近年來顯示裝置之技術有了突破性的成長，軟性顯示裝置，液晶顯視器等需求不斷成長，電子紙、電子書由於技術上的問題，能顯示的色階較少，一些低價或小型的顯示裝置基於成本的考量也會使用顯示色階較少的顯示裝置，而色階受到限制的顯示裝置需要將原始影像量化以符合顯示器之使用，最常見的方式就是延伸半色調技術到多色階應用，但研究半色調在多色階狀況下的應用，需要先瞭解半色調的特性，因此於論文中以半色調技術為主軸，參考相關文獻後在原始的多色階半色調架構下，提出一個改進多色半色調影像品質之方法。
當我們延伸半色調技術應用到多色階時，除了直接二位元搜尋法(Direct Binary Search, DBS)外，其餘的半色調技術在多色階的情況下，都具有多色階半色調才有的缺點，就是在色階中會出現一段單色的色階，我們稱為轉換間隙，半色調技術是利用人眼低通的特性，由點的疏密或形狀來產生色階連續色調的錯覺，這樣單色的區段無法形成色階之變化，因此會形成假邊現象(false contour)，雖然多色階半色調技術假邊現象的問題較為輕微，但仍對影像品質影響甚劇。對此，Lin和Allebach提出一個多色階有序抖動法，以解決轉換間隙的問題，方式是在產生轉換間隙的部份強制加入其他色調的點以避免單色之色階形成，於論文中我們提出以多色階直接二位元搜尋法所產生的色階來統計每個色階應有的色調比例，以這樣的比例為依據，在Lin和Allebach提出架構下，更進一步提升多色階有序抖動法的影像品質。
此外半色調用於量化時能夠有效的解決假邊現象，因此也常被應用在解決一些壓縮所造成的假邊現象上，區塊截斷編碼(Block Truncation Coding, BTC)是一種簡單且有效的壓縮技術，但BTC技術在壓縮率提高時影像品質會因量化而急速下降，最近被提出的半色調式區塊截斷編碼技術，利用半色調之特性解決了這項問題，但技術上無法兼顧速度及品質，在論文中我們提出一個新的方式，結合區塊交錯螺旋錯誤擴散法(Block-Interlaced Pinwheel Error Diffusion, BIPED)及BTC的技術來達到兼顧品質及速度的目的。

Recently, there is a rapid growth in the display devices, such as flexible display devices, LCD monitors. The E-paper and e-book cannot render sufficient grayscales for their technology limitations. Yet, some low-cost and small display devices still employ those display devices with less grayscales to reduce the overall cost. The most common way is to extend the half-toning techniques to the applications of multi-levels. For this, we need to fully investigate the characteristics of digital halftoning. Subsequently, we proposed an improved multitoning scheme based on the principal of traditional digital halftoning.
When halftoning is extended to multitoning, most of the multitoning schems, excepting for Direct Binary Search (DBS), exhibit monochrome grayscale which is generally called transition gap in some specific areas. Since a halftone image is to cooperate with the low-pass nature of human visual system to resemble a continuous tone image, those transition gap cannot fully characterize the grayscale fluctuations, and thus form the so-called false contours. For this, Lin and Allebach proposed a multi-level ordered dithering to solve the transform gap problem. In the paper, we propose a multitoning by exploiting the statistics generated by applying DBS for each grayscale. Subsequently, the statistic proportion is used to cooperate with Lin and Allebach’s method to improve the multi-level ordered dithering image quality.
In addition, since dithering can effectively solve the false contour issue when quantization is applied, it is widely used for compression applications. Block Truncation Coding (BTC) is a simple and efficient compression technology. However, the false contour is getting severe when the compression ratio is increased. Recently, some halftoning-based BTC schemes have been proposed. Yet, those methods cannot yield satisfactory image quality and processing speed simultaneously. For this, the block-Interlaced pinwheel error-diffused block truncation coding is proposed to solve this problem.

[1] Barten, Peter G. J., “Contrast sensitivity of the human eye and its effects on image quality,” SPIE-The International Society for Optical Engineering.
[2] F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, “Visibility of aperiodic patterns compared with that of sinusoidal gratings,” J. Physiol., vol. 204, pp. 283–298, 1969.
[3] J. L. Mannos and D. J. Sakrison, “The effects of a visual fidelity criterion on the encoding of images,” IEEE Trans. Inform. Theory, vol. IT-20, July 1974.
[4] R. Näsänen, “Visibility of halftone dot textures,” IEEE Trans. Syst., Man, Cybern., vol. 14, no. 6, pp. 920–924, 1984.
