From Triangulation to Simplex Mesh and Vice-versa - A Simple and Efficient Conversion

In the field of 3D images, relevant information can be difficult to interpret without further computer-aided processing. Generally, and this is particularly true in medical imaging, a segmentation process is run and coupled with a visualization of the delineated structures. Amongst all techniques based on deformable models, simplex meshes, in particular, present good propensities to handle a large variety of shape alterations altogether with a fine resolution and stability. However, they may not be well suited to cope satisfyingly with other related tasks, such as rendering, mechanical simulation or reconstruction from iso-surfaces. As a consequence, triangle meshes are often preferred. Thus, we propose an accurate method to shift from a model to another, and conversely. For this, we are taking advantage of the fact that they are topologically duals, turning it into a natural swap between these two models. Unfortunately, they are not geometrically equivalents, leading to loss of information and to geometry deterioration when performing the conversion. Therefore, optimal positions of the vertices in the dual mesh have to be found while avoiding shape degradation. An accurate and effective transformation technique is described in this paper, where we present a direct method to perform an appropriate interpolation of a simplex mesh to obtain its dual, and/or vice-versa. This original method is based on the distance minimization between the local tangent planes of the mesh and vertices of each face. Finally, probing resulting mesh conversions in both directions are commented.