Abstract
Heat diffusion has been widely used in image processing for surface fairing, mesh regularization and surface data smoothing. We present a new fast and accurate numerical method to solve heat diffusion on curved surfaces. This is achieved by approximating the heat kernel using high degree orthogonal polynomials in the spectral domain. The proposed polynomial expansion method avoids solving for the eigenfunctions of the Laplace-Beltrami operator, which is computationally costly for large-scale surface meshes, and the numerical instability associated with the finite element method based diffusion solvers. We apply the proposed method to localize the sex differences in cortical brain sulcal and gyral curve patterns.
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Acknowledgements
This study was funded by NIH Grant R01 EB022856. We would like to thank Won Hwa Kim of University of Texas Arlington and Vikas Singh of University of Wisconsin-Madison for providing valuable discussions on the diffusion wavelets.
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Huang, SG., Lyu, I., Qiu, A., Chung, M.K. (2019). Fast Polynomial Approximation to Heat Diffusion in Manifolds. In: Shen, D., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2019. MICCAI 2019. Lecture Notes in Computer Science(), vol 11767. Springer, Cham. https://doi.org/10.1007/978-3-030-32251-9_6
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DOI: https://doi.org/10.1007/978-3-030-32251-9_6
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