Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
SIAM Journal on Matrix Analysis and Applications
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
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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.