X-ray tomographic reconstruction typically uses voxel basis functions to represent volumetric images. Due to the structure in voxel basis representations, efficient ray-tracing methods exist allowing fast, GPU accelerated implementations. Tetrahedral mesh basis functions are a valuable alternative to voxel based image representations as they provide flexible, inhomogeneous partitions which can be used to provide reconstructions with reduced numbers of elements or with arbitrarily fine object surface representations. We thus present a robust parallelizable ray-tracing method for volumetric tetrahedral domains developed specifically for Computed Tomography image reconstruction. Tomographic image reconstruction requires algorithms that are robust to numerical errors in floating point arithmetic whilst typical data sizes encountered in tomography require the algorithm to be parallelisable in GPUs which leads to additional constraints on algorithm choices. Based on these considerations, this article presents numerical solutions to the design of efficient ray-tracing algorithms for the projection and backprojection operations. Initial reconstruction results using CAD data to define a triangulation of the domain demonstrate the advantages of our method and contrast tetrahedral mesh based reconstructions to voxel based methods.

中文翻译：

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并行架构上基于数值稳健的四面体层析成像前向和后向投影仪。

X 射线断层扫描重建通常使用体素基函数来表示体积图像。由于体素基础表示的结构，存在有效的光线追踪方法，允许快速、GPU 加速的实现。四面体网格基函数是基于体素的图像表示的一种有价值的替代方法，因为它们提供了灵活的、非均匀的分区，可用于提供具有减少元素数量或任意精细对象表面表示的重建。因此，我们针对体积四面体域提出了一种鲁棒的可并行化光线追踪方法，该方法专为计算机断层扫描图像重建而开发。断层扫描图像重建需要对浮点运算中的数值误差具有鲁棒性的算法，而断层扫描中遇到的典型数据大小要求该算法在 GPU 中可并行化，这导致对算法选择的额外限制。基于这些考虑，本文提出了为投影和反投影操作设计高效光线追踪算法的数值解决方案。使用 CAD 数据定义域三角剖分的初始重建结果证明了我们的方法和对比基于四面体网格的重建与基于体素的方法的优势。本文介绍了为投影和反投影操作设计高效光线追踪算法的数值解决方案。使用 CAD 数据定义域三角剖分的初始重建结果证明了我们的方法和对比基于四面体网格的重建与基于体素的方法的优势。本文介绍了为投影和反投影操作设计高效光线追踪算法的数值解决方案。使用 CAD 数据定义域三角剖分的初始重建结果证明了我们的方法和对比基于四面体网格的重建与基于体素的方法的优势。