Efficient EMD and Hilbert spectra computation for 3D geometry processing and analysis via space-filling curve
Efficient EMD and Hilbert spectra computation for 3D geometry processing and analysis via space-filling curve
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通过空间填充曲线进行 3D 几何处理和分析的高效 EMD 和希尔伯特谱计算
DOI：
10.1007/s00371-015-1100-4
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发表时间：
2015-04
期刊：
影响因子：
--
通讯作者：
Hong Qin
中科院分区：
文献类型：
--
作者：
Xiaochao Wang;Jianping Hu;Dongbo Zhang;Hong Qin
经验模态分解（EMD）已被证明是一种有效而强大的非平稳时间序列分析工具，并开始显示出其在三维几何分析中的建模潜力。然而，现有的基于emd的几何处理算法仅侧重于通过计算固有模态函数进行多尺度数据分解。更深入的分析性质，如希尔伯特光谱，由于缺乏理论和算法工具，很难研究三维表面信号。这阻碍了以emd为中心的算法更广泛地渗透到3D表面的各种新应用中。为了解决这一挑战，本文提出了一种新颖有效的EMD和希尔伯特谱计算方案，用于三维几何图形的处理和分析。我们方案的核心是通过空间填充曲线降低维数的策略。该策略将三维几何分析问题转化为一维时间序列处理，具有两大优势。首先，采用三次样条插值对一维信号进行包络计算，比现有的直接在三维表面上进行包络计算快得多。第二，它使我们能够在三维表面上直接计算希尔伯特谱。我们可以利用希尔伯特光谱的优势，它包含了丰富的未开发的特性，并利用它们作为一个可行的指标来指导我们基于emd的3D表面处理。此外，为了保持鲜明的特征，我们开发了一种分而治之的EMD方案，通过显式分离特征信号和非特征信号。大量的实验表明，我们的基于EMD和希尔伯特谱的新方法对于三维表面处理和分析既快速又强大。
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.
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DOI：
10.1109/tvcg.2012.117
发表时间：
2013-02
影响因子：
5.2
作者：
Yue Gao;Chenfeng Li;Bo Ren;Shimin Hu
通讯作者：
Yue Gao;Chenfeng Li;Bo Ren;Shimin Hu
水文时间序列预测的四阶段混合模型
影响因子：
3.7
作者：
Di C;Yang X;Wang X
通讯作者：
Wang X
DOI：
--
发表时间：
2014-04
期刊：
ArXiv
影响因子：
--
作者：
J. Solomon;Keenan Crane;Adrian Butscher;C. Wojtan
通讯作者：
J. Solomon;Keenan Crane;Adrian Butscher;C. Wojtan
影响因子：
2.5
作者：
Coifman, Ronald R.;Maggioni, Mauro
通讯作者：
Maggioni, Mauro
DOI：
10.1016/j.cag.2013.01.004
发表时间：
2013-08
期刊：
Comput. Graph.
影响因子：
--
作者：
E. Akleman;Qing Xing;Pradeep Garigipati;G. Taubin;Jianer Chen;Shiyu Hu
通讯作者：
E. Akleman;Qing Xing;Pradeep Garigipati;G. Taubin;Jianer Chen;Shiyu Hu