We address in this paper the ill-posed problem of initial alignment of pre-operative to intra-operative data for augmented reality during minimally invasive hepatic surgery. This problem consists of finding the rigid transformation that relates the scanning reference and the endoscopic camera pose, and the non-rigid transformation undergone by the liver w.r.t its scanned state. Most of the state-of-the-art methods assume a known initial registration. Here, we propose a method that permits to recover the deformation undergone by the liver while simultaneously finding the rotational and translational parts of the transformation. Our formulation considers the boundaries of the liver with its surrounding tissues as hard constraints directly encoded in an energy minimization process. We performed experiments on real in-vivo data of human hepatic surgery and synthetic data, and compared our method with related works.

This article introduces a method that generates a hexahedral-dominant mesh from an input tetrahedral mesh. It follows a three-step pipeline similar to the one proposed by Carrier Baudoin et al.: (1) generate a frame field, (2) generate a pointset P that is mostly organized on a regular grid locally aligned with the frame field, and (3) generate the hexahedral-dominant mesh by recombining the tetrahedra obtained from the constrained Delaunay triangulation of P . For step (1), we use a state-of-the-art algorithm to generate a smooth frame field. For step (2), we introduce an extension of Periodic Global Parameterization to the volumetric case. As compared with other global parameterization methods (such as CubeCover), our method relaxes some global constraints to avoid creating degenerate elements, at the expense of introducing some singularities that are meshed using non-hexahedral elements. For step (3), we build on the formalism introduced by Meshkat and Talmor, fill in a gap in their proof, and provide a complete enumeration of all the possible recombinations, as well as an algorithm that efficiently detects all the matches in a tetrahedral mesh. The method is evaluated and compared with the state of the art on a database of examples with various mesh complexities, varying from academic examples to real industrial cases. Compared with the method of Carrier-Baudoin et al., the method results in better scores for classical quality criteria of hexahedral-dominant meshes (hexahedral proportion, scaled Jacobian, etc.). The method also shows better robustness than CubeCover and its derivatives when applied to complicated industrial models.

Abstract We present CPH (Compact Primal Hierarchy): a compact representation of the hierarchical connectivity of surface and volume manifold meshes generated through primal subdivision refinements. CPH is consistently defined in several dimensions and supports multiple kinds of tessellations and refinements, whether regular or adaptive. The basic idea is to store only the finest mesh, encoded in a classical monoresolution structure that is enriched with a minimal set of labels. These labels allow traversal of any intermediate level of the mesh concurrently without having to extract it in an additional structure. Our structure allows attributes to be stored on the cells not only on the finest level, but also on any intermediate level. We study the trade‐off between the memory cost of this compact representation and the time complexity of mesh traversals at any resolution level.