The cone-beam algorithm of Feldkamp, Davis, and Kress preserves oblique line integrals

The algorithm of Feldkamp, Davis, and Kress [J. Opt. Soc. Am. A 1, 612-619 (1984)] is a widely used filtered-backprojection algorithm for three-dimensional image reconstruction from cone-beam (CB) projections measured with a circular orbit of the x-ray source. A well-known property of this approximate algorithm is that the integral of the reconstructed image along any axial line orthogonal to the plane of the orbit is exact when the cone-beam projections are not truncated. We generalize this result to oblique line integrals, thus providing an efficient method to compute synthetic radiographs from cone-beam projections. Our generalized result is obtained by showing that the FDK algorithm is invariant under transformations that map oblique lines onto axial lines.