After registering all the individual SPHARM models to a template model, all the SPHARM coefficients are normalized and comparable across objects, and then group analysis can be performed. In SPHARM-MAT, two simple statistical components are implemented to demonstrate its capability for group analysis.

The first component (see *Exercise 6.1 T Test*) aims to quantify and localize shape changes between two groups of objects. The basic processing pipeline includes the following steps: (1) uniformly sample each SPHARM surface to create a landmark representation; (2) surface signal extraction using different schemes (see [Shen2006b]); (3) perform a t-test on surface signals and visualize the result (e.g., t-map, uncorrected p-map) on the surface.

The second component (see *Exercise 6.2 PCA*) aims to establish a statistical shape model for one group of 3D objects by characterizing the mean and variability of the population. An ideal model should involve a small number of variables (i.e., simple) but capture major characteristics of the group (i.e., representative). Principal component analysis (PCA) is applied to SPHARM coefficients and characterize the shape group using the PCA eigenmodes. The first few principal components often explain most of the data variance and can be used to create a good statistical shape model that summarizes the whole group. Visualization can also be created for intuitive understanding of the group characteristics.

For more complicated statistical models, we suggest that SurfStat [Worsley2008] should be considered. Surfstat is a free software tool which performs statistical analysis of univariate and multivariate surface and volumetric data using linear mixed effects models and random field theory. Since SurfStat is also matlab-based, it is straightforward to integrate SurfStat with SPHARM-MAT for statistical surface analysis. For example, one can first use SPHARM-MAT to model and align surfaces and extract surface signals, and then use SurfStat for statistical inference on the surface.

This exercise was tested on a WinXP machine (3GHz CPU, 3.25G RAM) running Matlab 7.7.0 (R2008b). It took a few minutes to finish.

Major Steps

- T Test
- Stat Visualization

Task

Perform a vertex-by-vertex t test on a surface manifold.

Input

SpharmMatDir/data/Ex0601/hip06_reg/*_reg.mat: This folder is a copy ofSpharmMatDir/data/Ex0502/hip06_reg/*_reg.mat. Group 1 containsa*_reg.matobjects and Group 2 containsb*_reg.matobjects

SpharmMatDir/data/Ex0601/hip07_atlas/atlas.mat: The template surface or atlas

Output

SpharmMatDir/data/Ex0601/hip08_stat/*.mat: Resulting statistics

Steps

- Make an output directory
`SpharmMatDir/data/Ex0601/hip08_stat/` - Run
**SPHARM_MAT.m**under Matlab - Click
**Stat Analysis**button - In the right panel, let
**Method**be*t_map* - In the right panel, let
**Atlas**be`SpharmMatDir/data/Ex0601/hip07_atlas/atlas.mat`,**Smoothing_FWHM**be*5*,**EqualVariance**be*Yes*,**Signal**be*vl_defm_nrm*,**SampleMesh**be*icosa3*,**OutputNamePrefix**be*t_map*,**OutDirectory**be`SpharmMatDir/data/Ex0601/hip08_stat`,**GroupIDs**be*Ctrl,PT*, - In the right panel, click
`.....`button next to**Group1**, and select all the`a*_reg.mat`files under`SpharmMatDir/data/Ex0601/hip06_reg`as Group 1 files - In the right panel, click
`.....`button next to**Group2**, and select all the`b*_reg.mat`files under`SpharmMatDir/data/Ex0601/hip06_reg`as Group 2 files - Click
**OK**button (See*Screen Capture for T Test*)

Task

Visualize statistical maps: t-map and p-map

Input

SpharmMatDir/data/Ex0601/hip08_stat/t_map*.mat

Output

Figure on the screen

Steps

Click

**DisplayRes**buttonIn the right panel, let

**Method**be*res_t_map*,**Threshold_p_value**be*0.05*,**Colormap**be*jet*- Be sure to run this experiments twice by setting different configurations in the right panel as follows
- Run 1: let
**Overlay**be*t-map* - Run 2: let
**Overlay**be*p-value*

- Run 1: let

In the right panel, click

`.....`button next to**Select Input**, and select the`t_map*.mat`files under`SpharmMatDir/data/Ex0601/hip08_stat`Click

**OK**button (See*Screen Capture for Stat Visualization*)

Notes

- The visualization results are rendered on the screen (see
*Stat Visualization (t-map, p-map)*) - Only significant regions (uncorrected p<0.05) are color-mapped
- For getting corrected p values, see [Worsley2008] and [Chung2005]

Useful Tips

This exercise was tested on a WinXP machine (3GHz CPU, 3.25G RAM) running Matlab 7.7.0 (R2008b). It took a few minutes to finish.

Major Steps

- PCA
- PCA Visualization

Task

Perform principal component analysis on SPHARM coefficients.

Input

SpharmMatDir/data/Ex0602/hip06_reg/*_reg.mat: This folder is a copy ofSpharmMatDir/data/Ex0502/hip06_reg/*_reg.mat

Output

SpharmMatDir/data/Ex0602/hip07_stat/PCA_stat*.mat: Resulting statistics

Steps

- Make an output directory
`SpharmMatDir/data/Ex0602/hip07_stat/` - Run
**SPHARM_MAT.m**under Matlab - Click
**Stat Analysis**button - In the right panel, let
**Method**be*PCA* - In the right panel, let
**GroupID**be*All*,**OutputName**be*PCA_stat.mat*,**OutDirectory**be`SpharmMatDir/data/Ex0602/hip07_stat` - In the right panel, click
`.....`button next to**Select Input**, and select all the`*_reg.mat`files under`SpharmMatDir/data/Ex0602/hip06_reg`as input files - Click
**OK**button (See*Screen Capture for PCA*)

Task

Visualize PCA modes

Input

SpharmMatDir/data/Ex0602/hip07_stat/PCA_stat*.mat

Output

Figure on the screen

Steps

- Click
**DisplayRes**button - In the right panel, let
**Method**be*res_PCA* - In the right panel, let
**Level**be*4*,**Sigma**be*3*,**Mesh**be*quad32*,**MaxSPHARMDegree**be*15*, - In the right panel, click
`.....`button next to**Select Input**, and select the`PCA_stat*.mat`files under`SpharmMatDir/data/Ex0602/hip07_stat` - Click
**OK**button (See*Screen Capture for PCA Visualization*)

Notes

- The visualization results are rendered on the screen (see
*PCA Visualization*) - For details about such a visualization, see [Shen2008]

Useful Tips