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10 March 2020 A generalized method for computation of n-dimensional Radon transforms
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Abstract
Radon transforms allow to represent n-dimensional objects by all their possible (n-1)-dimensional integrals. They find broad usage in a variety of image processing topics, covering pattern recognition and tomographic imaging. Potentially the most frequently used version is the 2D Radon transform which is commonly computed by means of the ray tracing procedure (Siddon, Joseph etc.).1 The problem comes down to a method of approximating a line integral through a 2D pixelized image. For higher dimensions, however, this problem becomes more and more complex and typically involves a substantial amount of case differentiation, making it particularly ill-suited for use in massively parallelized computation (e.g. on GPUs). Additionally, implementation effort is substantial and quite error-prone. Here, we propose a simple strategy to compute the (n-1)-dimensional integrals in a generalized manner by reducing the sampling problem to a single matrix multiplication. We further present OpenCL implementations for n=2 and n=3, making use of hardware interpolation methods on texture memory of GPU devices to provide a fast computation of the transform.
© (2020) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Robert Frysch, Tim Pfeiffer, and Georg Rose "A generalized method for computation of n-dimensional Radon transforms", Proc. SPIE 11313, Medical Imaging 2020: Image Processing, 113132G (10 March 2020); https://doi.org/10.1117/12.2549586
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