[5] S. Daly, “Subroutine for the Generation of a Two Dimensional Human Visual Contrast Sensitivity Function,” Eastman Kodak, Tech. Rep. 233203y, 1987.
[6] S.H. Kim and J.P. Allebach, “Impact of HVS models on model-based halftoning,” IEEE Trans. Image Processing, vol. 11, pp. 258-269, Mar. 2002.
[7] R.A. Ulichney, “Dithering with blue noise,” Proc. IEEE, vol. 76, pp. 56-79, Jan. 1988.
[8] M. Analoui and J.P. Allebach, “Model based halftoning using direct binary search,” in Proc. SPIE, Human Vision, Visual Proc., and Digital Display III, San Jose, CA, Feb. 1992, vol. 1666, pp. 96-108.
[9] T. Pappas and D. Neuhoff, ‘‘Least-squares model-based halftoning,’’ in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE 1666, pp. 165–176, 1992.
[10] J. J. Mulligan and A. Ahumada, ‘‘Principled halftoning based on models of human vision,’’ in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE 1666, pp. 109–121, 1992.
[11] D. J. Lieberman, J. P. Allebach, “Efficient model based halftoning using direct binary search”, IEEE International Conference on Image Processing, vol. 1, pp. 775-778, Oct. 1997.
[12] D. J Lieberman, J. P Allebach, “A dual interpretation for direct binary search and its implications for tone reproduction and texture quality”, IEEE Trans. Image Processing, vol. 9, pp. 1950-1963, Nov. 2000.
[13] R. Ulichney, Digital Halftoning. Cambridge, MA: MIT Press, 1987.
[14] B. E. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” IEEE Int. Conf. Commum., Vol. 1, 1973.
[15] R. Ulichney, “The void-and-cluster method for dither array generation”, in Proc. SPIE, Human Vision, Visual Processing, Digital Displays IV, vol. 1913, pp. 332–343, 1993.
[16] J. P. Allebach and Q. Lin, ‘‘FM screen design using DBS algorithm’’, IEEE International Conference on Image Processing, Vol. 1, pp. 549–552, 1996.
[17] G. Y. Lin and J. Allebach, “Multilevel screen design using direct binary search”, J. Opt. Soc. Amer. A, vol. 19, no. 10, pp. 1969–1982, Oct. 2002.
[18] R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial greyscale,” Proc. Soc. Inf. Disp., vol. 17, no. 2, pp. 75–77, 1976.
[19] J. F. Jarvis, C. N. Judice, and W. H. Ninke, “A survey of techniques for the display of continuous-ton pictures on bilevel displays,” Comp. Graph. Image. Proc., Vol. 5, pp. 13-40, 1976.
[20] V. Ostromoukhov, “A simple and efficient error-diffusion algorithm,” in Proc. ACM SIGGRAPH 2001, Los Angeles, CA, Aug. 2001, pp. 567–572.
[21] J. M. Guo and J. H. Chen, “High Efficiency Digital Halftoning with Two-Element Error Kernel,” IEEE International Conference on Image Processing, GA, U.S.A. pp. 1501-1504, Oct. 2006.
[22] R. Eschbach, Z. Fan, K. T. Knox, and G. Marcu, “Threshold modulation and stability in error diffusion,” IEEE Signal Process. Mag., vol. 20, no. 4, pp. 39-50, Jul. 2003.
[23] S. Weissbach and F. Wyrowski, “Error diffusion procedure: theory and application in optical signal processing,” Appl. Opt. 31, 2518-2534, 1992.
[24] K.T. Knox and R. Eschbach, “Threshold modulation in error diffusion,” J. Electron. Imaging, vol. 2, pp. 185-192, 1993.
[25] T.D. Kite, B.L. Evans, A.C. Bovik, and T.L. Sculley, “Digital halftoning as 2-D delta-sigma modulation,” in Proc. IEEE Conf. Image Processing, 1997,vol. 1, pp. 799-802.
[26] I. H. Witten and R. M. Neal, “Using Peano curves for bilevel display of continuous-tone images,” IEEE Comput. Graph. Applicat., vol. 2, pp. 47–52, May 1982.
[27] D. E. Knuth, “Digital halftones by dot diffusion,” ACM Trans. Graph., vol. 6, no. 4, pp. 245–273, Oct. 1987.
[28] M. Mese and P. P. Vaidyanathan, “Optimized halftoning using dot diffusion and methods for inverse halftoning,” IEEE Trans. Image Processing, vol. 9, pp. 691–709, Apr. 2000.
[29] P. Li and J. P. Allebach, “Block interlaced pinwheel error diffusion”, SPIE and IS&T, Vol. 14(2), pp. 1-13, 2005.
