Basic Search / Detailed Display

Author: 黃詠淮
Yong-Huai Huang
Thesis Title: 植基於學習與紋理的演算法及其在影像壓縮 和半色調影像回復的應用
Novel Learning- and Texture-Based Approach with Applications to Image Coding and Inverse Halftoning
Advisor: 鍾國亮
Kuo-Liang Chung
Committee: 貝蘇章
Soo-Chang Pei
陳宏銘
Homer H. Chen
范國清
Kuo-Chin Fan
張寶基
Pao-Chi Chang
廖弘源
Mark Liao
陳世旺
Sei-Wang Chen
廖慶榮
Ching-Jong Liao
洪西進
Shi-Jinn Horng
Degree: 博士
Doctor
Department: 電資學院 - 資訊工程系
Department of Computer Science and Information Engineering
Thesis Publication Year: 2007
Graduation Academic Year: 95
Language: 英文
Pages: 115
Keywords (in Chinese): 算術編碼文件鄰屬決策樹離散餘弦轉換誤差擴散影像半色調影像回復最小平方法預測法lookup tree table無失真壓縮多重模版多重學習視窗預測編碼紋理向量量化小波轉換
Keywords (in other languages): Arithmetic coding, context, decision tree, DCT, error–diffused images, inverse halftoning, least-square–based prediction scheme, lookup tree–table, lossless compression, multiple–template, multiple–window, predictive coding, texture, vector quantization, wavelet transform.
Reference times: Clicks: 358Downloads: 3
Share:
School Collection Retrieve National Library Collection Retrieve Error Report

在影像處理中,紋理是一個相當重要的特徵且已經被廣泛的使用在多種應用上。以紋理分類為基礎,本篇論文提出了嶄新且有效的影像/視訊像處理演算法。這些演算法包括:針對誤差擴散影像(error diffused images)所設計的適應性算數編碼演算法(adaptive arithmetic coding),針對灰階影像所設計的預測編碼演算法(predictive coding),以及將半色調影像建為灰階影像的半色調影像回復演算法(inverse halftoning algorithm)。

針對文件鄰屬式(context)算數編碼技術,我們首先提出一個區塊式紋理學習機制來擷取影像中最具代表性的紋理特徵,並根據這些紋理特徵建立多重模版(multiple-template)。接著,利用已經建立的多重模版,本篇論文提出一個植基於紋理與多重模版的算數編碼技術來對誤差擴散影像進行無失真壓縮。在我們所提出的方法中,輸入的誤差擴散影像會先被分割成多個不重疊的區塊,依照各個區塊的紋理特徵,我們從多重模版中選擇一個最佳模版以便執行文件鄰屬式算數編碼。實驗結果顯示,與JBIG壓縮標準、Reavy和Boncelet以及Lee和Par所提出的演算法相較之下,我們所提出的演算法能夠達到更高的壓縮比。

針對預測編碼,為了提升最小平方法(least square)預測的準確性,我們提出一個植基於紋理的學習機制以便依據不同的影像內容建立多重學習視窗(multiple-window)。接著,利用已經建立的多重學習視窗,本篇論文提出一個植基於紋理與多重學習視窗的最小平方預測法來對灰階影像進行無失真壓縮。在我們所提出的方法中,針對輸入的灰階影像每個像素的紋理特徵,我們從多重學習視窗中選擇一個最佳學習視窗以便與用最小平方法來預測該像素的灰階值。實驗結果顯示,與先前所提出的預測方法相較之下,我們所提出的演算法能夠達到更準確的預測。

針對半色調影像回復,我們根據變異數增益決策樹(variance gain-based decision tree),提出了植基於紋理以及變異數增益決策樹的學習機制來建立一個lookup tree table以便進行半色調影像的回復。在重建灰階影像的過程中,對於影像的不平滑區域,我們使用了一個植基於邊的精煉過程(edge-based refinement)來的提昇重建灰階影像的品質。實驗結果顯示,與先前所提出的三種半色調影像回復演算相比之下,我們所提出的演算法能夠達到更高的影像品質。


Texture is an important feature in images and has been widely used in many applications. Based on the classified textures, this thesis presents a novel learning–and texture–based approach to design more efficient image and video processing algorithms such as the adaptive arithmetic coding for error–diffused images, the predictive coding for gray images, and the inverse halftoning algorithm to reconstruct gray images from halftones.

