Empirical mode decomposition on surfaces

Empirical Mode Decomposition (EMD) is a powerful tool for analysing non-linear and non-stationary signals, and has drawn a great deal of attentions in various areas. In this paper, we generalize the classical EMD from Euclidean space to the setting of surfaces represented as triangular meshes. Inspired by the EMD, we also propose a feature-preserving smoothing method based on extremal envelopes. The core of our generalized EMD on surfaces is an envelope computation method that solves a bi-harmonic field with Dirichlet boundary conditions. Experimental results show that the proposed generalization of EMD on surfaces works well. We also demonstrate that the generalized EMD can be effectively utilized in filtering scalar functions defined over surfaces and surfaces themselves.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► This paper generalizes the classical concept of Empirical Mode Decomposition (EMD) from Euclidean space to the setting of surfaces. ► The generalized EMD on surfaces is used for filtering scalar functions defined over surfaces and surfaces themselves. ► A novel feature-preserving surface smoothing method is proposed based on extremal envelopes inspired by the EMD.