Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
International Journal of Computer Vision
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
IEEE Transactions on Image Processing
High Angular Resolution Diffusion MRI Segmentation Using Region-Based Statistical Surface Evolution
Journal of Mathematical Imaging and Vision
HARDI Denoising: Variational Regularization of the Spherical Apparent Diffusion Coefficient sADC
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
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We present a method for segmenting white matter tracts from high angular resolution diffusion MR images by representing the data in a 5 dimensional space of position and orientation. Whereas crossing fiber tracts cannot be separated in 3D position space, they clearly disentangle in 5D position-orientation space. The segmentation is done using a 5D level set method applied to hyper-surfaces evolving in 5D position-orientation space. In this paper we present a methodology for constructing the position-orientation space. We then show how to implement the standard level set method in such a non-Euclidean high dimensional space. The level set theory is basically defined for N-dimensions but there are several practical implementation details to consider, such as mean curvature. Finally, we will show results from a synthetic model and a few preliminary results on real data of a human brain acquired by high angular resolution diffusion MRI.