Uniformity correction with homomorphic filtering on region of interest

MR images are generally distorted by a slowly varying inhomogeneity field which appears only on the tissue region. We propose a simple correction method that combines homomorphic filtering and a normalized convolution. The method estimates and removes the inhomogeneity bias field on the tissue region without artifacts at the boundary of this region as it may happen with usual homomorphic filtering. The normalized convolution utilizes a certainty map which is a coarse segmentation of the MR image into tissue or background regions. Results are presented on simulated and acquired images