Evaluation of 3D Correspondence Methods for Model Building, IPMI 2003, p 63-75

12. 12 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

13. 13 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

14. 14 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

15. 15 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

16. 16 P-value Correction Corrected significance map –As if only one test performed Bonferroni correction –Global, simple, very pessimistic –p corr = 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 Correction

17. 17 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

18. 18 The End Questions?

19. 19 Permutation Hypothesis Tests Estimate distribution –Permute group labels N a, N b in Group A and B Create M permutations Compute feature S j for each perm Histogram  Distribution p-value: #Perms larger / #Perms total S0S0 SjSj SjSj perm #