On the optimality of spectral compression of mesh data

作者: Mirela Ben-Chen , Craig Gotsman

DOI: 10.1145/1037957.1037961

关键词:

摘要: Spectral compression of the geometry triangle meshes achieves good results in practice, but there has been little or no theoretical support for optimality this compression. We show that, certain classes geometric mesh models, spectral decomposition using eigenvectors symmetric Laplacian connectivity graph is equivalent to principal component analysis on that class, when equipped with a natural probability distribution. Our proof treats connected one-and two-dimensional fixed convex boundaries, and based an asymptotic approximation distribution case. The key identical, up constant factor, inverse covariance matrix valid geometries. Hence, optimal, mean square error sense, these under some assumptions their

参考文章(28)
Carlos M. Jarque, Anil K. Bera, An efficient large-sample test for normality of observations and regression residuals Australian National University, Faculty of Economics and Research School of Social Sciences. ,(1981)
JM Arnold, BC, Castillo, E., Sarabia, Conditional specification of statistical models ,(1999)
Yehuda Koren, On spectral graph drawing computing and combinatorics conference. pp. 496- 508 ,(2003) , 10.1007/3-540-45071-8_50
Fan R K Chung, Spectral Graph Theory ,(1996)
Costa Touma, Craig Gotsman, Triangle mesh compression graphics interface. pp. 26- 34 ,(1998)
Craig Gotsman, Xianfeng Gu, Alla Sheffer, Fundamentals of spherical parameterization for 3D meshes international conference on computer graphics and interactive techniques. ,vol. 22, pp. 358- 363 ,(2003) , 10.1145/1201775.882276
Fan Chung, S.-T. Yau, Discrete Green's Functions Journal of Combinatorial Theory, Series A. ,vol. 91, pp. 191- 214 ,(2000) , 10.1006/JCTA.2000.3094
Gabriel Taubin, Jarek Rossignac, Geometric compression through topological surgery ACM Transactions on Graphics. ,vol. 17, pp. 84- 115 ,(1998) , 10.1145/274363.274365
D.J. Hartfiel, Carl D. Meyer, On the structure of stochastic matrices with a subdominant eigenvalue near 1 Linear Algebra and its Applications. ,vol. 272, pp. 193- 203 ,(1998) , 10.1016/S0024-3795(97)00333-9
Zachi Karni, Craig Gotsman, Spectral compression of mesh geometry international conference on computer graphics and interactive techniques. pp. 279- 286 ,(2000) , 10.1145/344779.344924