Vector Map Data Compression with Wavelets

Ioup, Juliette W.; Gendron, Marlin L.; Lohrenz, Maura C.

doi:10.1017/s0373463300001089

Cited by 10 publications

(2 citation statements)

References 8 publications

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“…For vector-valued functions, Stachera and Rokita [40] developed an algorithm to compress normal maps by decomposing them in the frequency domain. Ioup, Gendron, and Lohrenz [22] also proposed compressing vector map data in the frequency domain. Kolesnikov and Akimov [28] proposed an algorithm for distortion-constrained compression of vector maps, based on optimal polygonal approximations and dynamic quantizations of vector data.…”

Section: Related Workmentioning

confidence: 99%

Texture Map and Video Compression Using Beltrami Representation

Lui¹,

Lam²,

Wong³

et al. 2013

SIAM J. Imaging Sci.

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Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as three-dimensional coordinates each vertex is mapped to, which often requires lots of memory. This causes inconvenience in data transmission and data storage. To tackle this problem, we propose an effective algorithm for compressing surface homeomorphisms using Fourier approximation of the Beltrami representation. The Beltrami representation is a complex-valued function defined on triangular faces of the surface mesh with supreme norm strictly less than 1. Under suitable normalization, there is a 1-1 correspondence between the set of surface homeomorphisms and the set of Beltrami representations. Hence, every bijective surface map is associated with a unique Beltrami representation. Conversely, given a Beltrami representation, the corresponding bijective surface map can be exactly reconstructed using the linear Beltrami solver introduced in this paper. Using the Beltrami representation, the surface homeomorphism can be easily compressed by Fourier approximation, without distorting the bijectivity of the map. The storage requirement can be effectively reduced, which is useful for many practical problems in computer graphics and imaging. In this paper, we propose applying the algorithm to texture map compression and video compression. With our proposed algorithm, the storage requirement for the texture properties of a textured surface can be significantly reduced. Our algorithm can further be applied to compressing motion vector fields for video compression, which effectively improves the compression ratio.

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Section: Related Workmentioning

confidence: 99%

Texture Map and Video Compression Using Beltrami Representation

Lui¹,

Lam²,

Wong³

et al. 2013

SIAM J. Imaging Sci.

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“…A problem of linear WC applied to IMS data is that peak distortion occurs when the spectra are compressed . Nonlinear WC has been used in other applications such as temperature-constrained cascade correlation neural networks, vector map data compression, and optical tomography data . The advantage of nonlinear WC is that it can achieve high compression rates and high fidelity in the reconstructed spectra.…”

mentioning

confidence: 99%

Nonlinear Wavelet Compression of Ion Mobility Spectra from Ion Mobility Spectrometers Mounted in an Unmanned Aerial Vehicle

et al. 2004

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Linear and nonlinear wavelet compression of ion mobility spectrometry (IMS) data are compared and evaluated. IMS provides low detection limits and rapid response for many compounds. Nonlinear wavelet compression of ion mobility spectra reduced the data to 4-5% of its original size, while eliminating artifacts in the reconstructed spectra that occur with linear compression, and the root-mean-square reconstruction error was 0.17-0.20% of the maximum intensity of the uncompressed spectra. Furthermore, nonlinear wavelet compression precisely preserves the peak location (i.e., drift time). Small variations in peak location may occur in the reconstructed spectra that were linearly compressed. A method was developed and evaluated for optimizing the compression. The compression method was evaluated with in-flight data recorded from ion mobility spectrometers mounted in an unmanned aerial vehicle (UAV). Plumes of dimethyl methylphosphonate were disseminated for interrogation by the UAV-mounted IMS system. The daublet 8 wavelet filter exhibited the best performance for these evaluations.

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