DALM, Deformable Attenuation-Labeled Mesh for Tomographic Reconstruction and Segmentation

Most X-ray tomographic reconstruction methods represent a solution as an image on a regular grid. Such representation may be inefficient for reconstructing homogeneous objects from noisy or incomplete projections. Here, we propose a mesh-based method for reconstruction and segmentation of homogeneous objects directly from sinogram data. The outcome of our proposed method consists of curves outlining the regions of constant attenuation, and this output is represented using a labeled irregular triangle mesh. We find the solution by deforming the mesh to minimize the residual given by the sinogram data. Our method supports multiple materials, and allows for topological changes during deformation. An integral part of our algorithm is an efficient forward projection of the labeled mesh onto the sinogram domain. We initialize our algorithm based on graph total variation, also here taking advantage of the mesh representation. Experimental results on simulated datasets show that our method gives a compact representation of the reconstruction and also accurate segmentation results for challenging data with e.g. large noise, a small number of angles or problems with limited angle. We also demonstrate the result on real fan-beam data. The proposed geometric solution shows a further step towards using alternative representations for tomographic reconstruction.