Combining local filtering and multiscale analysis for edge, ridge, and curvilinear objects detection
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image processing techniques for assessing contractility in isolated neonatal cardiac myocytes
Journal of Biomedical Imaging
Journal of Visual Communication and Image Representation
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Although naturally at the heart of many fundamental physical computations, and potentially useful in many important image processing tasks, the Radon transform lacks a coherent discrete definition for two-dimensional (2D) discrete images which is algebraically exact, invertible, and rapidly computable. We define a notion of 2D discrete Radon transforms for 2D discrete images, which is based on summation along lines of absolute slope less than 1. Values at nongrid locations are defined using trigonometric interpolation on a zero-padded grid. Our definition is shown to be geometrically faithful: the summation avoids wrap-around effects. Our proposal uses a special collection of lines in $\mathbb{R}^{2}$ for which the transform is rapidly computable and invertible. We describe a fast algorithm using $O(N\log{N})$ operations, where $N =n^{2}$ is the number of pixels in the image. The fast algorithm exploits a discrete projection-slice theorem, which associates the discrete Radon transform with the pseudopolar Fourier transform [A. Averbuch et al., SIAM J. Sci. Comput., 30 (2008), pp. 764-784]. Our definition for discrete images converges to a natural continuous counterpart with increasing refinement.