Reconstruction of multi-label domains from partial planar cross-sections

• Authors: Gill Barequet;Amir Vaxman
• Venue: SGP '09 Proceedings of the Symposium on Geometry Processing
• Year: 2009

We present a novel algorithm for reconstructing a subdivision of the three-dimensional space (given arbitrarily-oriented slices of it) into labeled domains. The input to the algorithm is a collection of nonparallel planar cross-sections of an unknown object, where the sections might cover only portions of the supporting planes. (The information in the rest of these planes is, thus, "unknown.") Each cross-section consists of a partition of the plane into closed labeled ("colored") domains with no restrictions whatsoever on either their geometries or topologies, and without any assumptions about similarities between partitions of different sections. The problem is to reconstruct the original three-dimensional partition by interpolating simultaneously all the cross-sections, so that planar domains in the input are connected only to other domains of the same color, no two reconstructed spatial domains intersect, and no unnecessary gaps remain between the reconstructed colored domains. The problem of reconstructing multiple-labeled domains arises, for example, in medical imaging, where different types of tissues are scanned and reconstructed at the same time. Partial slices are typical, for example, in ultrasound scanning. In this work we use the three-dimensional straight-skeleton of the arrangement of the cross-sections. Since the sections might be partial, cells of the arrangement might be nonconvex. For this we use the unambiguous definition, as well as the implementation of the computation, of the straight skeleton of a three-dimensional polyhedron that we presented in a recent work [BEGV08]. First, we define these cells and compute their skeleton. Second, we compute overlays of portions of sampled contours in the cross-sections, using the cell skeletons to guide the reconstruction of the mesh.