CSDL Home IEEE Transactions on Visualization & Computer Graphics 2008 vol.14 Issue No.01 - January/February

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Issue No.01 - January/February (2008 vol.14)

pp: 186-199

ABSTRACT

<p><b>Abstract</b>—Visual data comprise of multi-scale and inhomogeneous signals. In this paper, we exploit these characteristics and develop a compact data representation technique based on a hierarchical tensor-based transformation. In this technique, an original multi-dimensional dataset is transformed into a hierarchy of signals to expose its multi-scale structures. The signal at each level of the hierarchy is further divided into a number of smaller tensors to expose its spatially inhomogeneous structures. These smaller tensors are further transformed and pruned using a tensor approximation technique. Our hierarchical tensor approximation supports progressive transmission and partial decompression. Experimental results indicate that our technique can achieve higher compression ratios and quality than previous methods, including wavelet transforms, wavelet packet transforms, and single-level tensor approximation. We have successfully applied our technique to multiple tasks involving multi-dimensional visual data, including medical and scientific data visualization, data-driven rendering and texture synthesis.</p>

INDEX TERMS

Multilinear Models, Multidimensional Image Compression, Hierarchical Transformation, Tensor Ensemble Approximation, Progressive Transmission, Texture Synthesis

CITATION

Tian Xia, Chun Chen, Hsueh-Yi Sean Lin, Hongcheng Wang, Yizhou Yu, "Hierarchical Tensor Approximation of Multi-Dimensional Visual Data",

*IEEE Transactions on Visualization & Computer Graphics*, vol.14, no. 1, pp. 186-199, January/February 2008, doi:10.1109/TVCG.2007.70406REFERENCES

- [4] P. Kroonenberg and J. de Leeuw, “Principal Component Analysis of Three-Mode Data by Means of Alternating Least Squares Algorithms,”
Psychometrika, vol. 45, pp. 324-1342, 1980.- [5] L.D. Lathauwer, B. de Moor, and J. Vandewalle, “On the Best Rank-1 and ${\rm{Rank}}{\hbox{-}}(R_{1}, R_{2}, \ldots, R_{n})$ Approximation of Higher-Order Tensors,”
SIAM J. Matrix Analysis and Applications, vol. 21, no. 4, pp. 1324-1342, 2000.- [7] A. Shashua and A. Levin, “Linear Image Regression and Classification Using the Tensor-Rank Principle,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2001.- [8] D. Xu, S. Yan, L. Zhang, H.-J. Zhang, Z. Liu, and H.-Y. Shum, “Concurrent Subspaces Analysis,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 203-208, 2005.- [9] M.A.O. Vasilescu and D. Terzopoulos, “Multilinear Analysis of Image Ensembles: Tensorfaces,”
Proc. European Conf. Computer Vision, pp. 447-460, 2002.- [12] R. Furukawa, H. Kawasaki, K. Ikeuchi, and M. Sakauchi, “Appearance Based Object Modeling Using Texture Database: Acquisition, Compression, and Rendering,”
Proc. 13th Eurographics Workshop Rendering, pp. 257-265, 2002.- [13] M. Vasilescu and D. Terzopoulos, “Tensortextures: Multilinear Image-Based Rendering,”
ACM Trans. Graphics, vol. 23, no. 3, pp.334-340, 2004.- [16] D. Lee and H. Seung, “Learning the Parts of Objects by Non-Negative Matrix Factorization,”
Nature, vol. 401, pp. 788-791, 1999.- [19] W. Hackbusch, “A Sparse Matrix Arithmetic Based on ${\cal H}{\hbox{-}}{\rm{Matrices}}$ . Part I: Introduction to ${\cal H}{\hbox{-}}{\rm{Matrices}}$ ,”
Computing, vol. 62, no. 2, pp.89-108, 1999.- [20] G. Garg, E.-V. Talvala, M. Levoy, and H.P.A. Lensch, “Symmetric Photography: Exploiting Data-Sparseness in Reflectance Fields,”
Proc. Eurographics Symp. Rendering, pp. 251-262, 2006.- [22] J. Shapiro, “Embedded Image Coding Using Zerotrees of Wavelet Coefficients,”
IEEE Trans. Signal Processing, vol. 41, no. 12, pp.3445-3462, 1993.- [26] A. Jensen and A. la Cour-Harbo,
Ripples in Mathematics: The Discrete Wavelet Transform. Springer, 2001.- [27] E. Candès and D. Donoho,
Curvelets—A Surprisingly Effective Nonadaptive Representation for Objects with Edges. Vanderbilt Univ. Press, 1999.- [28] E. Candès and D. Donoho, “Ridgelets: A Key to Higher-Dimensional Intermittency,”
Philosophical Trans. Royal Soc. of London A, pp. 2495-2509, 1999.- [30] JPEG 2000 Image Coding System (JPEG 2000 Part I Final Committee Draft Version 1.0), M. Boliek, C. Christopoulos, and E. Majani, eds., ISO/IEC FCD15444-1, http://www.jpeg.org/jpeg2000CDs15444.html , Mar. 2000.
- [31] D. Wood, D. Azuma, K. Aldinger, B. Curless, T. Duchamp, D. Salesin, and W. Stuetzle, “Surface Light Fields for 3D Photography,”
Proc. ACM SIGGRAPH '00, pp. 287-296, 2000.- [32] W.-C. Chen, J.-Y. Bouguet, M. Chu, and R. Grzeszczuk, “Light Field Mapping: Efficient Representation and Hardware Rendering of Surface Light Fields,”
ACM Trans. Graphics, vol. 21, no. 3, pp.447-456, 2002.- [36] M. Koudelka, S. Magda, P. Belhumeur, and D. Kriegman, “Acquisition, Compression, and Synthesis of Bidirectional Texture Functions,”
Proc. Third Int'l Workshop Texture Analysis and Synthesis, pp. 59-64, 2003.- [38] L.-Y. Wei and M. Levoy, “Fast Texture Synthesis Using Tree-Structured Vector Quantization,”
Proc. Int'l Conf. Computer Graphics and Interactive Techniques, pp. 479-488, 2000.- [39] A. Efros and W. Freeman, “Image Quilting for Texture Synthesis and Transfer,”
Proc. ACM Siggraph '01, pp. 341-346, 2001.- [41] V. Kwatra, A. Schödl, I. Essa, G. Turk, and A. Bobick, “Graphcut Textures: Image and Video Synthesis Using Graph Cuts,”
ACM Trans. Graphics, vol. 22, no. 3, pp. 277-286, 2003. |