Rough Sets for Bias Field Correction in MR Images Using Contraharmonic Mean and Quantitative Index

One of the challenging tasks for magnetic resonance (MR) image analysis is to remove the intensity inhomogeneity artifact present in MR images, which often degrades the performance of an automatic image analysis technique. In this regard, the paper presents a novel approach for bias field correction in MR images. It judiciously integrates the merits of rough sets and contraharmonic mean. While the contraharmonic mean is used in low-pass averaging filter to estimate the bias field in multiplicative model, the concept of lower approximation and boundary region of rough sets deals with vagueness and incompleteness in filter structure definition. A theoretical analysis is presented to justify the use of both rough sets and contraharmonic mean for bias field estimation. The integration enables the algorithm to estimate optimum or near optimum bias field. Some new quantitative indexes are introduced to measure intensity inhomogeneity artifact present in a MR image. The performance of the proposed approach, along with a comparison with other approaches, is demonstrated on both simulated and real MR images for different bias fields and noise levels.