Registration of high angular resolution diffusion MRI images using 4th order tensors

Abstract

Registration of Diffusion Weighted (DW)-MRI datasets has been commonly achieved to date in literature by using either scalar or 2nd-order tensorial information. However, scalar or 2nd-order tensors fail to capture complex local tissue structures, such as fiber crossings, and therefore, datasets containing fiber-crossings cannot be registered accurately by using these techniques. In this paper we present a novel method for non-rigidly registering DW-MRI datasets that are represented by a field of 4th-order tensors. We use the Hellinger distance between the normalized 4th-order tensors represented as distributions, in order to achieve this registration. Hellinger distance is easy to compute, is scale and rotation invariant and hence allows for comparison of the true shape of distributions. Furthermore, we propose a novel 4th-order tensor re-transformation operator, which plays an essential role in the registration procedure and shows significantly better performance compared to the re-orientation operator used in literature for DTI registration. We validate and compare our technique with other existing scalar image and DTI registration methods using simulated diffusion MR data and real HARDI datasets.

Fig. 1

Left: a) Synthetically generated dataset by simulating the MR signal [13]. b) Dataset generated by applying a non-rigid transformation to (a). Center: Crossing misalignment in ROI after registering datasets (a) and (b) using various methods. Right: Quantitative comparison of the registration errors. The errors were measured by Eq. 4 for the whole field.

Fig. 2

Left: Simulated dataset generated by stretching the fibers of Fig 1a. Rest of the plates: Comparison of results after registering dataset in Fig. 2(left) to that of Fig. 1a using tensor re-orientation only and our proposed tensor re-transformation.

Fig. 3

a and b) S₀ images from two HARDI volumes of human hippocampi. c, d) datasets before and after registration. Tensors from the ROI in (d) showing crossings.