For context–based arithmetic coding, the block– and texture–based training process is first applied to train the multiple–template according to the most representative texture features. Based on the trained multiple–template, we next present a texture– and multiple–template–based (TM–based) arithmetic coding algorithm for lossless compression of error–diffused images. In our proposed TM–based algorithm, the input image is divided into many blocks and for each block, the best template is adaptively selected from the multiple–template based on the texture feature of that block. Experimental results demonstrate that the compression ratio of our proposed TM–based algorithm is
superior to that of joint bilevel image group (JBIG) standard and the previous algorithms proposed by Reavy and Boncelet and by Lee and Park.

For predictive coding, to improve the accuracy of the least square–based prediction scheme, we present a new texture–based training process to construct the multiple–window for various image contents. Based on the trained multiple–window, the texture–and multiple–window–based (TMW–based) prediction scheme is presented for lossless compression of images. In our proposed TMW–based scheme, for each pixel of the input image, the best training window is adaptively selected from the multiple–window according
to the texture feature. Experimental results demonstrate that the accuracy of our proposed TMW–based prediction scheme is better than that of the previous LS–based prediction scheme.

For inverse halftoning, based on our proposed variance gain–based DT (VDT), a texture and VDT (TVDT)–based training process is presented to construct a lookup tree–table which will be used in the reconstructing process. In the reconstructing process, to enhance the quality of the non–smooth regions in the reconstructed image, we propose
an edge–based refinement scheme to enhance the quality of the reconstructed gray image. Experimental results demonstrate that our proposed TVDT–based inverse halftoning algorithm has the highest image quality when compared to the currently published three inverse halftoning algorithms, such as the DT–based algorithm, the lookup table–based algorithm, and the edge–and lookup table–based algorithm.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Motivations and purposes. . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Organization of the thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Problem Definitions and the Texture Considerations. . . . . . . . . . . . . 6 2.1 Context–based arithmetic coding. . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Basic definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Texture consideration. . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Predictive coding. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.1 Basic definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 Texture consideration. . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Inverse halftoning . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3.1 Basic definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3.2 Texture consideration. . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Texture– and Multiple–Template–Based Algorithm for Lossless Compression of Error–Diffused Images. . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1 Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 The past four works: JBIG, BACIC, PACIC, and FACIC algorithms. . . . . . 30 3.2.1 The JBIG and the BACIC algorithm . . . . . . . . . . . . . . . . . . . 30 3.2.2 The PACIC algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.3 The FACIC algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 Our proposed TMCIC algorithm . . . . . . . . . . . . . . . . . . . . . . 36 3.3.1 Training stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.2 Encoding and decoding stages . . . . . . . . . . . . . . . . . . . . . 42 3.4 Experimental result. . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.4.1 Results of our proposed training stage . . . . . . . . . . . . . . . . 45 3.4.2 Compression performance comparison . . . . . . . . . . . . . . . . . . 47 4 Texture– and Multiple–Window–Based Prediction Scheme for Predictive Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.1 Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.2 The Prediction Schemes for Lossless Image Compression. . . . . . . . . . 54 4.2.1 Context–based prediction scheme . . . . . . . . . . . . . . . . . . . 54 4.2.2 LS–based prediction scheme . . . . . . . . . . . . . . . . . . . . . 56 4.3 Our Proposed TMW–Based Prediction Scheme. . . . . . . . . . . . . . . . 59 4.3.1 Training stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.3.2 Prediction stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5 Efficient Inverse Halftoning Using Variance Gain–, Texture– and Decision Tree–Based Learning Approach . . . . . . . . . . . . . . . . . . . . . . . 70 5.1 Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.2 Relevant PastWorks . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2.1 The LIH algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2.2 The ELIH algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2.3 The DTIH algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.3 The Proposed TVDTIH Algorithm . . . . . . . . . . . . . . . . . . . . . 79 5.3.1 The proposed variance gain–based DT (VDT) . . . . . . . . . . . . . 81 5.3.2 The construction of approximate VDT. . . . . . . . . . . . . . . . . . 84 5.3.3 The classification and codebook generation for VDT–leaf . . . . . . . 86 5.3.4 The reconstructing process . . . . . . . . . . . . . . . . . . . . . . 89 5.3.5 Edge–based refinement scheme. . . . . . . . . . . . . . . . . . . . . 90 5.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

