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GPU-Based Ray-Casting of Spherical Functions Applied to High Angular Resolution Diffusion Imaging

Markus van Almsick, Tim H. J. M. Peeters, Vesna Prckovska, Anna Villanova, Bart ter Haar Romeny
Eindhoven University of Technology, Eindhoven
IEEE Transactions on Visualization and Computer Graphics, Vol. 99, No. 2. (5555)

@article{van2010gpu,

   title={GPU-based Ray-casting of Spherical Functions Applied to High Angular Resolution Diffusion Imaging},

   author={van Almsick, M. and Peeters, T.H.J.M. and Prckovska, V. and Villanova, A. and ter Haar Romeny, B.},

   journal={IEEE Transactions on Visualization and Computer Graphics},

   issn={1077-2626},

   year={2010},

   publisher={Published by the IEEE Computer Society}

}

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Any sufficiently smooth, positive, real-valued function $psi: S^2 rightarrow realset^+$ on a sphere $S^2$ can be expanded by a Laplace expansion into a sum of spherical harmonics. Given the Laplace expansion coefficients, we provide a CPU and GPU-based algorithm that renders the radial graph of $psi$ in a fast and efficient way by ray-casting the glyph of $psi$ in the fragment shader of a GPU. The proposed rendering algorithm has proven highly useful in the visualization of high angular resolution diffusion imaging (HARDI) data. Our implementation of the rendering algorithm can display simultaneously thousands of glyphs depicting the local diffusivity of water. The rendering is fast enough to allow for interactive manipulation of large HARDI data sets.
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