A Review on MR Image Intensity Inhomogeneity Correction <s> SURFACE FITTING <s> A number of supervised and unsupervised pattern recognition techniques have been proposed in recent years for the segmentation and the quantitative analysis of MR images. However, the efficacy of these techniques is affected by acquisition artifacts such as inter-slice, intra-slice, and inter-patient intensity variations. Here a new approach to the correction of intra-slice intensity variations is presented. Results demonstrate that the correction process enhances the performance of backpropagation neural network classifiers designed for the segmentation of the images. Two slightly different versions of the method are presented. The first version fits an intensity correction surface directly to reference points selected by the user in the images. The second version fits the surface to reference points obtained by an intermediate classification operation. Qualitative and quantitative evaluation of both methods reveals that the first one leads to a better correction of the images than the second but that it is more sensitive to operator errors. > <s> BIB001 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> SURFACE FITTING <s> Medical imaging data sets are often corrupted by multiplicative inhomogeneities, often referred to as nonuniformities or intensity variations, that hamper the use of quantitative analyses. The authors describe an automatic technique that not only improves the worst situations, such as those encountered with magnetic resonance imaging (MRI) surface coils, but also corrects typical inhomogeneities encountered in routine volume data sets, such as MRI head scans, without generating additional artifact. Because the technique uses only the patient data set, the technique can be applied retrospectively to all data sets, and corrects both patient independent effects, such as rf coil design, and patient dependent effects, such as attenuation of overlying tissue experienced both in high field MRI and X-ray computed tomography (CT). The authors show results for several MRI imaging situations including thorax, head, and breast. Following such corrections, region of interest analyses, volume histograms, and thresholding techniques are more meaningful. The value of such correction algorithms may increase dramatically with increased use of high field strength magnets and associated patient-dependent rf attenuation in overlying tissues. <s> BIB002 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> SURFACE FITTING <s> The authors propose a model-based method for fully automated bias field correction of MR brain images. The MR signal is modeled as a realization of a random process with a parametric probability distribution that is corrupted by a smooth polynomial inhomogeneity or bias field. The method the authors propose applies an iterative expectation-maximization (EM) strategy that interleaves pixel classification with estimation of class distribution and bias field parameters, improving the likelihood of the model parameters at each iteration. The algorithm, which can handle multichannel data and slice-by-slice constant intensity offsets, is initialized with information from a digital brain atlas about the a priori expected location of tissue classes. This allows full automation of the method without need for user interaction, yielding more objective and reproducible results. The authors have validated the bias correction algorithm on simulated data and they illustrate its performance on various MR images with important field inhomogeneities. They also relate the proposed algorithm to other bias correction algorithms. <s> BIB003 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> SURFACE FITTING <s> At its simplest, voxel-based morphometry (VBM) involves a voxel-wise comparison of the local concentration of gray matter between two groups of subjects. The procedure is relatively straightforward and involves spatially normalizing high-resolution images from all the subjects in the study into the same stereotactic space. This is followed by segmenting the gray matter from the spatially normalized images and smoothing the gray-matter segments. Voxel-wise parametric statistical tests which compare the smoothed gray-matter images from the two groups are performed. Corrections for multiple comparisons are made using the theory of Gaussian random fields. This paper describes the steps involved in VBM, with particular emphasis on segmenting gray matter from MR images with nonuniformity artifact. We provide evaluations of the assumptions that underpin the method, including the accuracy of the segmentation and the assumptions made about the statistical distribution of the data. <s> BIB004 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> SURFACE FITTING <s> Outlines a fully automatic method for the correction of intensity nonuniformity in MR images. This method does not require any a priori model of the tissue classes. The basic idea is that entropy is a good measure of the image quality which can be minimized in order to overcome the bias problem. Therefore, the optimal correcting field is defined by the minimum of a functional combining the restored image entropy and a measure of the field smoothness. This measure stems from the usual physical analogy with membranes. A third term added to the functional prevents the optimal field from being uniformly null. The functional is minimized using a fast annealing schedule. The performance of the method is evaluated using both real and simulated data. <s> BIB005 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> SURFACE FITTING <s> Shading is a prominent phenomenon in microscopy, manifesting itself via spurious intensity variations not present in the original scene. The elimination of shading effects is frequently necessary for subsequent image processing tasks, especially if quantitative analysis is the final goal. While most of the shading effects may be minimized by setting up the image acquisition conditions carefully and capturing additional calibration images, object-dependent shading calls for retrospective correction. In this paper a novel method for retrospective shading correction is proposed. Firstly, the image formation process and the corresponding shading effects are described by a linear image formation model, which consists of an additive and a multiplicative parametric component. Secondly, shading correction is performed by the inverse of the image formation model, whose shading components are estimated retrospectively by minimizing the entropy of the acquired images. A number of tests, performed on artificial and real microscopical images, show that this approach is efficient for a variety of differently structured images and as such may have applications in and beyond the field of microscopical imaging. <s> BIB006 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> SURFACE FITTING <s> In this paper the problem of retrospective correction of intensity inhomogeneity in MR images is addressed. A novel model-based correction method is proposed, based on the assumption that an image corrupted by intensity inhomogeneity contains more information than the corresponding uncorrupted image. The image degradation process is described by a linear model, consisting of a multiplicative and an additive component which are modeled by a combination of smoothly varying basis functions. The degraded image is corrected by the inverse of the image degradation model. The parameters of this model are optimized such that the information of the corrected image is minimized while the global intensity statistic is preserved. The method was quantitatively evaluated and compared to other methods on a number of simulated and real MR images and proved to be effective, reliable, and computationally attractive. <s> BIB007 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> SURFACE FITTING <s> An adaptive spatial fuzzy c-means clustering algorithm is presented in this paper for the segmentation of three-dimensional (3-D) magnetic resonance (MR) images. The input images may be corrupted by noise and intensity nonuniformity (INU) artifact. The proposed algorithm takes into account the spatial continuity constraints by using a dissimilarity index that allows spatial interactions between image voxels. The local spatial continuity constraint reduces the noise effect and the classification ambiguity. The INU artifact is formulated as a multiplicative bias field affecting the true MR imaging signal. By modeling the log bias field as a stack of smoothing B-spline surfaces, with continuity enforced across slices, the computation of the 3-D bias field reduces to that of finding the B-spline coefficients, which can be obtained using a computationally efficient two-stage algorithm. The efficacy of the proposed algorithm is demonstrated by extensive segmentation experiments using both simulated and real MR images and by comparison with other published algorithms. <s> BIB008
Since the inhomogeneity field is slowly varying, it is natural to approximate the IIH by a parametric smooth functional  BIB001 BIB002 BIB003    BIB004 BIB005 BIB006 BIB007 BIB008 . Very often, the parameter estimation is linked to image segmentation. In this way, the two different problems, IIH correction and image segmentation, are formulated in one framework and solved simultaneously. Alternatively, the parameter searching can be guided through the variation of some global image feature in an iterative process. A typical example is to minimize the entropy of gray-level histogram.