[1] C. S. Burrus and T. W. Parks, DFT/FFT and Convolution Algorithms: Theory and Implementation. New York: Wiley, 1985.
[2] N. Ahamed, T. Natarjan, K. R. Rao, “Discrete cosine transform,” IEEE Trans. Comput., vol. 23, pp. 90–93, Jan, 1974.
[3] T. Edward, Discrete Wavelet Transforms: Theory and Implementation. Stanford, CA: Stanford Univ., 1991.
[4] D. S. Taubman and M. W. Marcellin, JPEG 2000 Image Compression Fundamentals, Standards, and practice. Boston,MA, USA: Kluwer Aeademic Dablishers, 2002.
[5] A. C. Bovik, M. Clark, andW. S. Geisler, “Multichannel texture analysis using localized spatial filters,“ IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, pp. 55–73, Jan. 1990.
[6] I. S. Hsieh and K. C. Fan, “Multiple classifiers for color flag and trademark image retrieval,” IEEE Trans. Image Processing, vol. 10, pp. 938–950, June 2001.
[7] S. Liapis and G. Tziritas, “Color and texture image retrieval using chromaticity histograms and wavelet frames,” IEEE Trans. Multimedia, vol. 6, pp. 676-686, Oct. 2004.
[8] B. Ko and H. Byun, “FRIP: A region–based image retrieval tool using automatic image segmentation and stepwise boolean and matching,” IEEE Trans. Multimedia, vol. 7, pp. 105–113, Feb. 2005.
[9] P. R. Hill, C. N. Canagarajah, and D. R. Bull, “Image segmentation using a texture gradient based watershed transform,” Image Processing, vol. 12, pp. 1618–1633, Dec. 2003.
[10] J. Xie, Y. Jiang, and H. T. Tsui, “Segmentation of kidney from ultrasound images based on texture and shape priors,” IEEE Trans. Medical Imaging, vol. 24, pp. 45–57, Jan. 2005.
[11] C. Sagiv, N. A. Sochen, and Y. Y. Zeevi, “Integrated active contours for texture segmentation,” IEEE Trans. Image Processing, vol. 15, pp. 1633–1646, JUNE 2006.
[12] Y. H. Huang and K. L. Chung, ”Texture– and multiple–template–based algorithm for lossless compression of error-diffused images,” IEEE Trans. Image processing, vol. 16, pp. 1258–1268, 2007.
[13] K. L. Chung Y. H. Huang, ”Texture– and multiple–window–based algorithm for predictive coding, preparing.
[14] K. L. Chung, K. C. Wu, and Y. H. Huang, ”Efficient inverse halftoning using variance gain–, texture– and decision tree–based learning approach,” IEEE Trans. Image processing, revised.
[15] I. H. Witten, R. M. Neal, and J. G. Cleary, Arithmetic coding for data compression, Commun. ACM, vol. 30, pp. 520–540, June 1987.
[16] K. L. Chung, Data Compression: Theory and Applications (in Chinese). 2nd ed. Chiuan–Hua, Taipei, 2004.
[17] X.Wu and K. Barthel, “Piesewise 2D autoregression for predictive image coding,” in Proc. Int. Conf. Image Processing, vol. 3, Oct. 1998, pp. 882–889,1992.
[18] X. Li and M. T. Orchard, “Edge–directed prediction for lossless compression of natural images,” IEEE Trans. Image Processing, vol. 10, pp. 813–817, June 2001.
[19] M. Weinberger, G. Seroussi, and G. Sapiro, “The LOCO-I lossless image compression algorithm: Principles and standardization into JPEG–LS,” IEEE Trans. Image Processing, vol. 9, pp. 1309–1324, Aug. 2000.
