caa a22 4500 605541078 CHVBK 20210128100914.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00371-015-1100-4 doi (NATIONALLICENCE)springer-10.1007/s00371-015-1100-4 Efficient EMD and Hilbert spectra computation for 3D geometry processing and analysis via space-filling curve [Elektronische Daten] [Xiaochao Wang, Jianping Hu, Dongbo Zhang, Hong Qin] Empirical Mode Decomposition (EMD) has proved to be an effective and powerful analytical tool for non-stationary time series and starts to exhibit its modeling potential for 3D geometry analysis. Yet, existing EMD-based geometry processing algorithms only concentrate on multi-scale data decomposition by way of computing intrinsic mode functions. More in-depth analytical properties, such as Hilbert spectra, are hard to study for 3D surface signals due to the lack of theoretical and algorithmic tools. This has hindered much more broader penetration of EMD-centric algorithms into various new applications on 3D surface. To tackle this challenge, in this paper we propose a novel and efficient EMD and Hilbert spectra computational scheme for 3D geometry processing and analysis. At the core of our scheme is the strategy of dimensionality reduction via space-filling curve. This strategy transforms the problem of 3D geometry analysis to 1D time series processing, leading to two major advantages. First, the envelope computation is carried out for 1D signal by cubic spline interpolation, which is much faster than existing envelope computation directly over 3D surface. Second, it enables us to calculate Hilbert spectra directly on 3D surface. We could take advantages of Hilbert spectra that contain a wealth of unexploited properties and utilize them as a viable indicator to guide our EMD-based 3D surface processing. Furthermore, to preserve sharp features, we develop a divide-and-conquer scheme of EMD by explicitly separating the feature signals from non-feature signals. Extensive experiments have been carried out to demonstrate that our new EMD and Hilbert spectra based method is both fast and powerful for 3D surface processing and analysis. Springer-Verlag Berlin Heidelberg, 2015 Empirical mode decomposition nationallicence Hilbert spectra nationallicence Space-filling curve nationallicence Surface processing nationallicence Wang Xiaochao State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, 100191, Beijing, China aut Hu Jianping College of Sciences, Northeast Dianli University, 132012, Jilin, China aut Zhang Dongbo State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, 100191, Beijing, China aut Qin Hong Department of Computer Science, Stony Brook University, 11794-4400, Stony Brook, NY, USA aut The Visual Computer Springer Berlin Heidelberg 31/6-8(2015-06-01), 1135-1145 0178-2789 31:6-8<1135 2015 31 371 https://doi.org/10.1007/s00371-015-1100-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00371-015-1100-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Xiaochao State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, 100191, Beijing, China aut NATIONALLICENCE 700 1- Hu Jianping College of Sciences, Northeast Dianli University, 132012, Jilin, China aut NATIONALLICENCE 700 1- Zhang Dongbo State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, 100191, Beijing, China aut NATIONALLICENCE 700 1- Qin Hong Department of Computer Science, Stony Brook University, 11794-4400, Stony Brook, NY, USA aut NATIONALLICENCE 773 0- The Visual Computer Springer Berlin Heidelberg 31/6-8(2015-06-01), 1135-1145 0178-2789 31:6-8<1135 2015 31 371