A Review on MR Image Intensity Inhomogeneity Correction <s> Estimate without explicit modeling <s> A statistical model to segment clinical magnetic resonance (MR) images in the presence of noise and intensity inhomogeneities is proposed. Inhomogeneities are considered to be multiplicative low-frequency variations of intensities that are due to the anomalies of the magnetic fields of the scanners. The measurements are modeled as a Gaussian mixture where inhomogeneities present a bias field in the distributions. The piecewise contiguous nature of the segmentation is modeled by a Markov random field (MRF). A greedy algorithm based on the iterative conditional modes (ICM) algorithm is used to find an optimal segmentation while estimating the model parameters. Results with simulated and hand-segmented images are presented to compare performance of the algorithm with other statistical methods. Segmentation results with MR head scans acquired from four different clinical scanners are presented. <s> BIB001 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> Estimate without explicit modeling <s> Abstract We present a novel algorithm for obtaining fuzzy segmentations of images that are subject to multiplicative intensity inhomogeneities, such as magnetic resonance images. The algorithm is formulated by modifying the objective function in the fuzzy C-means algorithm to include a multiplier field, which allows the centroids for each class to vary across the image. First and second order regularization terms ensure that the multiplier field is both slowly varying and smooth. An iterative algorithm that minimizes the objective function is described, and its efficacy is demonstrated on several test images. <s> BIB002 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> Estimate without explicit modeling <s> In this paper, we present a novel algorithm for adaptive fuzzy segmentation of MRI data and estimation of intensity inhomogeneities using fuzzy logic. MRI intensity inhomogeneities can be attributed to imperfections in the RF coils or some problems associated with the acquisition sequences. The result is a slowly-varying shading artifact over the image that can produce errors with conventional intensity-based classification. Our algorithm is formulated by modifying the objective function of the standard fuzzy c-means (FCM) algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel (voxel) to be influenced by the labels in its immediate neighborhood. The neighborhood effect acts as a regularizer and biases the solution towards piecewise-homogeneous labeling. Such a regularization is useful in segmenting scans corrupted by salt and pepper noise. Experimental results on both synthetic images and MR data are given to demonstrate the effectiveness and efficiency of the proposed algorithm. <s> BIB003 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> Estimate without explicit modeling <s> In this paper, we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data and estimation of intensity inhomogeneities using fuzzy logic. MRI intensity inhomogeneities can be attributed to imperfections in the radio-frequency coils or to problems associated with the acquisition sequences. The result is a slowly varying shading artifact over the image that can produce errors with conventional intensity-based classification. Our algorithm is formulated by modifying the objective function of the standard fuzzy c-means (FCM) algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel (voxel) to be influenced by the labels in its immediate neighborhood. The neighborhood effect acts as a regularizer and biases the solution toward piecewise-homogeneous labelings. Such a regularization is useful in segmenting scans corrupted by salt and pepper noise. Experimental results on both synthetic images and MR data are given to demonstrate the effectiveness and efficiency of the proposed algorithm. <s> BIB004
There are methods BIB001  BIB002 BIB003 BIB004 which consider the IIH as model parameters formulated in a segmentation framework. Suppose the segmentation is to optimize a functional Φ(y, θ, β), where y denotes the observed data, β the IIH term, and θ Rajapakse and Kruggel BIB001 used an MRF formulation, whereas Farag and his group exploited the fuzzy c-means clustering framework  BIB002 BIB003 BIB004 . It is noted that in these methods no explicit assumption has been made on the IIH field, which can be advantageous over model-based methods, since the assumptions with a model could be violated in practice. On the other hand, the absence of constraints on the IIH solution could result in erroneous IIH maps that deviate far away from the truth. In addition, voxel-wise updating the IIH in an iterative process is time-consuming, hence techniques such as multigrid computing may help reduce the computation load.