A nonparametric method for intensity inhomogeneity correction in MRI brain images by fusion of Gaussian surfaces

Intensity inhomogeneity (IIH) or bias field in magnetic resonance imaging (MRI) severely affects quantitative image analysis. This paper presents a nonparametric IIH-correction strategy in MRI brain images by fusing multiple Gaussian surfaces. The IIH is modeled as a slowly varying multiplicative noise along with the actual tissue signals. The method does not require a priori knowledge on the intensity probability distribution; rather, it works directly on spatial domains using local image gradients. The method has four steps. Firstly, it extracts different potential tissue regions by considering image histogram. Secondly, an approximated bias field is estimated by fitting a Gaussian surface on the gradient map of each of the homogeneous tissue regions by considering its center as the center of mass. The intensity inhomogeneity field of the entire image is then obtained by fusion of these bias fields. Finally, this IIH field is iteratively removed from the image to obtain the IIH-corrected image. The proposed method is evaluated extensively on popular BrainWeb simulated MRI brain databases and also on some real-patient MRI brain images. Both qualitative and quantitative evaluations of the proposed method reveal its efficiency in removing the bias field in MRI brain images. The standard deviation, coefficient of variation of different tissue regions and coefficient of joint variation between gray matter and white matter are significantly reduced in greater proportion as compared to other standard methods in the case of T2-weighted MRI and come very closer to the ground truths.