Streamable Laguerre-Voronoi Tessellation Model for Tomographic Images

Introduction. Nowadays, the interest in foam materials is growing in several engineering
fields [1]. Foams can exhibit a nonlinear mechanical behavior [2], which is highly depen-
dent on their microstructure [3]. Thus designing foams with specific mechanical properties
can be very challenging. The present contribution is part of the ARC-Bridging project [4],
whose objective is to predict the mechanical behavior of complex microstructured mate-
rials via numerical simulations. A possible classification of foam models into two groups
is: random models and deterministic models [5]. The random models frequently require
statistical estimations of their parameters [6], whereas the deterministic models generally
require numerically expensive image analyse. Indeed, classical analysis steps involve a
distance tranform, a watershed and, optionally, a h-minima transform [5, p. 22], which
can be computationally demanding [7, 8, 9].
Contribution. In the present Laguerre–Voronoi tessellation model, the image analysis
part neither involes the watershed transform, nor the h-minima transform. Instead, fol-
lowing the original idea of A.M. Lopez-Reina et E. Béchet [10], these two transforms are
respectively replaced by a Hessian-based removal of spurious extrema and a clustering
of the remaining maxima. This substitution allows the processing of large 3D-images by
slices, i.e. “streaming”. The only limitation is enforced by the distance transform: the
“feature” voxel of a given voxel should belong to the same slice. For foam images, this
condition is fulfilled as long as the slice’s thickness is larger than the maximal foam cell’s
size.
Conclusion and perspectives. The aim of this contribution is to provide an efficient
tessellation model for tomographic images of foams. From input tomographic images,
this model provides a geometry model which will be used as an input for finite element
simulations under the ARC-Briding project [4]. Simulation results will be compared with
experimental measures.