ISSN 2079-3537      


Scientific Visualization, 2018, volume 10, number 2, pages 48 - 60, DOI: 10.26583/sv.10.2.04

Diffusive Smoothing of 3D Noisy Data

Author: G. Patane

CNR-IMATI, Genova - Italy

ORCID: 0000-0002-2276-9553,



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 Pade-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.


Keywords: Heat kernel smoothing, Surface-based representations, Pade-Chebyshev method, Medical data.