Orthonormal Vector Sets Regularization with PDE's and Applications
International Journal of Computer Vision
Flux Maximizing Geometric Flows
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
Regularizing Flows for Constrained Matrix-Valued Images
Journal of Mathematical Imaging and Vision
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Mathematical Imaging and Vision
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's
International Journal of Computer Vision
Curvature-Driven PDE Methods for Matrix-Valued Images
International Journal of Computer Vision
Nonlinear Mean Shift over Riemannian Manifolds
International Journal of Computer Vision
Denoising Intra-voxel Axon Fiber Orientations by Means of ECQMMF Method
MICAI '09 Proceedings of the 8th Mexican International Conference on Artificial Intelligence
Simultaneous smoothing and estimation of the tensor field from diffusion tensor MRI
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Algebraic methods for direct and feature based registration of diffusion tensor images
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Curvature-Preserving regularization of multi-valued images using PDE's
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Fast regularization of matrix-valued images
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
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To understand evolving pathology in the central nervous system (CNS) and develop effective treatments, it is essential to correlate the nerve fiber connectivity with the visualization of function. Diffusion tensor imaging (DTI) can provide the fundamental information required for viewing structural connectivity. In this paper, we present a novel algorithm for automatic fiber tract mapping in the CNS specifically, the spinal cord. The automatic fiber tract mapping problem will be solved in two phases, namely a data smoothing phase and a fiber tract mapping phase. In the former, smoothing is achieved via a new weighted TV-norm minimization (for vector-valued data) which strives to smooth while retaining all relevant detail. For the fiber tract mapping, a smooth 3D vector field indicating the dominant anisotropic direction at each spatial location is computed from the smoothed data. Fiber tracts are then determined as the smooth integral curves of this vector field in a variational framework.