Improved, feature-centric EMD for 3D surface modeling and processing

Hu, Jianping; Wang, Xiaochao; Qin, Hong

doi:10.1016/j.gmod.2014.03.006

Cited by 17 publications

(22 citation statements)

References 33 publications

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“…Motivated by such success, it has also been used for 3D surface processing [12,18,26]. The earlier method [18] based on 2D interpolation and mesh parameterizations technology prevents its further application to topologically more complex surface.…”

Section: Related Workmentioning

confidence: 99%

“…The earlier method [18] based on 2D interpolation and mesh parameterizations technology prevents its further application to topologically more complex surface. An alternative based on bi-harmonic interpolation [12,26] is extremely time-consuming for large-sized models. To overcome these limitations, we present an efficient EMD and Hilbert spectra computation for 3D surface analysis and processing via space-filling curve.…”

Section: Related Workmentioning

confidence: 99%

“…Different from previous algorithms [12,26], we expect a signal can be fully decomposed, which will give us more flexibility to manipulate the signal. So, the maximum number of IMFs is not limited.…”

Section: Algorithm 1 Emd Algorithm On 1d Signalmentioning

confidence: 99%

“…In this paper, the signal G(v i ) of mean curvatures used in [12] is adopted, which is rotation-invariant, translation-invariant and facilitates the computation of multi-scale features of surface. The signal G(v i ) is defined on vertices of 3D surface and can be transformed into 1D signal G(t) according to the order of vertex appearing in Hamiltonian cycle.…”

Section: Signal Definition and Reconstructionmentioning

confidence: 99%

“…Until now, fewer work on EMD for 3D surface has been reported [12,18,26]. One main challenge of extending the original EMD to 3D surface is how to calculate the envelopes of the data in an effective way.…”

Section: Introductionmentioning

confidence: 99%

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Efficient EMD and Hilbert spectra computation for 3D geometry processing and analysis via space-filling curve

Wang

Zhang

et al. 2015

Vis Comput

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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 multiscale 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 spacefilling 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 B Jianping Hu 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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