topology-conform segmented volume meshing of volume images (oct 2012)

1 Challenge the future

Topology-conform segmented volume meshing of volume images


A Review – the basic challenge



topologically wrong (deformed) mesh

Unordinary mesh elements



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 ?

?



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


First Result ...


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)


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


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

topology-conform segmented volume meshing of volume images (oct 2012)

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