Texture Map and Video Compression Using Beltrami Representation

Ronald Lok Ming Lui The Chinese University of Hong Kong Ka Chun Lam The Chinese University of Hong Kong Tsz Wai Wong University of California at Irvine Xianfeng Gu Stony Brook University

Computational Geometry mathscidoc:1609.09022

SIAM Journal on Imaging Sciences, 6, (4), 1880–1902, 2013.10
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.
Beltrami representation, registration, linear Beltrami solver, texture map compression, video compression, motion vector compression
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  title={Texture Map and Video Compression Using Beltrami Representation},
  author={Ronald Lok Ming Lui, Ka Chun Lam, Tsz Wai Wong, and Xianfeng Gu},
  booktitle={SIAM Journal on Imaging Sciences},
Ronald Lok Ming Lui, Ka Chun Lam, Tsz Wai Wong, and Xianfeng Gu. Texture Map and Video Compression Using Beltrami Representation. 2013. Vol. 6. In SIAM Journal on Imaging Sciences. pp.1880–1902. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905205345828448634.
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