Conference Paper

Efficient Spherical Harmonics Representation of 3D Objects

Claude Bernard Univ., Lyon
DOI: 10.1109/PG.2007.39 Conference: Computer Graphics and Applications, 2007. PG '07. 15th Pacific Conference on
Source: IEEE Xplore


In this paper, we present a new and efficient spherical harmonics decomposition for spherical functions defining 3D triangulated objects. Such spherical functions are intrinsically associated to star-shaped objects. However, our results can be extended to any triangular object after segmentation into star-shaped surface patches and recomposition of the results in the implicit framework. There is thus no restriction about the genus number of the object. We demonstrate that the evaluation of the spherical harmonics coefficients can be performed by a Monte Carlo integration over the edges, which makes the computation more accurate and faster than previous techniques, and provides a better control over the precision error in contrast to the voxel-based methods. We present several applications of our research, including fast spectral surface reconstruction from point clouds, local surface smoothing and interactive geometric texture transfer.

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Available from: Eric Galin, Oct 05, 2015
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    • "Instead of using Fourier analysis as a theoretical tool to analyze approximations of filters, Vallet and Levy computed the Fourier transform of the signal on the mesh directly [32]. Spherical harmonic analysis, which is also called Fourier analysis on the unit sphere, was employed to conduct surface filtering, surface reconstruction, and texture transfer [17] [41]. The short-time Fourier transforms are also used for signal processing of point cloud surfaces, where each surface patch is resampled on a regular grid using a fast scattered data approximation [20]. "
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    ABSTRACT: processing non-linear and non-stationary signals. Nonetheless, the research on exploring EMD-relevant techniques in the domain of geometric modeling and processing is extremely rare. Directly applying EMD to coordinate functions of 3D shape geometry will not take advantage of the attractive EMD properties. To ameliorate, in this paper we articulate a novel 3D surface modeling and processing framework founded upon improved, feature-centric EMD, with a goal of realizing the full potential of EMD. Our strategy starts with a measure of mean curvature as a surface signal for EMD. Our newly-formulated measure of mean curvature is computed via the inner product of Laplacian vector and vertex normal. Such measure is both rotation-invariant and translation-invariant, facilitates the computation of different scale features for original surfaces, and avoids boundary shrinkage when processing open surfaces. Moreover, we modify the original EMD formulation by devising a feature-preserving multiscale decomposition algorithm for surface analysis and synthesis. The key idea is to explicitly formulate details as oscillation between local minima and maxima. Within our novel framework, we could accommodate many modeling and processing operations, such as filter design, detail transfer, and feature-preserving smoothing and denoising. Comprehensive experiments and quantitative evaluations/comparisons on popular models have demonstrated that our new surface processing methodology and algorithm based on the improved, feature-centric EMD are of great value in digital geometry processing, analysis, and synthesis.
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    • "Since our model generates bubbles that are non-spherical, it would be valuable to explore how the realism of the bubble sounds are affected by more advanced models. There has been recent work in graphics by Mousa et al. for efficiently calculating spherical harmonics from a triangular mesh [21], [22] and there is a large body of work in the physics and engineering communities about generating sounds from spherical harmonics. We also expect the surface tension of the bubble to pull it towards a spherical shape, so higher order harmonics should become negligible relatively quickly. "
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    ABSTRACT: We present a novel algorithm for simulating the sound generated by liquids. We use a smoothed particle hydrodynamics formulation, modified to allow for the simulation of both liquids and bubbles within those liquids. We couple to that a sound generation engine capable to the fluid simulator capable of extracting the pertinent information from the bubbles in the liquid and generating appropriate sounds.
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    • "The concept then leads to a frequency representation of mesh, which has been used in a wide variety of applications (e.g. [10], [11], and [12]). The SHT is regarded as Fourier transforms of spheres [9]. "
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    ABSTRACT: Mesh geometry processing utilities are frequently used in computer graphics applications. In this paper we propose a novel geometry data processing technique by applying a variation of empirical mode decomposition (EMD) on mesh surface. Unlike typical frequency-domain techniques that adjust given signal by separating its frequency components based on predefined basis functions, our work extracts the ingredients of mesh data on a signal-driven fashion. The proposed algorithm first parametrizes a closed zero-genus mesh over 2-sphere. In second stage the radii of transformed vertices are decomposed into intrinsic mode functions (IMFs) in mesh-defined topology space. Comparing to many other frequency-domain techniques, our method does not require re-sampling of geometry data, hence no distortion is introduced through the process. In this paper we also show an application of proposed method in surface filtering.
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