This paper proposes an accurate, computationally efficient, and spectrum-free formulation of the heat diffusion smoothing on 3D shapes, represented as triangle meshes. The idea behind our approach is to apply a [Formula: see text]-degree Padé-Chebyshev rational approximation to the solution of the heat diffusion equation. The proposed formulation is equivalent to solve r sparse, symmetric linear systems, is free of user-defined parameters, and is robust to surface discretization. We also discuss a simple criterion to select the time parameter that provides the best compromise between approximation accuracy and smoothness of the solution. Finally, our experiments on anatomical data show that the spectrum-free approach greatly reduces the computational cost and guarantees a higher approximation accuracy than previous work.

译文

:本文提出了一种精确,计算有效且无频谱的3D形状(以三角形网格表示)上的热扩散平滑公式。我们的方法背后的想法是将[公式:参见文本]度Padé-Chebyshev有理逼近应用于热扩散方程的解。所提出的公式等效于求解稀疏的对称线性系统,没有用户定义的参数,并且对表面离散具有鲁棒性。我们还将讨论一个简单的准则来选择时间参数,以便在近似精度和解的平滑度之间取得最佳折衷。最后,我们对解剖数据的实验表明,无谱方法大大降低了计算成本,并保证了比以前的工作更高的逼近精度。

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