Empirical mode decomposition on surfaces

  • Authors:

  • Hui Wang;Zhixun Su;Junjie Cao;Ye Wang;Hao Zhang

  • Affiliations:

  • School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China and GrUVi Lab, School of Computing Science, Simon Fraser University, Burnaby V5A1S6, Canada;School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China and State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics ...;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;GrUVi Lab, School of Computing Science, Simon Fraser University, Burnaby V5A1S6, Canada

  • Venue:
  • Graphical Models
  • Year:
  • 2012

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Abstract

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.