IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 19, NO. 12, DECEMBER 2009 1755 Early Determination of Zero-Quantized 8 × 8 DCT Coefficients Xiangyang Ji, Sam Kwong, Debin Zhao, Hanli Wang, Member, IEEE, C.-C. Jay Kuo, Fellow, IEEE, and Qionghai Dai, Senior Member, IEEE Abstract—This paper proposes a novel approach to early related by block-wise spatial prediction or temporal prediction determination of zero-quantized 8 × 8 discrete cosine transform with motion estimation (ME) and motion compensation (MC) (DCT) coefficients for fast video encoding. First, with the dynamic and then, each prediction error block goes through DCT to range analysis of DCT coefficients at different frequency posi- tions, several sufficient conditions are derived to early determine exploit spatial redundancy. Finally, transform coefficients are whether a prediction error block (8 × 8) is an all-zero or a quantized and fed into entropy encoder to yield desired video partial-zero block, i.e., the DCT coefficients within the block are bit streams. At the decoder, the inverse sequential operations all or partially zero-quantized. Being different from traditional are performed to decode video for playback. methods that utilize the sum of absolute difference (SAD) of In video encoders such as H.263 [1] and MPEG-4 Part 2 the entire prediction error block, the sufficient conditions are × derived based on the SAD of each row of the prediction error [2], ME, 8 8 DCT, quantization (Q), inverse quantization block. For partial-zero blocks, fast DCT/IDCT algorithms are (IQ), and inverse DCT (IDCT) are usually computationally further developed by pruning conventional 8-point butterfly- intensive [3], [4]. Many fast ME algorithms [5]–[13] have been based DCT/IDCT algorithms. Experimental results exhibit that proposed to reduce the encoding complexity. Consequently, the proposed early determination algorithm greatly reduces saving the computational complexity for DCT, Q, IQ, and computational complexity in terms of DCT/IDCT, quantization, and inverse quantization, as compared with existing algorithms. IDCT becomes important. In [14], according to the execution time distribution for the Foreman sequence, DCT/IDCT and Index Terms—Butterfly-based DCT, computational complexity, Q/IQ accounts for approximately 40% of the total encoding discrete cosine transform, sum of absolute difference, zero- quantized coefficients. time when the XVID encoder is used for evaluation with the PMVFAST ME algorithm [13] employed. It is also claimed in [14] that the execution time distribution is similar for other test I. Introduction sequences. On the other hand, as stated in [15], average time OST VIDEO compression standards, such as MPEG-x cost in terms of DCT/IDCT and Q/IQ accounts for 34.8% of M and H.26x, are designed based on a hybrid video the total encoding time when a software H.263 encoder (based coding framework. In such a framework, video is first decor- on H.263 TMN-5) is used for testing. Typically, asignificant number of prediction error blocks Manuscript received March 17, 2008; revised February 2, 2009. First version will have all-zero coefficients after Q in low bit-rate video cod- published July 7, 2009; current version published December 1, 2009. This work was supported by Hong Kong RGB Competitive Earmarked Research ing. Even in higher bit-rate video coding, some well-predicted Grant Projects 9041236 (CityU 114707), 9041353 (CityU 115408), and a blocks may have all-zero DCT coefficients after Q. If these Grant from the Major State Basic Research Development Program 973 of blocks can be determined earlier, computations of DCT, Q, IQ, China, No. 2009CB320905. This paper was recommended by Associate Editor J. Boyce. and IDCT can be completely skipped. Yu et al. [16] proposed a X. Ji is now with the Broadband Networks and Digital Media Labora- method of early predicting all-zero blocks by comparing SAD tory, Automation Department, Tsinghua University, Beijing 100084, China. of the predicted error block with a predefined threshold to skip He was with both the Graduate School and the Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100080, China (e-mail: DCT, Q, IQ, and IDCT, where no additional SAD computa- [email protected]). tions are required since the SAD values can be obtained after S. Kwong is with the Department of Computer Science, City University of ME. However, the corresponding coding efficiency is highly Hong Kong, Kowloon, Hong Kong, China (e-mail: [email protected]). D. Zhao is with the Department of Computer Science, Harbin Institute of dependent on the threshold selection mechanism and video Technology, Harbin 150001, China (e-mail: [email protected]). quality can be degraded due to an improper threshold. Zhou H. Wang is with the Fern Universitat¨ in Hagen, Lehrgebiet Information- et al. [17] performed a theoretical analysis on the dynamic stechnik, Hagen 58084, Germany ([email protected]). C.