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

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

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

Associated Legendre Polynomials

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

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

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

Heat Equation Mapping

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

Uniform Area Para 1 4 10

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

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

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

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

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

Example Dataset Hippocampus, coronal slice segmentation in Brains2 All control subjects Dartmouth Data: UNC shape pipeline worked without any modification Data received: Sept 8 2005 Analysis done: Sept 14 2005

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>

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

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

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

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

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

SPHARM Mean Hippo Overall Mean Left Mean Right Mean

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

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

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

Hippocampal subdivision Agreement with local shape analysis Trend P < 0.5

Hippocampus Thickness Pruned Voronoi Skeleton VSkelTool 1 mm 4 mm

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