[20] X.Wu and N. Memon, “Context-based adaptive lossless image coding,” IEEE Trans. Commun., vol. 45, pp. 437–444, Apr. 1997.
[21] Coded Representation of Picture and Audio Information–Progressive Bi–Level Image Compression, ISO/IEC Int. Std. 11544, 1993.
[22] JBIG2 Final Draft International Standard, ISO/IEC JTC1/SC29/WG1 N1545, 1999.
[23] Standardization of group 3 facsimile apparatus for document transmission, ITU-T Recommendation T.4, 1980.
[24] Facsimile Coding Schemes and Coding Control Function for Group 4 Facsimile Apparatus ITU-T Recommendation T.6, 1984.
[25] A. Cohen, I. Daubechies, and J. C. Feauveau, “Biorthogonal bases of compactly supported wavelets,” Communications on Pure and Applied Math, vol. 45, pp. 485–560, June 1992.
[26] M. N. Gurcan, O. N. Gerek, and A. E. Cetin, “Binary morphological subband decomposition for image coding,” in Proc. IEEE Signal Processing Int. Symp. Time- Frequency and Time-Scale Analysis, 1996, pp. 357–360.
[27] C. S. Lee and H. Park “Near-lossless/lossless compression of error-diffused images using a two-pass approach,” IEEE Trans. Image Processing, vol. 12, pp. 170–175, Feb. 2003.
[28] C. S. Lee and H. Park “Progressive coding of error–diffused bilevel images” J. Electronic Imaging, vol. 12, pp. 173-178, Jan, 2003.
[29] B. Martins and S. Forchhammer, “Tree coding of bilevel image,” IEEE Trans. Image Processing, vol. 7, pp. 517–528, Apr. 1998.
[30] D. L. Neuhoff and T. N. Pappas, “Perceptual coding of images for halftone display,”IEEE Trans. Image Processing, vol. 3, pp. 341–354, July. 1994.
[31] K. Nguyen-Phi and H.Weinrichter, “A new binary source coder and its application in bi–level image compression,” in Proc. GLOBALCOMM ’96, vol. 3, 1996, pp. 1483–1487.
[32] M. D. Reavy and C. G. Boncelet “An algorithm for compression of bilevel images,”IEEE Trans. Image Processing, vol. 10, pp. 669–676, May, 2001.
[33] J. Rissanen and G. G. Langdon, Jr., ”Universal modeling and coding,” IEEE Trans. Information Theory, vol. 27, pp. 12–23, Jan. 1981.
[34] J. Rissanen, “A universal data compression system,” IEEE Trans. Inform. Theory, vol. 29, pp. 656–664, Sept. 1983.
[35] J. Rissanen, “Complexity of strings in the class of Markov sources,” IEEE Trans. Inform. Theory, vol. 32, pp. 526–532, July 1986.
[36] G. R. Robertson, M. F. Aburdene, and R. J. Kozick, “Differential block coing of bilevel images,” IEEE Trans. Image Processing, vol. 5, pp. 1368–1370, Sept. 1996.
[37] M. D. Swanson and A. H. Tewfik, “A binary wavelet decomposition of binary images,”IEEE Trans. Image Processing, vol. 5, pp. 1637–1650, Dec. 1996.
[38] R. Ulichney,Digital Halftoning. Cambridge, MA: MIT Press, 1987.
[39] C. Zhu and L. M. Po, “Minimax partial distortion competitive learning for optimal codebook design,” IEEE Trans. Image Processing, vol. 5, pp. 1400–1409, Oct. 1998.
[40] http://www.systems.caltech.edu/mese/halftone/
[41] http://interfacelift.com/wallpaper/
[42] N. Memon and X. Wu, “Recent developments in context-based predictive techniques for lossless image compression,” Comput. J., vol. 40, pp. 127–136, 1997.
