Estimating the bias field of MR images

The authors propose a modification of Wells et al. (ibid., vol. 15, no. 4, p. 429-42, 1996) technique for bias field estimation and segmentation of magnetic resonance (MR) images. They show that replacing the class other, which includes all tissue not modeled explicitly by Gaussians with small variance, by a uniform probability density, and amending the expectation-maximization (EM) algorithm appropriately, gives significantly better results. The authors next consider the estimation and filtering of high-frequency information in MR images, comprising noise, intertissue boundaries, and within tissue microstructures. The authors conclude that post-filtering is preferable to the prefiltering that has been proposed previously. The authors observe that the performance of any segmentation algorithm, in particular that of Wells et al. (and the authors\´ refinements of it) is affected substantially by the number and selection of the tissue classes that are modeled explicitly, the corresponding defining parameters and, critically, the spatial distribution of tissues in the image. The authors present an initial exploration to choose automatically the number of classes and the associated parameters that give the best output. This requires the authors to define what is meant by "best output" and for this they propose the application of minimum entropy. The methods developed have been implemented and are illustrated throughout on simulated and real data (brain and breast MR).