NA-MIC National Alliance for Medical Image Computing UNC Shape Analysis Pipeline Martin Styner Guido...

NA-MICNational Alliance for Medical Image Computing

UNC Shape Analysis Pipeline

Martin Styner

Guido Gerig, Ipek Oguz, Christine Xu,

National Alliance for Medical Image Computing http://na-mic.org

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

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

),(

),(

),(

),(

φθ

φθ

φθ

φθ

z

y

x

r

),(),(0

φθφθ ∑∑= −=

=K

k

k

km

mk

mk Ycr ⎟

⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

=mzk

myk

mxk

mk

c

c

c

c

1

10

3

6

• Given: Points on surface• Compute:

1. Spherical Parametrization2. Fit basis functions through

Points using Parametrization


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 Para1 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

Hippocampus Segmentation

Preprocessing &Parameterization

SPHARM-PDM Shape

QCShape &Corresp.

Alignment& Scale

Feature ComputationPoint Location,

Subdivision, Thickness

QC of Features & Statistical Results

Statistical AnalysisOf 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

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.


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 usingVSkelTool (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 RightAsymmetry ofMean 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 Raw p-valueMean Overlay


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

NA-MIC National Alliance for Medical Image Computing UNC Shape Analysis Pipeline Martin Styner Guido...

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