Sampling properties of the discrete radon transform

Authors:
Imants Svalbe
Affiliations:
Centre for X-ray Physics and Imaging, School of Physics and Materials Engineering, Monash University, Melbourne 3800, Australia
Venue:
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Year:
2004

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Abstract

The discrete radon transform (DRT) forms a set of digital projections of discrete data, similar to the sinogram of the continuous space radon transform. An advantage of the DRT is that it provides an exact and easily invertible representation for any prime-sized array of arbitrary digital data. The digital projection mechanism is especially suited to the representation and detection of straight lines in digital images. This paper details the angle distribution of the digital projections and characterises the spatial data sampling properties of the DRT digital rays, for regular square and hexagonal lattices. Understanding these properties will aid the design of algorithms to filter and analyse 2D image data that is stored as 1D digital projections in projection space. The DRT can also be applied to reconstruct images from real projection data and may provide a physical basis for modelling the properties of real discrete systems. The DRT also generates binary arrays with special translation-invariant properties.