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In line with previous studies (Chua et al., 2009), a moderate amount of spatial smoothing (i.e., 1 mm FWHM) led to a considerable increase of the CJV accuracy . The same solution did not prove to be as effective when using CVWM and CVGM instead of CJV. In actual MR data, a common approach to assess INU correction is the one based on indirect measures relying on intensity variability.

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This analysis revealed that the CJV generally provides lower absolute distances, and therefore more accurate results than CVWM and CVGM. For CJV, CVWM, and CVGM calculated on low-dynamic profile MR images, D was 0.6, 1.4, and 1.1%, respectively. For the high-dynamic profile, it was 0.8, 1.5, and 1.1%, respectively. Not only did a smaller absolute distance characterize the selected parameter configuration, but also the matrix patterns better resemble the matrix of absolute distances D.

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Notably, this algorithm would largely benefit from an optimization approach, as it is largely sensitive to the selection of the input parameters, namely the regularization and the smoothing factor (Ganzetti et al., 2016). Rather than implementing an iterative algorithm for the determination of the optimal set of INU correction parameters, we opted for a search across the whole space of possible combinations. In first instance, this choice can be justified by the limited problem size, but also by the simplicity of implementation. A number of INU correction algorithms, for instance SPM, typically show relatively similar performance between parameters configurations that are close in the parameter space. These algorithms are therefore suited for the implementation of an iterative search algorithm, which tries to identify a gradient that leads to the configuration with minimum metric value.

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• In order to assess the performance of intensity inhomogeneity correction for each indirect metric, we analyzed several parameter configurations.
• Based on the CJV, we developed a data-driven approach for selecting INU correction parameters, which could effectively work on actual MR images.
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The use, distribution or reproduction in other forums is permitted, provided the original author or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The need of a procedure for the definition of reliable WM and GM masks was confirmed by a complementary analysis conducted on the CJV, using the template (not subject-specific) masks derived from SPM . When comparing D-values obtained using the SPM template masks and the average-based individual masks, the performance obtained using the former was found to be much inferior. On the other hand, by implementing our data-driven procedure, it was possible to achieve performance similar to the ones derived from the BrainWeb simulator masks used in the first part of the study .

• Intensity non-uniformity correction on actual MR images.
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For each parameter configuration, the WM and GM probability maps produced by the ‘Segmentation’ toolbox were registered to the SPM template in MNI space, using the deformation field generated by the toolbox itself. Afterward, we binarized the WM and GM probability maps registered to MNI space using a threshold equal to 0.9 to minimize the contaminating effect of partial volume voxels. For each parameter configuration, we calculated the Dice Similarity Index between the registered and the SPM template masks for both WM and GM (Zou et al., 2004). The mean DSI for each parameter configuration was computed by averaging the two DSI values for WM and GM, respectively.

This may indicate that the selected input configuration, rather than being subject-specific, more likely depends on the MR hardware and acquisition sequence used. It remains, however, to be verified if this finding for images collected at 3 T generalizes also to higher field strengths, for which tissue-induced inhomogeneities are more prominent. This may indeed lead to an increased inter-subject variability in the selected parameter configuration. Importantly, we also observed that the segmentation results for the same subject scanned in two separate sessions were more similar when using optimized than standard configurations . It is commonly accepted that intensity inhomogeneity primarily affects the accuracy of image segmentations (Belaroussi et al., 2006; Zheng et al., 2009). Accordingly, this finding might be taken as indirect evidence of an increased INU correction performance.

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Intensity non-uniformity in magnetic resonance imaging is a major issue when conducting analyses of brain structural properties. An inaccurate INU correction may result in qualitative and quantitative misinterpretations. Several INU correction methods exist, whose performance largely depend on the specific parameter settings that need to be chosen by the user. Here we addressed the question of how to select the best input parameters for a specific INU correction algorithm. Our investigation was based on the INU correction algorithm implemented in SPM, but this can be in principle extended to any other algorithm requiring the selection of input parameters. Using simulated MR data, we observed the CJV to be more accurate than CVWM and CVGM, provided that the noise level in the INU-corrected image was controlled by means of spatial smoothing.

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