We propose a novel diffusion-based, empirical mode decomposition (EMD) algorithm for image analysis. Although EMD has been a powerful tool in signal processing, its algorithmic nature has made it difficult to analyze theoretically. For example, many EMD procedures rely on the location of local maxima and minima of a signal followed by interpolation to find upper and lower envelope curves which are then used to extract a “mean curve” of a signal. These operations are not only sensitive to noise and error but they also present difficulties for a mathematical analysis of EMD. Two-dimensional extensions of the EMD algorithm also suffer from these difficulties. Our PDEs-based approach replaces the above procedures by simply using the diffusion equation to construct the mean curve (surface) of a signal (image). This procedure also simplifies the mathematical analysis. Numerical experiments for synthetic and real images are presented. Simulation results demonstrate that our algorithm can outperform the standard two-dimensional EMD algorithms as well as requiring much less computation time.
CITATION STYLE
Wang, H., Mann, R., & Vrscay, E. R. (2018). A Diffusion-Based Two-Dimensional Empirical Mode Decomposition (EMD) Algorithm for Image Analysis. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10882 LNCS, pp. 295–305). Springer Verlag. https://doi.org/10.1007/978-3-319-93000-8_34
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