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

Abstract

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 partitionings 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.

A Review of Image-Based Simulation Applications in High-Value Manufacturing

“…Furthermore, algorithms are being developed to bring additional benefits, e.g., reduced artefacts during image reconstruction or higher simulation accuracies with adaptive meshing. There is also research into a method to convert 2D image projections directly into FEA meshes [ 355 ], which would remove the need for many of the interim workflow stages. The limitations caused by computational expense was mentioned in a significant proportion of papers as a factor leading to the choice to investigate ROIs.…”