Comments on an evolutionary intensity inhomogeneity correction algorithm

We discuss some aspects of a well known algorithm for inhomogeneity intensity correction in Magnetic Resonance Imaging (MRI), the parametric bias correction (PABIC) algorithm. In this approach, the intensity inhomogeneity is modelled by a linear combination of 2D or 3D Legengre polynomials (computed as outer products of 1D polynomials). The model parameter estimation process proposed in the original paper is similar to a (1+1) Evolution Strategy, with some small and subtle differences. In this paper we discuss some features of the algorithm elements, trying to uncover sources of undesired behaviors and the limits to its applicability. We study the energy function proposed in the original paper and its relation to the image formation model. We also discuss the original minimization algorithm behavior. We think that this detailed discussion is needed because of the high impact that the original paper had in the literature, leading to an implementation into the well known ITK library, which means that it has become a de facto standard.