A Method for Standardizing MR Intensities between Slices and Volumes

The first section of this paper describes a method for correcting inter-slice intensity variations in MR images. The method does not rely on a tissue model or segmentation, and is not affected by the presence of abnormalities. The second section of this work extends this technique to the correction of inter-volume intensity variations in MR images of the brain, using a characterization of bi-lateral symmetry to confer robustness to the presence of large abnormalities such as tumors or edema. 1 Inter-Slice Intensity Variation Reduction Due to gradient eddy currents and ‘crosstalk’ between slices in ‘multislice’ acquisition sequences, the twodimensional slices acquired under some MRI acquisition protocols may have a constant slice-by-slice intensity offset [1]. It is noteworthy that these variations have different properties than the intensity inhomogeneity observed within slices, or typically observed across slices. As opposed to being slowly varying, these variations are characterized by sudden intensity changes in adjacent slices. A common result of inter-slice intensity variations is an interleaving between ‘bright’ slices and ‘dark’ slices [2], (the ‘evenodd’ effect). While most intensity inhomogeneity correction methods can correct for slowly varying intensity variations, most methods for intensity inhomogeneity reduction do not consider these sudden changes. This work, therefore, presents a simple method to reduce sudden intensity variations between adjacent slices. In comparison to the estimation of slowly varying intensity inhomogeneities, correcting inter-slice intensity variations has received little attention in the medical imaging literature. One early attempt to correct this problem in order to improve segmentation was presented in [3]. This work presented a system for the segmentation of normal brains using Markov Random Fields, and presented two simple methods to re-estimate tissue parameters between slices (after patient-specific training on a single slice). One method thresholded pixels with high probabilities of containing a single tissue type, while the other used a least squares estimate of the change in tissue parameters. A similar approach was used in one of the only systems thus far to incorporate this step for tumor segmentation [4]. This system first used patient-specific training of a neural network classifier on a single slice. When segmenting an adjacent slice, this neural network was first used to classify all pixels in the adjacent slice. The locations of pixels that received the same label in both slices were then determined, and these pixels in the adjacent slice were used as a new training set for the neural network classifier used to classify the adjacent slice. Each of these approaches require not only a tissue model, but patient-specific training, making them unsuitable for use in automatic systems for detecting and segmenting large abnormalities. One of the most impressive inter-slice intensity correction methods to date was presented in [1]. This work presented two methods to incorporate inter-slice variation correction within an EM segmentation framework. The first simply incorporated slice-by-slice constant intensity offsets into the inhomogeneity estimation, while the second method computed a two-dimensional inhomogeneity field in each slice and used these to produce a three-dimensional inhomogeneity field that allowed inter-slice intensity variations. The method used by the INSECT system for this step was presented in [5] to improve the segmentation of Multiple Sclerosis lesions. This method estimated a linear intensity mapping based on pixels at the same location in adjacent slices that were of the same tissue type. Unfortunately, despite the lack of patient-specific training, these methods each still require a tissue model (in each slice) that may be violated in data containing significant pathology. A method free of a tissue model was presented in [6]. This method used a median filter to reduce noise, and pruned pixels from the intensity estimation by band thresholding of histogram, and removing pixels representing edges. The histogram was divided into bins and a parabola was fit to the heights of the 3 central bins, used to determine the intensity mapping. Although model-free, this method makes major assumptions about the distribution of the histogram, that may not be true in all modalities or in images with pathological data. In addition, this method ignores spatial information. Inter-slice intensity variation correction can be addressed using the same techniques employed in Intensity Standardization, which will be discussed in the next section. However, most methods for Intensity Standardization employ a tissue model or a histogram matching method that will be sensitive to outliers. It was ultimately chosen not to use one of the existing histogram matching methods, since real data may have anisotropic pixels, where the tissue distributions can change significantly between slices. The methods in [5, 4] are more appealing since these methods use spatial information to determine appropriate pixels for use in estimation. However, these methods rely on a tissue model that could be inappropriate for data with significant pathology. Although the method of [6] is a histogram matching method, removing points from the estimation in a modelfree way is appealing. We present in this section a simple method to identify good candidates for estimating the intensity between slices as in [5, 4], but without an explicit tissue model. We will assume that the intensity mapping between slices can be described by a multiplicative scalar value w, a model commonly used [5, 1]. If we assume that the slices are exactly aligned such that each pixel in slice X corresponds to a pixel in slice Y of the same tissue type, then the scalar w could be estimated by solving the equation below (where X and Y are vectors of intensities and X(i) has the same spatial location as Y (i) within the image):