本論文中，我們提出新的紋理壓縮演算法以及對應的紋理快取設計。針對
紋理中不同的顏色變化特性分別使用兩種編碼方法，顏色平滑部分使用類神
經網路模型幫助紋素值的近似，將其類神經網路模型編碼成固定長度的位元
串。而顏色變化劇烈的邊界部分則使用傳統編碼方法ETC2。所提出的演算法
可以在不影響影像編碼品質下提供更好的壓縮率。平均比起單純使用ETC2 可
以提升約0.112dB PSNR 同時約可以提升15% 壓縮率。此外，配合所提出的
演算法在系統應用中我們設計FIFO 暫存類神經網路的編碼位元串，可以減少
對紋理快取讀取的時間。由於較好的壓縮率及區塊編碼特性在繪圖時，比起
單純使用ETC2 可以有效減少向下層記憶體(DRAM) 讀取壓縮紋理資料時間，
約為67.6%。配合FIFO 的設計整體系統運算時間(包含解壓縮) 約為97.1%。

For modern Graphics Processing Units (GPU), the texture mapping is introduced to
reduce the transmission bandwidth and save the memory usage. Compared to ren-
dering a whole 3D image directly, using texture mapping technique is not only more
efficient but also lowering the computing complexity. Therefore, texture compres-
sion plays an important role in modern GPU rendering. In this paper, we propose
to combine Radial Basis Function Neural Network (RBFNN) with the traditional
block based texture compression method Ericsson Texture Compression 2 (ETC2).
We first cut a texture into several blocks with different sizes. Then, for each block,
we choose to encode either by the ETC2 or by the neural network according to the
texture property of the block. For the blocks with low frequency texture, we use
the function approximation of RBFNN for better compression ratio. On the other
hand, we use ETC2 in the high frequency area to keep the texture quality. Experi-
ment results shows an improvement over ETC2 by 0.112 dB in average PSNR, with
a reduction of about 15% in average bit rate. And because of the better compression
ratio and block property, we can improve the texture cache hit rate about 1.43%, and
further improve about 2.9% total system rendering cycles in average compare with
ETC2.
Keywords: Texture compression, Texture cache, Neural network

[1] E. Delp and O. Mitchell, “Image compression using block truncation coding,”
IEEE Transactions on Communications, vol. 27, pp. 1335–1342, Sep 1979.
[2] F. Rosenblatt, “The perceptron: A probabilistic model for information storage
and organization in the brain.,” Psychological review, vol. 65, no. 6, p. 386,
1958.
[3] D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning internal representations
by error propagation,” tech. rep., DTIC Document, 1985.
[4] D. S. Broomhead and D. Lowe, “Radial basis functions, multi-variable functional
interpolation and adaptive networks,” tech. rep., Royal Signals and Radar
Establishment Malvern (United Kingdom), 1988.
[5] Y. Song, J. Wang, L.-Y. Wei, and W. Wang, “Vector regression functions for
texture compression,” ACM Transactions on Graphics (TOG), vol. 35, no. 1,
p. 5, 2015.
[6] H. G. Levkin, “ImageProcessing/VideoCodecs/Programming. test still images.
[online]. aviable: http://www.hlevkin.com/default.htmltestimages,” 2004.
[7] R. Gonzalez, R. Woods, and S. Eddins, “Image databases, http://www. imageprocessingplace.
com,” retrieved on,(October 2006), 2010.
[8] A. C. Beers, M. Agrawala, and N. Chaddha, “Rendering from compressed textures,”
in Proceedings of the 23rd annual conference on Computer graphics and
interactive techniques, pp. 373–378, ACM, 1996.
[9] W. B. Pennebaker and J. L. Mitchell, JPEG: Still image data compression standard.
Springer Science & Business Media, 1992.
[10] J. Ziv and A. Lempel, “A universal algorithm for sequential data compression,”
IEEE Transactions on information theory, vol. 23, no. 3, pp. 337–343, 1977.
[11] K. I. Iourcha, K. S. Nayak, and Z. Hong, “System and method for fixed-rate
block-based image compression with inferred pixel values,” Sept. 21 1999. US
Patent 5,956,431.
[12] J. Ström and T. Akenine-Möller, “Packman: texture compression for mobile
phones,” in ACM SIGGRAPH 2004 Sketches, p. 66, ACM, 2004.
[13] J. Ström and T. Akenine-Möller, “i packman: High-quality, low-complexity
texture compression for mobile phones,” in Proceedings of the ACM SIGGRAPH/
EUROGRAPHICS conference on Graphics hardware, pp. 63–70,
ACM, 2005.
[14] J. Ström and M. Pettersson, “Etc 2: texture compression using invalid combinations,”
2007.
[15] C. Van Der Malsburg, “Frank rosenblatt: Principles of neurodynamics: perceptrons
and the theory of brain mechanisms,” in Brain Theory, pp. 245–248,
Springer, 1986.
[16] H. Bourlard and Y. Kamp, “Auto-association by multilayer perceptrons and singular
value decomposition,” Biological cybernetics, vol. 59, no. 4, pp. 291–294,
1988.
[17] D. E. Rumelhart, G. E. Hinton, R. J. Williams, et al., “Learning representations
by back-propagating errors,” Cognitive modeling, vol. 5, no. 3, p. 1, 1988.
[18] G. Campbell, T. A. DeFanti, J. Frederiksen, S. A. Joyce, and L. A. Leske, “Two
bit/pixel full color encoding,” in ACM SIGGRAPH Computer Graphics, vol. 20,
pp. 215–223, ACM, 1986.
[19] S. Fenney, “Texture compression using low-frequency signal modulation,” in
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics
hardware, pp. 84–91, Eurographics Association, 2003.
[20] J. Nystad, A. Lassen, A. Pomianowski, S. Ellis, and T. Olson, “Adaptive scalable
texture compression,” in Proceedings of the Fourth ACM SIGGRAPH/Eurographics
conference on High-Performance Graphics, pp. 105–114, Eurographics
Association, 2012.
[21] M. J. Schulte and J. E. Stine, “Approximating elementary functions with symmetric
bipartite tables,” IEEE Transactions on Computers, vol. 48, no. 8,
pp. 842–847, 1999.
[22] P.-T. P. Tang, “Table-driven implementation of the logarithm function in
ieee floating-point arithmetic,” ACM Transactions on Mathematical Software
(TOMS), vol. 16, no. 4, pp. 378–400, 1990.
[23] S. A. Tawfik and H. A. Fahmy, “Algorithmic truncation of minimax polynomial
coefficients,” in Circuits and Systems, 2006. ISCAS 2006. Proceedings. 2006
IEEE International Symposium on, pp. 4–pp, IEEE, 2006.
[24] R. Franzen, “Kodak lossless true color image suite: Photocd pcd0992. available:
http://www.imageprocessingplace.com/root files v3/image databases.htm,”
2002.