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 (. r, r)-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.
Patané, G. (2015). Diffusive smoothing of 3D segmented medical data. Journal of Advanced Research, 6(3), 425–431. https://doi.org/10.1016/j.jare.2014.09.003