Computation of the forward and inverse Radon transform via the central slice theorem employing a nonscanning optical technique

Rupert C. D. Young; Christopher R. Chatwin

doi:10.1117/12.235664

15 March 1996 Computation of the forward and inverse Radon transform via the central slice theorem employing a nonscanning optical technique

Rupert C. D. Young, Christopher R. Chatwin

Author Affiliations +

Proceedings Volume 2752, Optical Pattern Recognition VII; (1996) https://doi.org/10.1117/12.235664
Event: Aerospace/Defense Sensing and Controls, 1996, Orlando, FL, United States

Abstract

The forward Radon transform operating on edge enhanced images is identical to the Hough transform in its (rho) -(phi) parametrization. The inverse operation may be used to recover an image from its projection data, acquired using tomography. Both forward and inverse operations may be efficiently computed by exploiting the central slice theorem, the major computational operations then becoming two dimensional and one dimensional Fourier transformation with an intervening coordinate conversion. The paper describes a non-scanning optical arrangement to implement both the forward and inverse Radon transform which may thus be used to compute both the Hough transform of image data and, by exchanging the input and output sections, the reconstruction of projection data. Simulations of the computation of the Hough transform via the central slice theorem are presented which include pixel interpolation in the polar mapping coordinate conversion to more closely approximate the analogue transformation which may be accomplished by the optical processor.

Citation Download Citation

Rupert C. D. Young and Christopher R. Chatwin "Computation of the forward and inverse Radon transform via the central slice theorem employing a nonscanning optical technique", Proc. SPIE 2752, Optical Pattern Recognition VII, (15 March 1996); https://doi.org/10.1117/12.235664

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