Smoothing fields of frames using conjugate norms on reproducing kernel Hilbert spaces

Hsiao-Fang Chou; Laurent Younes

doi:10.1117/12.815280

2 February 2009 Smoothing fields of frames using conjugate norms on reproducing kernel Hilbert spaces

Hsiao-Fang Chou, Laurent Younes

Proceedings Volume 7246, Computational Imaging VII; 724607 (2009) https://doi.org/10.1117/12.815280
Event: IS&T/SPIE Electronic Imaging, 2009, San Jose, California, United States

Abstract

Diffusion tensor imaging provides structural information in medical images in the form of a symmetric positive matrix that provides, at each point, the covariance of water diffusion in the tissue. We here describe a new approach designed for smoothing this tensor by directly acting on the field of frames provided by the eigenvectors of this matrix. Using a representation of fields of frames as linear forms acting on smooth tensor fields, we use the theory of reproducing kernel Hilbert spaces to design a measure of smoothness based on kernels which is then used in a denoising algorithm. We illustrate this with brain images and show the impact of the procedure on the output of fiber tracking in white matter.

Citation Download Citation

Hsiao-Fang Chou and Laurent Younes "Smoothing fields of frames using conjugate norms on reproducing kernel Hilbert spaces", Proc. SPIE 7246, Computational Imaging VII, 724607 (2 February 2009); https://doi.org/10.1117/12.815280

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