Bilateral Filtering of Diffusion Tensor MR Images

Abstract

In this paper we present a bilateral image filtering algorithm for edge-preserving smoothing of diffusion tensor magnetic resonance imaging (DTMRI) data. The bilateral filtering is performed in the Log-Euclidean framework which guarantees valid output tensors. Smoothing is achieved by weighted averaging of neighboring tensors. Analogous to bilateral filtering of scalar images, the weights are chosen to be inversely proportional to two distance measures: The geometrical Euclidean distance between the spatial locations of tensors and the dissimilarity of tensors. The following methods for tensor dissimilarity measures are compared: The Log-Euclidean, the similarity-invariant Log-Euclidean, the square root of the J-divergence, and the distance scaled mutual diffusion coefficient. We describe the non-iterative DT smoothing equation in closed form. Interpolation of DT data is treated as a special case of bilateral filtering where only spatial distance is used. We present qualitative and quantitative smoothing and interpolation results on both synthetic tensor field data and real cardiac and brain DTMRI data.