Figure 4.11 and Figure 4.12and Figure 4.13 Figure 4.14 are rendering results of wool and corduroy and ceiling BTF data. All these data are modeled using our optimal reparameteri-zation, wool and corduroy data are modeled with twenty BTF kernels and three multivariate
4.6 Rendering Results 27
BTF Data Data Size Lighting and Viewing Directions Resolution
Corduroy 327MB 81*81 256*256
Wool 346MB 81*81 256*256
Ceiling 2.05GB 81*81 800*800
Impalla 314MB 81*81 256*256
Table 4.2: Data size of data in BTF database Bonn. All textures are stored with JPEG format Data Size J K Min. Mipmap Level
52.1MB 20 3 1
26.1MB 10 3 1
204MB 20 3 0
104MB 10 3 0
Table 4.3: Data size of our BTF modeling. J and K denote number of multivariate SRBF kernels and number of multivariate modes.
modes, ceiling data are modeled with ten BTF kernels and three multivariate modes.
Figure 4.11: Rendering result of wool with optimal reparameterization. (J=20,K=3)
4.6 Rendering Results 28
Figure 4.12: Rendering result of corduroy with optimal reparameterization. (J=20,K=3)
Figure 4.13: Rendering result of ceiling with optimal reparameterization. (J=10,K=3)
4.6 Rendering Results 29
Figure 4.14: Rendering result of ceiling with optimal reparameterization. (J=10,K=3)
The FPS of our BTF rendering is shown in Table 4.4. Evaluation time for each pixel fol-lows the number of multivariate SRBF kernels direct proportion relation, so the FPS using 20 multivariate SRBF kernels is about half of using 10 multivariate SRBF kernels.
Model triangle FPS J K
Plane 800 50.23 10 3
Plane 800 26.10 20 3
Bunny 69630 18.77 10 3 Bunny 69630 9.42 20 3 cloth 59168 11.63 10 3 cloth 59168 6.15 20 3
Table 4.4: FPS of rendering. J and K denote number of multivariate SRBF kernels and number of multivariate modes.
C H A P T E R 5
Conclusion and Future Work
In this thesis, we use a data-driven parametric representation in viewing and lighting space to model the BTF data. Unlike fixed reparameterization, we can define reparameterization function and optimize their parameters to get the optimal reparameterization function. This optimal reparameterization can make BTF modeling more accurately.
To use spatial coherence efficiently, we construct mipmaps of BTF data and use mipmap hierarchy in our optimization process. We can speed up BTF modeling and keep the properties of mipmap which improves the performance and quality in rendering.
EM algorithm are used to speed up the heave work of optimization. We use EM algorithm to find a proper initial guess, so our optimization process works much faster and still remain great quality of results.
Our experiments has shown the improvement of our multivariate SRBF kernel and our op-timal reparameterization method compared to univariate SRBF kernel and half-way reparame-terization. Our BTF model is efficient both in modeling and rendering, our BTF model use only about one sixths than original BTF data and we can render our BTF model in real time.
Currently, there are some artifacts caused by mipmap and smooth terms. Fitting using multi-resolution hierarchy can speed up our framework a lot, but we assume corresponding textels in
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different mipmap levels are similar. When the corresponding textels are totally different, it will induce large error, so how to solve this problem is the most important task in the future.
We smooth our BTF model in spatial dimension by adding difference value of nearby(5*5 square) into objective function. When the data differs a lot in this square, our smooth terms will cause bad influence, it increase error ratio in represent result. In the future, robust error matrix will be applied into our method to fix this problem.
Bibliography
[1] M. Alex, O. Vasilescu, and D. Terzopoulos. Tensortextures: Multilinear image-based rendering. ACM Transactions on Graphics, pages 336–342, 2004.
[2] W. chun Ma, S. hsiang Chao1, Y. ting Tseng, Y. yu Chuang, C. fa Chang, B. yu Chen, and M. Ouhyoung. Level-of-detail representation of bidirectional texture functions for real-time rendering. In Proceedings of I3D 2005, pages 187–194, 2005.
