assessment of the log-euclidean metric performance in diffusion tensor image segmentation

introduction: appropriate definition of the distance measure between diffusion tensors has a deep impact on diffusion tensor image (dti) segmentation results. the geodesic metric is the best distance measure since it yields high-quality segmentation results. however, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. the main goal of this paper is to assess the possible substitution of the geodesic metric with the log-euclidean one to reduce the computational cost of a statistical surface evolution algorithm. materials and methods: we incorporated the log-euclidean metric in the statistical surface evolution algorithm framework. to achieve this goal, the statistics and gradients of diffusion tensor images were defined using the log-euclidean metric. numerical implementation of the segmentation algorithm was performed in the matlab software using the finite difference techniques. results: in the statistical surface evolution framework, the log-euclidean metric was able to discriminate the torus and helix patterns in synthesis datasets and rat spinal cords in biological phantom datasets from the background better than the euclidean and j-divergence metrics. in addition, similar results were obtained with the geodesic metric. however, the main advantage of the log-euclidean metric over the geodesic metric was the dramatic reduction of computational cost of the segmentation algorithm, at least by 70 times. discussion and conclusion: the qualitative and quantitative results have shown that the log-euclidean metric is a good substitute for the geodesic metric when using a statistical surface evolution algorithm in dtis segmentation.