Topology-conform segmented volume meshing of volume images (Oct 2012)
1 like554 views
The document discusses challenges in meshing volume images, particularly addressing topologically incorrect meshes and the requirements for Delaunay triangulation. It presents concepts related to neighbourhood approximation and proposes a proof of concept for generating volume meshes with relaxed sampling requirements. The findings highlight the potential to convert conformal surface meshes into volume meshes without the need for Steiner-point insertion.
Topology-conform segmented volume meshing of volume images (Oct 2012)
- 1. 1Challenge the future Topology-conform segmented volume meshing of volume images
- 2. 2Challenge the future A Review – the basic challenge
- 3. 3Challenge the future A Review – the basic challenge topologically wrong (deformed) mesh Unordinary mesh elements
- 4. 4Challenge the future A Review – the basic challenge 0,, xxBESx 3D Delaunay Triangulation – ε-sample requirement: Problem: Sharp features Corners Edges Medial Axis touches edges & corners λ(x) = 0 => unlimited samples at features How can we mesh sharp features ? ?
- 5. 5Challenge the future A Review – the basic challenge Assumption: Any conformal surface mesh can be converted into a volume mesh via 3D Delaunay Tetrahedralization without Steiner-Point insertion on the surface Local Triangulation of the surface in 2D-tangent plane
- 6. 6Challenge the future First Result ...
- 7. 7Challenge the future Further concept Reason for whole: Neighbourhood approximation (k-Nearest Neighbours) • nearest neighbours ≠ real neighbours (1-Ring Neighbourhood) in non-uniformal samples N(x) ϵ S, d(x, s) < μ • d(x, s1) kNN (k=6)
- 8. 8Challenge the future Further concept • Solution: Natural Neighbours • reflecting 1-Ring Neighbourhood • Centres of neighbouring Voronoi Cells Delaunay Vertices • Problem: Neighbours = 3D Delaunay Triangulation Vertices ε-sampling requirement ?! No: only candidates needed, not exclusively Neighbours N(x) ϵ {NN1, NN2, ... NNn, p1, p2 ...} ≠ S
- 9. 9Challenge the future Guideline for Proof of Concept practical proof of concept: CH-LDT with subsequent 3D Delaunay Tetrahedralization can generate volumes meshes with relaxed, sparse sample requirement independent from ε-sample requirement Local Delaunay Triangulation (LDT) with Convex Hull-constraint