Presentation given at 3D NordOst 2012

1. 1Challenge the future
Conformal multi-material mesh
generation from labelled medical
volumes

2. 2Challenge the future
Introduction
• Generation of volume meshes for FEA
• Particular use case: hip prostheses analysis
• Typical pipeline:
Segmentation from patient’s CT-scan (a) to labelled volume image (b). Volume Meshing (c) of the
image and FEA for stress-strain results (d,[Dick2011]).

3. 3Challenge the future
Introduction
• Mesh requirements:
• precise meshes
• segmentation-conform
• minimal mesh element number  feature-adaptive

4. 4Challenge the future
Related Work
Weighted Delaunay Tetrahedralization
refinement [Boltcheva2009]
Dynamic Particle System Meshing
[Meyer2007]
Multi-labelled volumes
meshes with particle
systems [Meyer2008]

5. 5Challenge the future
Challenges
• long computation time
• oversampling of edges and corners
• no sharp-feature recreation  ε-sample
requirement
wrong topology,
bad
reconstruction
too many
samples

6. 6Challenge the future
Contribution
• Application of Integer Medial Axis (IMA) as fast, discrete
medial axis scheme
• proposal of local surface triangulation scheme for volume
images

7. 7Challenge the future
Integer Medial Axis - Analysis

8. 8Challenge the future
Integer Medial Axis - Idea
BioMesh3D – Centres of
maximal spheres
IMA – shortest path in feature
transform

9. 9Challenge the future
Integer Medial Axis – Results
Runtime
dataset BioMesh3D DeVIDE FE-Mesher
artificial 26 min 0.1 sec
Tooth 1h 41 min 1 sec
real femur 14h 11 min 2 sec

10. 10Challenge the future
Integer Medial Axis – Results
Quality
Tooth # Tetra 142795 DeVIDE FE-Mesher
Max. Min. Avg. Variance # bad
Tetra
%
bad
Aspect
Ratio
119.69 1.01 1.94 1.00 9282 6.50
Radius
Ratio
105.43 1.00 1.69 0.83 6736 4.72
Volume 272.34 0.0 2.96 21.74 0 0.0
Tooth # Tetra 118110 Simpleware FE+
Max. Min. Avg. Variance # bad
Tetra
%
bad
Aspect
Ratio
44.59 1.02 1.54 0.16 816 0.69
Radius
Ratio
921.55 1.00 1.37 7.92 997 0.84
Volume 46.68 0.0 3.41 14.24 0 0.0

11. 14Challenge the future
Integer Medial Axis – Results
Precision

12. 16Challenge the future
Minimal Sample for accurate Meshing
Concept
• ε-sampling:
• ensures topologic conformity
• applies to dense and sparse
samples
• Loss of sharp features
• only applies for 3D meshes
without additional information
• our idea:
• mesh surface locally
• take surface mesh to
generate volume mesh
   0,,  xxBESx 

13. 17Challenge the future
Minimal Sample for accurate Meshing
Concept
1. Get TBN-Matrix per sample
vertex
2. Get Neighbourhood per
vertex
3. re-project points in
tangent plane
4. mesh via Local Delaunay
Triangulation tangent
plane neighbourhood
5. use established
connections in 3D

14. 18Challenge the future
Minimal Sample for accurate Meshing
Results
VTK CGAL – no constraint CGAL – Convex Hull
constraint
formation of holes due unsuitable Neighbourhood
determination

15. 19Challenge the future
Conclusion and Future Work
• Improved runtime behaviour due to Medial Axis Transform
Algorithm change
• Local Triangulation in tangent space not ε-sample bound, but
dependent on Neighbourhood operation
• k-Nearest Neighbour not suitable for non-uniformal, sparse
samples
• In future: usage of natural neighbours for neighbourhood
determination