Exploiting triangulated surface extraction using tetrahedraldecomposition

摘要

Beginning with digitized volumetric data, we wish to rapidly andnefficiently extract and represent surfaces defined as isosurfaces in theninterpolated data. The Marching Cubes algorithm is a standard approachnto this problem. We instead perform a decomposition of each 8-cellnassociated with a voxel into five tetrahedra. We guarantee the resultingnsurface representation to be closed and oriented, defined by a validntriangulation of the surface of the body, which in turn is presented asna collection of tetrahedra. The entire surface is “wrapped”nby a collection of triangles, which form a graph structure, and whereneach triangle is contained within a single tetrahedron. Thenrepresentation is similar to the homology theory that uses simplicesnembedded in a manifold to define a closed curve within each tetrahedron.nWe introduce data structures based upon a new encoding of the tetrahedranthat are at least four times more compact than the standard datanstructures using vertices and triangles. For parallel computing andnimproved cache performance, the vertex information is stored local tonthe tetrahedra. We can distribute the vertices in such a way that nontetrahedron ever contains more than one vertex, We give methods tonevaluate surface curvatures and principal directions at each vertex,nwhenever these quantities are defined. Finally, we outline a method fornsimplifying the surface, that is reducing the vertex count whilenpreserving the geometry. We compare the characteristics of our methodsnwith an 8-cell based method, and show results of surface extractionsnfrom CT-scans and MR-scans at full resolution