1446 C-M.Song et aL Signal Processing:Image Communication 28 (2013)1435-1447 and AQ-2BT,and obviously cheaper than FS with eight-bit [6]T.Koga,K.Linuma,A.Hirano,Y.Lijima,T.Ishiguro,Motion- depth pixels. compensated interframe coding for video conferencing.in:Proceed- ings of the IEEE NTC'S1.voL 4.New Orleans.LA,1981.pp.G5.3.1- C525 [7]S.Zhu.K.K.Ma.A new diamond search algorithm for fast block- 7.Conclusion matching motion estimation,IEEE Trans.Image Process.9(2)(2000) 287-290. This study addresses a novel bit transform for low bit- [8]C.H.Cheung.LM.Po.Novel cross-diamond-hexagonal search algo- resolution motion estimation by exploiting the quantiza- rithms for fast block motion estimation,IEEE Trans.Multimedia 7(1) (2005)16-22. tion theory and fuzzy membership function.We formulate [9]C.Zhu.X.Lin,L-P.Chau,Hexagon-based search pattern for fast block the bit-depth downsampling of eight bit-depth pixels into motion estimation,IEEE Trans.Circuits Syst.Video Technol.12 (5) optimum quantization in terms of mean squared error. (2002)349-355. [10]Y.Ismail,J.B.McNeely.M.Shaaban,H.Mahmoud,M.A.Bayoumi,Fast Subsequently,we present an approximate solution using motion estimation system using dynamic models for H.264/AVC histogram equalization and uniform quantization,which is video coding.IEEE Trans.Circuits Syst Video Technol.22 (1)(2012) refined by a membership function with the variance of 2842. inter-frame noises as a variable.The membership function [11]A.Saha.J.Mukherjee,S.Sural.A neighborhood elimination approach for block matching in motion estimation,Signal Process.:Image is able to reduce the interval partitioning errors due to Commun.26(8-9)(2011)438-454. camera capability and coding distortions,so as to improve [12]C.-C.Lou,S.-W.Lee,C.-CJ.Kuo.Adaptive motion search range bit transform accuracy and motion estimation efficiency. prediction for video encoding.IEEE Trans.Circuits Syst.Video TechnoL.20(12)(2010)1903-1908. Extensive experimental results verify the effectiveness of [13]W.Lin,K.Panusopone,D.M.Baylon,M.-T.Sun,Z.Chen,H.Li. our bit transform and its application in low bit-resolution A fast sub-pixel motion estimation algorithm for H.264/AVC motion estimation. video coding.IEEE Trans.Circuits Syst.Video TechnoL 21(2)(2011) 237-243. Note that we employ full search strategy in Algorithm 3 [14]C.K.Cheung.LM.Po,Normalized partial distortion search algorithm to eliminate the influences by different search strategies, for block motion estimation,IEEE Trans.Circuits Syst.Video TechnoL thus making fair comparisons among several bit transform 10(3)(2000)417-422. [15]Y.-Q.Zhang.S.Zafar,Motion-compensated wavelet transform coding algorithms.In fact,the proposed bit transform method can for color video compression IEEE Trans Circuts svsr video Technol be both combined with fast motion estimation and applied 2(3)(1992)285-296. to complexity scalable motion estimation as an initial [16]Y.Liu,N.K.Ngan,Fast multiresolution motion estimation algorithms for wavelet-based scalable video coding.Signal Process.:Image search. Commun.22(5)(2007)448-465. [17]R.Zhang.ML Comer.Rate distortion performance of pyramid and subband motion compensation based on quantization theory.IEEE Trans.Circuits Syst Video TechnoL 20(12)(2010)1876-1881. Acknowledgments 18]Y.Wang.Y.Wang.H.Kuroda.A globally adaptive pixel-decimation algorithm for block-motion estimation,IEEE Trans.Circuits Syst vide0 echno106200011006-1011 This work is supported by the National Natural Science [19]J.Kim.T.Choi.A fast full-search motion estimation algorithm using Foundation of China (NSFC)under Grant nos.41271422. representative pixels and adaptive matching scan,IEEE Trans. 61073098.and 61373059.the Scientific Research Founda- Circuits Syst.Video Technol.10(7)(2000)1040-1048. tion for Ph.D.of Liaoning Province of China under Grant [20]X.Bao.D.Zhou,P.Liu,S.Goto.An advanced hierarchical motion estimation scheme with lossless frame recompression and early- no.20121076,and the Open Foundation of National Key level termination for beyond high-definition video coding.IEEE Laboratory for Novel Software Technology of Nanjing Trans.Multimedia 14 (2)(2012)237-249. 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(2007)109-112.and AQ-2BT, and obviously cheaper than FS with eight-bit depth pixels. 7. Conclusion This study addresses a novel bit transform for low bit￾resolution motion estimation by exploiting the quantiza￾tion theory and fuzzy membership function. We formulate the bit-depth downsampling of eight bit-depth pixels into optimum quantization in terms of mean squared error. Subsequently, we present an approximate solution using histogram equalization and uniform quantization, which is refined by a membership function with the variance of inter-frame noises as a variable. The membership function is able to reduce the interval partitioning errors due to camera capability and coding distortions, so as to improve bit transform accuracy and motion estimation efficiency. Extensive experimental results verify the effectiveness of our bit transform and its application in low bit-resolution motion estimation. Note that we employ full search strategy in Algorithm 3 to eliminate the influences by different search strategies, thus making fair comparisons among several bit transform algorithms. In fact, the proposed bit transform method can be both combined with fast motion estimation and applied to complexity scalable motion estimation as an initial search. Acknowledgments This work is supported by the National Natural Science Foundation of China (NSFC) under Grant nos. 41271422, 61073098, and 61373059, the Scientific Research Founda￾tion for Ph.D. of Liaoning Province of China under Grant no. 20121076, and the Open Foundation of National Key Laboratory for Novel Software Technology of Nanjing University under Grant nos. KFKT2011B09 and KFKT2010B11, and the Jiangsu Key Laboratory’s Open Foundation of Image Processing and Image Communica￾tion of Nanjing University of Posts & Telecommunications under Grant no. 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