In flat-detector CT, imperfect or defect detector elements may cause concentric ring artifacts due to their continuous over- or underestimation of attenuation values, which often disturb image quality. Especially due to the demand for high-spatial resolution images and the necessary pixel read-out without arbitrary pixel-binning, ring artifacts become more pronounced and the reduction of these artifacts becomes a necessity. We here present a comparison of two dedicated ring artifact correction methods for flat-detector CT, on the basis of different median and mean filterings of the reconstructed image but each working in different geometric planes. While the first method works in Cartesian coordinates, the second method performs a transformation to polar coordinates. Both post-processing methods efficiently reduce ring artifacts in the reconstructed images and improve image quality. The transformation to polar coordinates turned out to be a necessary step for efficient ring artifact correction, since correction in Cartesian coordinates suffers from newly introduced artifacts as well as insufficient correction of artifacts close to the center of rotation.