[43] W. Pennebaker and J. Mitchell, JPEG: Still Image Data Compression Standard. London, U.K.: Chapman & Hall, 1992.
[44] X. Wu and K. Barthel, “Piesewise 2D autoregression for predictive image coding,”in Proc. Int. Conf. Image Processing, vol. 3, Oct. 1998, pp. 901–905.
[45] M. Kwon, H. J. Kim, C.W. Lee, and S. U. Lee, “A lossless image coder with context–based minimizing MSE prediction and entropy coding,” in Proc. Int. Symp. Circuits Systems, vol. 4, 1999, pp. 479–482.
[46] G. Motta, J. A. Storer, and B. Carpentieri, “Adaptive linear prediction lossless image coding,” in Proc. Data Compression Conf., Mar. 1999, pp. 491–500.
[47] H. Ye, G. Deng, and J. Devlin, “Least squares approach for lossless image coding,”in Proc. 5th Int. Symp. Signal Processing Applications, vol. 1, 1999, pp. 63–66.
[48] B. Aiazzi, S. Baronti, L. Alparone, “Lossless image compression based on an enhanced fuzzy regression prediction,” in Proc. Int. Conf. Image Processing, vol. 1, Oct. 1999, pp. 435–439.
[49] L. J. Kau and Y. P. Lin, “Adaptive lossless image coding using least squares optimization with edge–look–ahead,” IEEE Trans. Circuits and Ststem–II, vol. 52, Nov. 2005, pp. 751–755.
[50] J. P. Allebach, “Reconstruction of continuous–tone from halftone by projections onto convex sets,” in Proc. Int. Conf. Advances Commun. Control Systems, Baton Rouge,
LA, Oct. 19–21, 1988, pp. 469–478.
[51] M. Analoui and J. P. Allebach, “New results on reconstruction of continuous–tone from halftone,” in Proc. Int. Conf. Acoustics, Speech, Signal Processing, San Fraancisco, CA, Mar. 23–26, 1992, pp. 313–316.
[52] J. Canny, “A computational approach to edge detection,” in IEEE Trans. Pattern Anal. and Machine Intelligence, vol. 8, pp. 679–698, Nov. 1986.
[53] P. C. Chang, C. S. Yu, and T. H. Lee, “Hybrid LMS–MMSE inverse halftoning technique,” IEEE Trans. Image Processing, vol. 10, pp. 95–103, Jan. 2001.
[54] K. L. Chung and S. T. Wu, “Inverse halftoning algorithm using edge–based lookup table approach,” IEEE Trans. Image Processing, vol. 14, pp. 1583–1589, Oct. 2005.
[55] N. Damera-Venkata, T. D. Kite, and B. L. Evans, “Fast blind inverse halftoning,” in Proc. IEEE Int. Conf. Image Processing, vol. 2, Oct. 1998, pp. 64–68.
[56] J. C. Dunn, “A fuzzy relative of the ISODATA process and its use in detecting compact well–seperated clusters,” J. Cybernet. vol. 3, pp. 32–57, 1974.
[57] W. H. Equitz, “A new vector quantization clustering algorithm,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 37, pp. 1568–1575, Oct. 1989.
[58] Z. Fan, “Retrieval of gray image from digital halftones,” in Proc. Int. Symp. Circuits Systems, May 1992, pp. 2477–2480.
[59] Z. Fan and R. Eschbach, “Limit cycle behavior of error diffusion,” in Proc. IEEE Int. Conf. Image Processing, vol. 2, Nov. 1994, pp. 1041–1045.
[60] S. Hein and A. Zakhor, “Halftone to continuous–tone conversion of error–diffusion coded images,” IEEE Trans. Image Processing, vol. 4, pp. 208–216, Feb. 1995.
[61] Y. L. Huang and R. F. Chang, “Texture features for DCT–coded image retrival and classification,” in Proc. ICASSP, vol.6, Apr. 1999, pp. 3013–3016.