[30] E. J. Delp and O. R. Mitchell, “Image compression using block truncation coding,” IEEE Trans. Commun., vol. COMM-27, pp. 1335-1342, Sept., 1979.
[31] J. M. Guo, “Improved block truncation coding using modified error diffusion,” IET Electronics Letters, vol. 44, no. 7, pp. 462-464, March 2008.
[32] J. M. Guo and M. F. Wu, “Improved block truncation coding based on the void-and-cluster dithering approach,” IEEE Trans. Image Processing, vol. 18, no. 1, pp. 211-213, January 2009.
[33] P. Li and J. P. Allebach, “Tone dependent error diffusion,” IEEE Trans. Image Processing, vol. 13, no. 2, pp. 201–215, 2004.
[34] M. Kamel, C. T. Sun, and L. Guan, “Image compression by variable block truncation coding with optimal threshold,” IEEE Trans. Signal Processing, vol. 39, no. 1, pp. 208-212, January 1991.
[35] T. M. Amarunnishad, V. K. Govindan, and T. M. Abraham, “Block truncation coding using a set of predefined bit planes,” International Conference on Computational Intelligence and Multimedia Applications, vol. 3, pp. 73-78, Dec. 2007.
[36] C. S. Huang and Y. Lin, “Hybrid block truncation coding, ” IEEE Signal Processing Letters, vol. 4, no. 12, pp. 328-330, Dec., 1997.
[37] Y. C. Hou, S. F. Tu, and Y. H. Chang, “Block truncation coding by using genetic algorithm,” International Communications, Control, and Signal Processing, pp. 1273-1278, March 2008.
[38] J. W. Han, Y. J. Yoon, T. S. Wang, M. C. Hwang, and S. J. Ko, “Improved block truncation coding for color image compression in LCD overdrive,” IEEE International Symposium on Consumer Electronics, pp. 1-4, April 2008.
[39] S. F. Tu and C. S. Hsu, “A BTC-based watermarking scheme for digital images” International Journal on Information & Security, vol. 15 no. 2, pp.216-228, 2004.
[40] D. L. Lau and G. R. Arce, “Modern Digital Halftoning,” Marcel Dekker, Inc. New York. Basel, 2000.
[41] D. L. Lau and G. R. Arce, “Robust halftoning with green-noise,” In Proceedings of the IS&T’s Image Processing, Image Quality, Image Capture Systems Conference, pages 315-320, Savannah, GE, April 25-28 1999. IS&T.
[42] D. L. Lau, G. R. Arce, and N. C. Gallagher, “Green-noise digital halftoning,” Proceedings of the IEEE, 86(12): 2424-2444, December 1998.
[43] D. L. Lau, G. R. Arce, and N. C. Gallagher, “Digital halftoning via green-noise masks,” Journal of the Optical Society of America, 16(7): 1575-1586, July 1999.
[44] D. L. Lau, G. R. Arce, and N. C. Gallagher., “Digital color halftoning via generalized error-diffusion and vector green-noise masks,” IEEE Transactions on Image Processing, 9(5), May 2000.
[45] D. L. Lau, G. R. Arce, and R. Ulichney, “Blue and green noise halftoning models,” IEEE Signal Processing Magazine, vol. 20, issue: 4, pp. 28-38, July 2003.
[46] J. H. Lee and T. Horiuchi and S. Tominaga, “Multilevel confined error diffusion algorithm for flat panel”, IEICE Trans. Inf. & Syst. Vol. E91-D, no. 1, pp. 62-69, Jan. 2008.
[47] N. Suetake and M. Togashi, “High quality multilevel error diffusion method employing variable threshold”, Electrical Engineering in Japan, vol. 149, pp. 25-33, no. 2, 2004.
[48] J. B. Rodriguez and G. R. Arce and D. L. Lau, “Blue noise multitone dithering”, IEEE Trans. Image Processing, Vol. 17, no. 8, pp. 1368-1382, Aug. 2008.
[49] D. L. Lau, R. Ulichney, “Blue-noise halftoning for hexagonal grids”, IEEE Trans. Image Processing, vol. 15, pp. 1270-1284, May. 2006.
[50] C. Lee and J. P. Allebach, “The Hybrid Screen—Improving the Breed,” IEEE Trans. Image Processing, Vol. 19, no. 2, pp. 435-450, Feb. 2010.
[51] J. M. Guo and C. Y. Lin, “Parallel and element-reduced error-diffused block truncation coding,” IEEE Trans. on Communications, vol. 58, no. 5, May 2010.