Chapter

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2006

Volume 4191 of the series Lecture Notes in Computer Science pp 234-242

Riemannian Graph Diffusion for DT-MRI Regularization

  • Fan ZhangAffiliated withDepartment of Computer Science, University of York
  • , Edwin R. HancockAffiliated withDepartment of Computer Science, University of York

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Abstract

A new method for diffusion tensor MRI (DT-MRI) regularization is presented that relies on graph diffusion. We represent a DT image using a weighted graph, where the weights of edges are functions of the geodesic distances between tensors. Diffusion across this graph with time is captured by the heat-equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigen-system with time. Tensor regularization is accomplished by computing the Riemannian weighted mean using the heat kernel as its weights. The method can efficiently remove noise, while preserving the fine details of images. Experiments on synthetic and real-world datasets illustrate the effectiveness of the method.