na-mic national alliance for medical image computing unc shape analysis pipeline martin styner guido...
TRANSCRIPT
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
National Alliance for Medical Image Computing http://na-mic.org
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
National Alliance for Medical Image Computing http://na-mic.org
Associated Legendre Polynomials
National Alliance for Medical Image Computing http://na-mic.org
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
National Alliance for Medical Image Computing http://na-mic.org
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
National Alliance for Medical Image Computing http://na-mic.org
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
National Alliance for Medical Image Computing http://na-mic.org
Heat Equation Mapping
National Alliance for Medical Image Computing http://na-mic.org
Optim: Uniform Area
• Initialize with heat equation mapping• Optimize to uniform area mapping and
minimal distortion of quadrilateral• Time consuming, large matrices…
National Alliance for Medical Image Computing http://na-mic.org
Uniform Area Para1 4 10
National Alliance for Medical Image Computing http://na-mic.org
Correspondence
• Corresponding 3D poles 1st order ellipsoid• In between, correspondence by uniform area • Rotational symmetry can be a problem
National Alliance for Medical Image Computing http://na-mic.org
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
National Alliance for Medical Image Computing http://na-mic.org
Hippocampus example
Input:Binary Seg.
Heat Equation Para Optimized Para SPHARM -PDM
National Alliance for Medical Image Computing http://na-mic.org
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
National Alliance for Medical Image Computing http://na-mic.org
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.
National Alliance for Medical Image Computing http://na-mic.org
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
National Alliance for Medical Image Computing http://na-mic.org
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>
National Alliance for Medical Image Computing http://na-mic.org
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Tools: Parametrization
• Voxel surface mesh from Segmentation• Spherical parametrization• Tool: GenParaMesh <insegfile>
National Alliance for Medical Image Computing http://na-mic.org
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
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
National Alliance for Medical Image Computing http://na-mic.org
SPHARM Shape QC
• Overlay of voxel segmentation (red) with SPHARM (blue)
• Average Error ~ 0.12mm
National Alliance for Medical Image Computing http://na-mic.org
SPHARM Correspondence
QC usingVSkelTool (not yet OpenSource) and Scripting
National Alliance for Medical Image Computing http://na-mic.org
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
National Alliance for Medical Image Computing http://na-mic.org
SPHARM Mean Hippo
Overall Mean Left Mean Right Mean
National Alliance for Medical Image Computing http://na-mic.org
Tool: MeshValmet
Measures Distance Histograms between meshes
Left vs RightAsymmetry ofMean Shapes(only 6 cases)
National Alliance for Medical Image Computing http://na-mic.org
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
National Alliance for Medical Image Computing http://na-mic.org
Hippocampal Subdivision
• Skeleton based Subdivision (11 parts)
• VSkelTool based (not yet open source)
National Alliance for Medical Image Computing http://na-mic.org
Hippocampal subdivision
• Agreement with local shape analysis
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Trend
P < 0.5
National Alliance for Medical Image Computing http://na-mic.org
Hippocampus Thickness
• Pruned Voronoi Skeleton
• VSkelTool
1 mm 4 mm
National Alliance for Medical Image Computing http://na-mic.org
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