Adaptive Discrete Radon Transforms for Grayscale Images

The Discrete Radon Transform (DRT) sums intensities along digital rays in a 2D, p × p Euclidean function I(x, y) such as an image. The ray sums along the line x = my + t are mapped to projection space R(t,m). Due to the global integration of intensity in the Radon transform, it is often beneficial to perform the DRT on a local subset of the image and investigate the transform as the subset is translated and scaled within the image (when detecting linear features), or over subsequent video frames (when tracking an object). This paper presents algorithms to adaptively update the DRT of a p × p subset of I, whilst the subset undergoes translation and scaling. The computational efficiency of each algorithm is discussed. An expanded representation of Radon space, R(k, θ) is introduced. This space expands the (t, m) transform by removing the modulo p arithmetic and is closer to the continuous space Radon sinogram. This mode of the transform is conducive to adaptively scaling projections up or down to the transform of an image subset of size p.