RF-Inhomogeneity Correction (aka bias) artifact is an important research field in Magnetic Resonance Imaging (MRI). Bias corrupts MR images altering their illumination even though they are acquired with the most recent scanners. Homomorphic Unsharp Masking (HUM) is a filtering technique aimed at correcting illumination inhomogeneity, but it produces a halo around the edges as a side effect. In this paper a novel correction scheme based on HUM is proposed to correct the artifact mentioned above without introducing the halo. A wide experimentation has been performed on MR images. The method has been tuned and evaluated using the simulated Brainweb image database. In this framework, the approach has been compared successfully against the Guillemaud filter and the SPM2 method. Moreover, the method has been successfully applied on several real MR images of the brain (0.18 T, 1.5 T and 7 T). The description of the overall technique is reported along with the experimental results that show its effectiveness in different anatomical regions and its ability to compensate both underexposed and overexposed areas. Our approach is also effective on non-radiological images, like retinal ones.