The Sinogram Polygonizer for Reconstructing 3D Shapes

Abstract

This paper proposes a novel approach, the sinogram polygonizer, for directly reconstructing 3D shapes from sinograms (i.e., the primary output from X-ray computed tomography (CT) scanners consisting of projection image sequences of an object shown from different viewing angles). To obtain a polygon mesh approximating the surface of a scanned object, a grid-based isosurface polygonizer, such as Marching Cubes, has been conventionally applied to the CT volume reconstructed from a sinogram. In contrast, the proposed method treats CT values as a continuous function and directly extracts a triangle mesh based on tetrahedral mesh deformation. This deformation involves quadratic error metric minimization and optimal Delaunay triangulation for the generation of accurate, high-quality meshes. Thanks to the analytical gradient estimation of CT values, sharp features are well approximated, even though the generated mesh is very coarse. Moreover, this approach eliminates aliasing artifacts on triangle meshes.

Numerically robust tetrahedron-based tomographic forward and backward projectors on parallel architectures

“…Approaches to refine the a mesh have been published (e.g. by Yamanaka et al [11] for tetrahedra reconstruction with FDK) whilst solutions to align available CAD models to projection measured data also exist [26]. The following experiment highlights the difference between having accurate knowledge of a prior model and having an ideally aligned mesh generated by a prior model.…”

“…These results are however restricted to 2D or small scale 3D tomography, which numerically is considerably more robust. Yamanaka et al [11] proposed a surface reconstruction model for CT using tetrahedral images as basis elements, however their method is only valid for relatively regular tetrahedral meshes of a size not much larger than the detector pixel size. The used reconstruction methods are also limited, as their approach was only valid for the FDK algorithm.…”

Numerically robust tetrahedron-based tomographic forward and backward projectors on parallel architectures

“…Approaches to refine the a mesh have been published (e.g. by Yamanaka et al [5] for tetrahedra reconstruction with FDK) whilst solutions to align available CAD models to projection measured data also exist [20]. The following experiment highlights the difference between having accurate knowledge of a prior model and having an ideally aligned mesh generated by a prior model.…”

“…These results are however restricted to 2D tomography, which numerically is considerably more robust. Yamanaka et al [5] proposed a surface reconstruction model for CT using tetrahedral images as basis elements, however their method is only valid for relatively regular tetrahedral meshes of a size not much larger than the detector pixel size. The used reconstruction methods are also limited, as their approach was only valid for the FDK algorithm.…”

Computing segmentations directly from x-ray projection data via parametric deformable curves

“…Further processing is suggested in methods from [21] and [22], where segmentation edges between the triangles are detected and iteratively refined. A similar approach for 3D reconstruction is [23].…”