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.

中文翻译：

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DALM，可变形衰减标签网格，用于层析重建和分割

大多数X射线断层摄影重建方法将解决方案表示为规则网格上的图像。这样的表示对于从嘈杂的或不完整的投影重建均匀物体可能是无效的。在这里，我们提出了一种基于网格的方法，直接从正弦图数据中重建和分割同构对象。我们提出的方法的结果包括概述恒定衰减区域的曲线，并使用标记的不规则三角形网格表示此输出。我们通过使网格变形以最小化正弦图数据给出的残差来找到解决方案。我们的方法支持多种材料，并允许变形期间的拓扑变化。我们算法不可或缺的一部分是将标记网格有效地正投影到正弦图域上。我们基于图的总变化初始化算法，这里也利用网格表示法。在模拟数据集上的实验结果表明，对于具有较大噪声，少量角度或角度受限的问题的挑战性数据，我们的方法给出了重构的紧凑表示以及准确的分割结果。我们还将在真实的扇形束数据上演示结果。所提出的几何解决方案显示了朝着使用替代表示进行断层摄影重建的又一步。少数角度或角度受限的问题。我们还将在真实的扇形束数据上演示结果。所提出的几何解决方案显示了朝着使用替代表示进行断层摄影重建的又一步。少数角度或角度受限的问题。我们还将在真实的扇形束数据上演示结果。所提出的几何解决方案显示了朝着使用替代表示进行断层摄影重建的又一步。