ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction
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- Aganj I., Lenglet C., Sapiro G. (2010) ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction. In: Jiang T., Navab N., Pluim J.P.W., Viergever M.A. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010. MICCAI 2010. Lecture Notes in Computer Science, vol 6362. Springer, Berlin, Heidelberg
By revealing complex fiber structure through the orientation distribution function (ODF), q-ball imaging has recently become a popular reconstruction technique in diffusion-weighted MRI. In this paper, we propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order real and symmetric spherical harmonic basis, the maxima of the two-dimensional ODF lie on an analytically derived one-dimensional space, from which we can detect the ODF maxima. This method reduces the computational complexity of the maxima detection, without compromising the accuracy. We demonstrate the performance of our technique on both artificial and human brain data.
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