[62] T. D. Kite, N. Damera-Venkata, B. L. Evans and A. C. Bovik, “A fast, high–quality inverse halftoning algorithm for error diffused halftones,”IEEE Trans. Image Processing, vol. 9, pp. 1583–1592, Sept. 2000.
[63] H. Y. Kim and R. de Queiroz, “Inverse halftoning by decision tree learning,” in Proc. IEEE Int. Conf. Image Processing, vol. 2, Sept. 2003, pp. 913–916.
[64] D. S. Kim and S. U. Lee, “Image vector quantizer based on a classification in the DCT domain,” IEEE Trans. Commun., vol. 39, pp. 549–556, Apr. 1991.
[65] Z. C. Lai and J. Y. Yen, “Inverse error–diffusion using classified vector quantization,”IEEE Trans. Image Processing, vol. 7, pp. 1753–1758, Dec. 1998.
[66] Z. C. Lai and J. Y. Yen, “Inverse halftoning of color images using classified vector quantization,” Journal of Visual Commun. and Image Representation, vol. 9, pp. 223–233. Sep. 1998.
[67] S. H. Liu and J. S. Lin, “Vector quantization in DCT domain using fuzzy possibilistic c-means based on penalized and compensated constraints,” Pattern Recognition, vol. 35, pp. 2201–2211, Oct. 2002.
[68] J. Luo, R. L. de Queiroz and Z. Fan “Universal descreening technique via wavelet analysis,” in Proc. IS&T/SPIE Symp. on Electronic Imaging: Science and Technology, Color Imaging, San Jose, CA, SPIE, vol. 3018, Feb. 1997, pp. 18–29.
[69] J. Luo, R. L. de Queiroz and Z. Fan “A robust technique for image descreening based on the wavelet transform,” IEEE Trans. Signal Processing, vol. 46, pp. 1179–1185, Apr. 1998.
[70] Y. Linde, A. Buzo, R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun., vol. 28, pp. 1645–1651, Jan. 1980.
[71] M. Mese and P. P. Vaidyanathan, “Look up table (LUT) method for inverse halftoning,”IEEE Trans. Image Processing, vol. 10, pp. 1566–1578, Oct. 2001.
[72] M. Mese and P. P. Vaidyanathan, “Tree–structured method for LUT inverse halftoning and for image halftoning,” IEEE Trans. Image Processing, vol. 11, pp. 644–655, June 2002.
[73] S. Mitra and T. Acharya, Data Mining. John Wiley & Sons Press, NY, 2003.
[74] T. M. Mitchell, Machine Learning, WCB/McGraw-Hill, NY, 1997.
[75] K. R. Rao and P. Yip, Discrete Cosine Transform—Algorithms, Advantages, Applications. Academic Press. NY. 1990.
[76] J. R. Quinlan, “Induction of decision trees,” Machine Learning, vol. 1, pp. 81–106, 1986.
[77] M. Y. Shen and C.-C. J. Kuo, “A robust nonlinear filtering approach to inverse halftoning,” J. Visual Commun. and Image Representation, vol. 12, pp. 84–95, Mar. 2001.
[78] R. L. Stevenson, “Inverse halftoning via MAP estimation,” IEEE Trans. Image Processing, vol. 6, pp. 574–583, Apr. 1997.
[79] P. W. Wong, “Inverse halftoning and kernel estimation for error diffusion,” IEEE Trans. Image Processing, vol. 4, pp. 486–498, Apr. 1995.
[80] L. A. Zedeh, “Fuzzy Sets,” Inform. Control, vol. 8, pp. 338–353, 1965.
[81] Z. Xiong, M. T. Orchard, and K. Ramchandran, “Inverse halftoning using wavelets,”IEEE Trans. Image Processing, vol. 8, pp. 1479–1482, Oct. 1999.

QR CODE