1. UNC Shape Analysis Pipeline
Martin Styner
Guido Gerig, Ipek Oguz, Christine Xu,

2. TOC: Shape Pipeline SPHARM methods Workflow Intermixed:
Procedures
Implementations, Tools
Example: Dartmouth Hippocampus data
Conclusion & Outlook

3. SPHARM Theory
Fit coefficients weighting basis functions to data (think Fourier Transform)
Only for objects of spherical topology
Can be extended to toroidal topology
Basis Functions: Spherical Harmonics

4. Associated Legendre Polynomials

5. SPHARM series
l=0
l=1
l=2
l=3
l=4
l=5
m= m= m= m= m= m=5

6. SPHARM shape Given: Points on surface Compute:
Spherical Parametrization
Fit basis functions through Points using Parametrization 1 3 6 10

7. Parametrization
Similar to 2D Fourier shape, arc-length parametrization
Difficult in 3D, no unique ordering of points
Find a way to map a surface to a sphere
Uniform sphere-sector parameterization for correspondence

8. Heat Equation Mapping

9. Optim: Uniform Area Initialize with heat equation mapping
Optimize to uniform area mapping and minimal distortion of quadrilateral
Time consuming, large matrices…

10. Uniform Area Para 1 4 10

11. Correspondence Corresponding 3D poles 1st order ellipsoid
In between, correspondence by uniform area
Rotational symmetry can be a problem

12. SPHARM-PDM Uniform area ratio para Uniformly subdivide unit sphere
Recursive subdivision schemes
Graphics
Polyhedron: Octahedro, Dodecahedron
Icosahedron
Typical examples for use of parametric description
Least-square fit (smoothing)
Correspondence
Surfaces with equal sampling

13. Hippocampus example Input: Binary Seg. Heat Equation Para
Optimized Para
SPHARM -PDM

14. Shape Analysis Workflow
SPHARM-
PDM Shape
Preprocessing &
Parameterization
Hippocampus
Segmentation QC
Shape &
Corresp.
Feature Computation
Point Location,
Subdivision, Thickness
Alignment
& Scale
QC of Features &
Statistical Results
Statistical Analysis
Of Features

15. General Remarks Tools Command line, ITK based in NAMIC Sandbox
Ready for submission to Insight Journal
Not yet ready for clinicians since no point&click UI

16. Example Dataset Hippocampus, coronal slice segmentation in Brains2
All control subjects
Dartmouth Data:
UNC shape pipeline worked without any modification
Data received: Sept
Analysis done: Sept

17. Tools: Preprocessing Resampling to 0.5mm3 Interior hole filling
Closing operation
Major component
Levelset smoothing
Ensuring 6 connectedness
Ensures spherical topology
Tool: SegPostProcess <infile> <outfile>

18. Tools: Parametrization
Voxel surface mesh from Segmentation
Spherical parametrization
Tool: GenParaMesh <insegfile>

19. Tools: SPHARM-PDM Tool: ParaToSPHARMMesh <surf> <para>
SPHARM + SPHARM-PDM
3 outputs
Original space
Alignment 1st order ellipsoid + mirror
Alignment rigid Procrustes to template + mirror

20. SPHARM Shape QC Overlay of voxel segmentation (red) with SPHARM (blue)
Average Error ~ 0.12mm

21. SPHARM Correspondence
QC using
VSkelTool (not yet OpenSource) and Scripting

22. Statistical Analysis Tool: StatNonParamTestPDM
Non-parametric permutation based statistical testing including correction for multiple comparison problem
More about this in next talk
Outputs: Statistics & Mean surfaces

23. SPHARM Mean Hippo
Overall Mean
Left Mean
Right Mean

24. Tool: MeshValmet Measures Distance Histograms between meshes
Left vs Right
Asymmetry of
Mean Shapes
(only 6 cases)

25. Statistical Testing
Only 6 cases: Do not interprete this data, it’s just an example
Global p-value for asymmetry shape difference: 0.34
Mean difference
Mean Overlay
Raw p-value

26. Hippocampal Subdivision
Skeleton based Subdivision (11 parts)
VSkelTool based (not yet open source)

27. Hippocampal subdivision
Agreement with local shape analysis
Trend
P < 0.5

28. Hippocampus Thickness
Pruned Voronoi Skeleton
VSkelTool
1 mm
4 mm

29. Conclusion & Outlook
A set of tools, OpenSource (except VSkelTool with subdivision)
Robust, proven shape analysis pipeline
Next:
Statistical visualization tools (Ipek Oguz)
Better correspondence (Ipek & Christine)
Linear Regression Models for correcting Gender, Age and other Patient variables (Martin)
Subdivision using ITK, OpenSource
Thickness using ITK, OpenSource