-C. Jay Kuo is with the Department of Electrical Engineering and range of DCT coefficients and proposed a sufficient condition Integrated Media Systems Center, University of Southern California, Los to check whether a given prediction error block has all-zero Angeles, CA 90089 USA (e-mail: [email protected]). coefficients based on the SAD of the prediction error. With Q. Dai is with the Broadband Networks and Digital Media Laboratory, Automation Department, Tsinghua University, Beijing 100084, China (e-mail: this approach, DCT, Q, IQ, and IDCT can be completely [email protected]). skipped for all-zero blocks without video quality degradation. Color versions of one or more of the figures in this paper are available Hsueh et al. [18] derived a similar sufficient condition and online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCSVT.2009.2026839 applied a looser condition in the early determination of all- 1051-8215/$26.00 c 2009 IEEE 1756 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 19, NO. 12, DECEMBER 2009 zero blocks. Sousa [19] developed a tighter sufficient condition II. Proposed Early Determination Strategy than Zhou’s model [17] by comparing sufficient conditions A. Sousa’s Model for All-Zero Block Determination for different frequency components quantized to zeros. As f N × N a result, Sousa’s model could detect all-zero blocks more When applying 2-D DCT to a given block of sam- F u v efficiently and thus reduces the computational complexity ples, each frequency component ( , ) can be calculated by N− N− furthermore. Jun et al. [20] proposed a new criterion for 1 1 (2x +1)uπ F(u, v)=C(u)C(v) f (x, y) cos the early determination of all-zero blocks, where the sign of 2N each predicted residual is considered. This method demands x=0 y=0 a higher computational overhead since it needs additional (2y +1)vπ × cos (1) SAD calculation for the prediction error block (i.e., no SAD 2N reuse in the ME stage) as well as a sign evaluation for each with ⎧ residual sample. All aforementioned models were designed ⎨ 1 , n N for =0 for 8 × 8 DCT used in H.263 and MPEG-4 Part 2. More C(n)= ⎩ 2 , n> . recently, Wang et al. [21] applied Sousa’s model [19] to the N for 0 DCT-like 4 × 4 integer transform in H.264/AVC. Kim et al. × [22] proposed a novel all-zero blocks detecting algorithm Foran8 8 inter-block with motion-compensated predic- for the DCT-like 4 × 4 integer transform in H.264/AVC. tion, its prediction error signals can be computed by Recently, Wang et al. [23] derived more effective sufficient f (x, y)=s(x, y) − p(x, y), for x, y =0, 1, ..., 7. (2) conditions to early determination of all-zero 4 × 4 blocks in H.264/AVC. Here, s and p represent the original block and the motion- All methods reviewed above are only used to early deter- compensated prediction block, respectively. mine all-zero blocks. However, although some of the pre- In encoding, DCT coefficients of each prediction error diction error blocks cannot be determined as all-zero ones block are quantized to represent them in a reduced range of under a sufficient condition, partial coefficients in those blocks values. For a uniform scalar quantization in H.263 [1] and can be quantized to zeros and determined by new sufficient MPEG-4 Part 2 [2], the quantized coefficient FQ(u, v) can be obtained by conditions. For example, Wang et al. [4] proposed a new analytical model to eliminate redundant DCT, Q, IQ, and |F(u, v)| − (Qp/2) FQ(u, v) = sign(F(u, v)) (3) IDCT. By a finer analysis on the dynamic range of DCT 2Qp coefficients, the model in [4] is capable of detecting zero- quantized coefficients at both block and individual frequency where Qp is the quantization scalar and the symbol denotes levels. rounding to the nearest integer. It can be observed for an 8 × 8 block that when In this paper, we first perform a theoretical analysis on 7 7 the dynamic range of 8 × 8 DCT coefficients at different |F(u, v)| ≤ C(u)C(v) x y |f (x, y)| =0 =0 frequency positions, and then derive a more precise sufficient × (2x +1)uπ (2y +1)vπ condition than Sousa’s model [19] for early determination of max cos 16 cos 16 (4) all-zero blocks. As compared with existing analytical models, = C(u)C(v) × SAD our proposed sufficient condition is not based on SAD of × (2x +1)uπ (2y +1)vπ max cos 16 cos 16 the entire prediction error block but that of each row of the 5 < Qp. prediction error block. Second, several sufficient conditions 2 for early determination of partial-zero blocks are derived.