Image Operations in Discrete Radon Space
Imants Svalbe · 2002
The Discrete Radon Transform (DRT) preserves discrete digital image information whilst recasting 2D image data in a form that closely resembles 1D analog projections. The projective representation makes the DRT an effective tool for data compression and for tomographic reconstruction, in particular to obtain images from a limited set of real projection data. For prime sized images formed on regular square or hexagonal arrays, the projective mapping operation is arithmetic addition. Algorithms are presented for efficient computation of the forward and inverse DRT transformation and to perform elementary image rotation and translation operations in the digital projection space. Manipulating image data as DRT projections rather than in the spatial domain avoids the need for expensive reconstruction and re-projection of the data. Comparing objects in projection space may accelerate iterative reconstruction schemes. For some general image-processing operations, projection-based algorithms may produce efficiencies not realisable in the spatial domain. The patterns of pixel locations that combine to form each projection element are shown to have interesting distributional properties that derive from the prime, cyclic nature of the DRT. Key Words: discrete image processing, computer algorithms, Radon transforms.