A generalized method for computation of n-dimensional Radon transforms

Robert Frysch; Tim Pfeiffer; Georg Rose

doi:10.1117/12.2549586

10 March 2020 A generalized method for computation of n-dimensional Radon transforms

Robert Frysch, Tim Pfeiffer, Georg Rose

Author Affiliations +

Proceedings Volume 11313, Medical Imaging 2020: Image Processing; 113132G (2020) https://doi.org/10.1117/12.2549586
Event: SPIE Medical Imaging, 2020, Houston, Texas, United States

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.

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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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