A parametric gradient descent MRI intensity inhomogeneity correction algorithm Maite Garcı ´a-Sebastia ´n, Elsa Ferna ´ndez, Manuel Gran ˜a * , Francisco J. Torrealdea Dept. CCIA, UPV/EHU, Apdo. 649, 20080 San Sebastian, Spain Received 21 July 2005; received in revised form 5 April 2007 Available online 24 May 2007 Communicated by G. Borgefors Abstract Given an appropriate imaging resolution, a common Magnetic Resonance Imaging (MRI) model assumes that the object under study is composed of homogeneous tissues whose imaging intensity is constant, so that MRI produces piecewise constant images. The intensity inhomogeneity (IIH) is modeled by a multiplicative inhomogeneity field. It is due to the spatial inhomogeneity in the excitatory Radio Frequency (RF) signal and other effects. It has been acknowledged as a greater source of error for automatic segmentation algorithms than additive noise. We propose a parametric IIH correction algorithm for MRI that consists of the gradient descent of an error function related to the classification error of the IIH corrected image. The inhomogeneity field is modeled as a linear combination of 3D products of Legendre polynomials. In this letter we test both the image restoration capabilities and the classification accuracy of the algorithm. In restoration processes the adaptive algorithm is used only to estimate the inhomogeneity field. Test images to be restored are IIH cor- rupted versions of the BrainWeb site simulations. The algorithm image restoration is evaluated by the correlation of the restored image with the known clean image. In classification processes the algorithm is used to estimate both the inhomogeneity field and the intensity class means. The algorithm classification accuracy is tested over the images from the IBSR site. The proposed algorithm is compared with Maximum A Posteriori (MAP) and Fuzzy Clustering algorithms. Ó 2007 Elsevier B.V. All rights reserved. Keywords: MRI; Intensity inhomogeneity correction; Parametric methods 1. Introduction Magnetic Resonance Imaging (MRI) allows to visualize with great contrast the soft tissues in the body and has rev- olutionized the capacity to diagnose the pathologies that affect them (Dhawan, 2003). MRI has a high spatial reso- lution and provides much information on the anatomical structure, allowing quantitative pathological or clinical studies, the derivation of digitized anatomical atlases and a guidance before and during therapeutic intervention. It is based on the phenomenon known as Nuclear Magnetic Resonance (NMR). The image results from the aggregated measurements of the tissue composition at the molecular level. Given an appropriate imaging resolution, a common MRI model assumes that the object under study is com- posed of piecewise constant materials, so that MRI would produce piecewise constant images. Under this model, once the expected intensities of each tissue are known, we can obtain a good approximation to the optimal bayesian clas- sifier of minimum classification error, assuming that the intensity distribution is a mixture of gaussians whose means are the tissue expected intensities, to perform the image segmentation task. However several imaging condi- tions introduce an additional multiplicative noise fac- tor: the intensity inhomogeneity (IIH) field. The sources of IIH are generally divided in two groups (Vovk et al., 0167-8655/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.patrec.2007.04.016 * Corresponding author. Tel.: +34 943018000; fax: +34 943015590. E-mail addresses: ccpgrrom@si.ehu.es, manuel.grana@ehu.es (M. Gran ˜a). www.elsevier.com/locate/patrec Pattern Recognition Letters 28 (2007) 1657–1666