A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
SIAM Review
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
SIAM Journal on Numerical Analysis
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations
Journal of Computational Physics
Interactive Deformation and Visualization of Level Set Surfaces Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Signed Distance Transform Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
A hamilton-jacobi-bellman approach to high angular resolution diffusion tractography
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Adaptive Riemannian metrics for improved geodesic tracking of white matter
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Neural process reconstruction from sparse user scribbles
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part I
CUDA-accelerated geodesic ray-tracing for fiber tracking
Journal of Biomedical Imaging - Special issue on Parallel Computation in Medical Imaging Applications
Correlation analysis on GPU systems using NVIDIA's CUDA
Journal of Real-Time Image Processing
A Fast Iterative Method for Solving the Eikonal Equation on Triangulated Surfaces
SIAM Journal on Scientific Computing
Fast parallel unbiased diffeomorphic atlas construction on multi-graphics processing units
EG PGV'09 Proceedings of the 9th Eurographics conference on Parallel Graphics and Visualization
The Journal of Supercomputing
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In this paper we present a method to compute and visualize volumetric white matter connectivity in diffusion tensor magnetic resonance imaging (DT-MRI) using a Hamilton-Jacobi (H-J) solver on the GPU (Graphics Processing Unit). Paths through the volume are assigned costs that are lower if they are consistent with the preferred diffusion directions.The proposed method finds a set of voxels in the DTI volume that contain paths between two regions whose costs are within a threshold of the optimal path.The result is a volumetric optimal path analysis, which is driven by clinical and scientific questions relating to the connectivity between various known anatomical regions of the brain.To solve the minimal path problem quickly, we introduce a novel numerical algorithm for solving H-J equations, which we call the Fast Iterative Method (FIM). This algorithm is well-adapted to parallel architectures, and we present a GPU-based implementation, which runs roughly 50-100 times faster than traditional CPU-based solvers for anisotropic H-J equations. The proposed system allows users to freely change the endpoints of interesting pathways and to visualize the optimal volumetric path between them at an interactive rate. We demonstrate the proposed method on some synthetic and real DT-MRI datasets and compare the performance with existing methods.