Sylvain Théry

Continuous free form deformation

Abstract In this paper, we present a new free-form deformation model which uses 3D lattices as deformation tool. With this technique called CFFD, the deformation tool made of Bezier tetrahedral volumes can describe any 3D space subdivision. Furthermore, this model maintains the continuity of the surface of objects throughout the deformation. We show that the C1 continuity constraint between tetrahedral lattices is useless to control the continuity of the deformation. Thus, in order to maintain it, we introduce a new type of constraint which applies only on the lattice deformation. We first define this constraint on a set of two tetrahedral lattices. Then, using this outcome, we study the case of m tetrahedral lattices around a central edge.

Discrete Delaunay: Boundary extraction from voxel objects

We present a discrete approach for boundary extraction from 3D image data. The proposed technique is based on the duality between the Voronoi graph computed accross the digital boundary and the Delaunay triangulation. The originality of the approach is that algorithms perform only integer arithmetic and the method does not suffer from standard round problems and numerical instabilities in the case of floating point computations. This method has been applied both on segmented anatomical structures and on manufactured objects presenting corners and edges. The experimental results show that the method allows to produce a polygonal boundary representation which is guaranteed to be a 2-manifold. This representation is successfully transformed into a triangular quality mesh which meets all topological and geometrical requirements of applications such as augmented reality or simulation.