[3] O. G. Cula and K. J. Dana. Compact representation of bidirectional texture functions. In Proceedings of CVPR 2001, pages 1041–1047, 2001.
[4] K. J. Dana, B. V. Ginneken, S. K. Nayar, and J. J. Koenderink. Reflectance and texture of real-world surfaces. In Proceedings of ACM SIGGRAPH 1999, volume 18, pages 1–34, 1999.
[5] W. R. Davis. Cornelius Lanczos Collected Published Papers With Commentaries. North Carolina State University, 1999.
[6] D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz. Shape and spatially-varying brdfs from photometric stereo. In Proceedings of ICCV 2005, pages 341–348, 2005.
[7] J. Kautz and M. D. Mccool. Interactive rendering with arbitrary brdfs using separable approximations. In Proceedings of EGWR 1999, pages 247–260, 1999.
32
Bibliography 33
[8] M. L. Koudelka, S. Magda, P. N. Belhumeur, and D. J. Kriegman. Acquisition, compres-sion, and synthesis of bidirectional texture functions. In Proceedings of Texture 2003, pages 59–64, 2003.
[9] E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg. Non-linear approxima-tion of reflectance funcapproxima-tions. In Proceedings of ACM SIGGRAPH 1997, pages 117–126, 1997.
[10] D. Lathauwer, B. D. Moor, and J. Vandewalle. On the best rank-1 and rank-(r1,r2,. . .,rn) approximation of higher-order tensors. SIAM J Matrix Anal Appl, 21:1324–1342, 2000.
[11] J. Lawrence, A. Ben-artzi, C. Decoro, W. Matusik, H. Pfister, R. Ramamoorthi, and S. Rusinkiewicz. Inverse shade trees for non-parametric material representation and edit-ing. ACM Transactions on Graphics, 25:735–745, 2006.
[12] S. Lefebvre and H. Hoppe. Appearance-space texture synthesis. In Proceedings of ACM SIGGRAPH 2006, pages 541–548, 2006.
[13] T. Leung and J. Malik. Representing and recognizing the visual appearance of materials using three-dimensional textons. Proceedings of Texture 2003, 43(1):29–44, 2001.
[14] M. D. McCool, J. Ang, and A. Ahmad. Homomorphic factorization of brdfs for high-performance rendering. In Proceedings of ACM SIGGRAPH 2001, pages 171–178, 2001.
[15] F. J. Narcowich and J. D. Ward. Nonstationary wavelets on the m-sphere for scattered data. Applied and Computational Harmonic Analysis, 3(4):324–336, 1996.
[16] R. Ramamoorthi and P. Hanrahan. Frequency space environment map rendering. In Pro-ceedings of ACM SIGGRAPH 2002, pages 517–526, 2002.
[17] S. M. Rusinkiewicz. A new change of variables for efficient brdf representation. In Euro-graphics Workshop on Rendering, pages 11–22, 1998.
Bibliography 34
[18] M. Sattler, R. Sarlette, and R. Klein. Efficient and realistic visualization of cloth. In Proceedings of Eurographics Symposium on Rendering, pages 167–178, 2003.
[19] Y. ting Tsai and Z. chung Shih. All-frequency precomputed radiance transfer using spher-ical radial basis functions and clustered tensor approximation. ACM Transactions on Graphics, 25:967–976, 2006.
[20] H. Wang, Q. Wu, L. Shi, Y. Yu, and N. Ahuja. Out-of-core tensor approximation of multi-dimensional matrices of visual data. In Proceedings of ACM SIGGRAPH 2005, pages 527–535, 2005.
[21] T. Zickler, S. Enrique, R. Ramamoorthi, and P. Belhumeur. Reflectance sharing: Image-based rendering from a sparse set of images. In Proceedings of Eurographics Symposium on Rendering, pages 253–264, 2005.