A variant of the popular nonparametric nonuniform intensity normalization (N3) algorithm is proposed for bias field correction. Given the superb performance of N3 and its public availability, it has been the subject of several evaluation studies. These studies have demonstrated the importance of certain parameters associated with the B-spline least-squares fitting. We propose the substitution of a recently developed fast and robust B-spline approximation routine and a modified hierarchical optimization scheme for improved bias field correction over the original N3 algorithm. Similar to the N3 algorithm, we also make the source code, testing, and technical documentation of our contribution, which we denote as "N4ITK," available to the public through the Insight Toolkit of the National Institutes of Health. Performance assessment is demonstrated using simulated data from the publicly available Brainweb database, hyperpolarized (3)He lung image data, and 9.4T postmortem hippocampus data.

This work shows that multi-fibre reconstruction techniques, such as Persistent Angular Structure (PAS) MRI or QBall Imaging, provide much more information than just discrete fibre orientations, which is all that previous tractography algorithms exploit from them. We show that the shapes of the peaks of the functions output by multiple-fibre reconstruction algorithms reflect the underlying distribution of fibres. Furthermore, we show how to exploit this extra information to improve Probabilistic Index of Connectivity (PICo) tractography. The method uses the Bingham distribution to model the uncertainty in fibre-orientation estimates obtained from peaks in the PAS or QBall Orientation Distribution Function (ODF). The Bingham model captures anisotropy in the uncertainty, allowing the method to track through fanning and bending structures, which previous methods do not recover reliably. We devise a new calibration procedure to construct a mapping from peak shape to Bingham parameters. We test the accuracy of the calibration using a bootstrap experiment. Finally, we show that exploiting the peak shape in this way can provide improved PICo tractography results.

The continuous medial representation (cm-rep) is an approach that makes it possible to model, normalize, and analyze anatomical structures on the basis of medial geometry. Having recently presented a partial differential equation (PDE)-based approach for 3-D cm-rep modeling [1], here we present an equivalent 2-D approach that involves solving an ordinary differential equation. This paper derives a closed form solution of this equation and shows how Pythagorean hodograph curves can be used to express the solution as a piecewise polynomial function, allowing efficient and robust medial modeling. The utility of the approach in medical image analysis is demonstrated by applying it to the problem of shape-based normalization of the midsagittal section of the corpus callosum. Using diffusion tensor tractography, we show that shape-based normalization aligns subregions of the corpus callosum, defined by connectivity, more accurately than normalization based on volumetric registration. Furthermore, shape-based normalization helps increase the statistical power of group analysis in an experiment where features derived from diffusion tensor tractography are compared between two cohorts. These results suggest that cm-rep is an appropriate tool for normalizing the corpus callosum in white matter studies.