International INTERNATIONAL JOURNAL OF ELECTRONICS (IJECET), ISSN              Journal of Electronics and Communication En...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 097...
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A computationally efficient method to find transformed residue

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A computationally efficient method to find transformed residue

  1. 1. International INTERNATIONAL JOURNAL OF ELECTRONICS (IJECET), ISSN Journal of Electronics and Communication Engineering & Technology AND0976 –COMMUNICATION ENGINEERING & October- December (2012), © IAEME 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, TECHNOLOGY (IJECET)ISSN 0976 – 6464(Print)ISSN 0976 – 6472(Online)Volume 3, Issue 3, October- December (2012), pp. 84-102 IJECET© IAEME: www.iaeme.com/ijecet.aspJournal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEMEwww.jifactor.com A COMPUTATIONALLY EFFICIENT METHOD TO FIND TRANSFORMED RESIDUE COEFFICIENTS IN INTRA 4x4 MODE DECISION IN H.264ENCODER P. Essaki Muthu, Research Scholar, Dr. MGR Educational and Research Institute, Chennai, INDIA Dr. R M O Gemson, Professor, SCT Institute of Technology, Bangalore, INDIA pessakimuthu@yahoo.com, mogratnam@rediffmail.comABSTRACTTo achieve the best coding efficiency and video quality, H.264 encoder has to evaluateexhaustively all the mode combinations of intra predictions for deciding coding mode. Thecomputational complexity and time taken for predicting for all intra modes, subtracting fromoriginal blockand forward transforming the residues are heavy. A novel Intra 4x4 Predictionmethod to reduce the computational complexity, thus enhancing the time savings is proposedhere. The experimental results demonstrate that proposed method reduces at least 40% ofcomputational complexity without compromising the coding efficiency and performance.This can be used in any hardware / processor platforms.Keywords : H.264/AVC, Mode decision, Intra 4x4 Prediction, Computational ComplexitySECTION 1: INTRODUCTION The newest international video coding standard H.264/ advanced video coding (AVC) hasbeen approved by ITU-T as recommended H.264 and by ISO/IEC as the MPEG-4 part 10AVC international Standard [1]. The emerging H.264/AVC achieves significantly betterperformance in both peak signal-to-noise ratio (PSNR) and visual quality at the same bit ratecompared with prior video coding standards. H.264/AVC can save up to 39%, 49%, and 64%of the bit rate, when compared with MPEG-4, H.263, and MPEG-2 [2]. H.264 uses oneimportant technique calledLagrangian rate-distortion optimization (RDO) performed for intraand inter mode decision. The rate-distortion optimization technique is very time consumingand the computational complexity of H.264/AVC is drastically high using the RDOtechnique. The computational complexity refers the basic operations (e.g., Add, Shift). The method ofcalculating the computational complexity of the intra prediction module was done by numberof cycles taken by basic operations by Zouch[3]. Mustafa et al [4], [5] used number ofadditions and shifts performed in intra prediction, as metric for computational complexity. 84
  2. 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME H.264 has Intra 4x4 prediction, Intra 16x16 prediction, Intra 8x8 prediction and IntraChroma prediction. This paper focuses on Intra 4x4 prediction only. Intra 4x4 prediction hasnine different modes and these modes have identical equations and calculating these commonequations for each mode is unnecessary. The Pixel equality based computation reduction(PECR) technique used in [4] focussed only on pixel domain predictions. It savedcomputational complexity, but it did not include the computational complexity forcomparison operation which is generally equivalent to addition operation. Still there is ascope of optimization in the data reuse techniques presented in [5] to reduce thecomputational complexity. The techniques used in [6], [7], [8], [9] and [10] reduce the amount of computationsperformed by Intra prediction by trying selected intra prediction modes rather than trying allpossible intra prediction modes, thus lacking in video quality and consuming more bits. The objective of this paper is (i) to calculate the computational complexity of pixeldomain prediction and its forward transformation, (ii) to reduce the computational complexityof Intra 4x4 Prediction of a given 4x4 sub-macroblock, and (iii)to give the transform domainresidue directly. This paper is organized in five sections. Section 2 explains the pixel domain Intra 4x4Prediction for all modes and its computational complexity. Section 3explains thecomputational complexity of finding residue and its standard forward transform. Section 4explains the novel method to find key pixel domain predicted values, transformedcoefficients and its computational complexity. Finally,in Section 5, the comparison and theinferences of the proposed method are presented.SECTION 2:COMPLEXITY OF PIXEL DOMAIN INTRA 4x4 PREDICTION An intra (I) macroblock is coded without referring to any data outside the current slice. I-macroblocks may occur in any slice type. Every macroblock in an I-slice is an I-macroblock.I-macroblocks are coded using intra prediction, i.e. prediction from previously-coded data inthe same slice. For a typical block of luma or chroma samples, there is a relatively highcorrelation between samples in the block and samples that are immediately adjacent to theblock. Intra prediction therefore uses samples from adjacent, previously coded blocks topredict the values in the current block [11]. There are four different Intra prediction types based on block size and components. Theyare Intra 16x16, Intra 8x8 and Intra 4x4 for Luma components and Intra Chroma for Chromacomponents. Intra 16x16 Prediction has 4 different ways of prediction, namely, Vertical,Horizontal, DC and Plane Prediction. There are 9 different Intra 4x4 Prediction modesnamely, Vertical, Horizontal, DC, Diagonal-Down-Left, Diagonal-Down-Right, Vertical-Right, Horizontal-Down, Vertical-Left and Horizontal-Up, possible for a given 4x4 sub-macroblock in Intra 4x4 Prediction. The same Intra 4x4 Prediction techniques are followedby Intra 8x8 Prediction. Intra Chroma modes are DC, Horizontal, Vertical and PlanePrediction. The mode for a Macroblock is decided based on the Rate-Distortion Cost (RD-Cost) calculated for Intra 16x16, Intra 4x4 and Intra 8x8 Predictions. In the process of RD-Cost calculation of Intra 4x4 Prediction for a given Macroblock, each4x4 sub-macroblock is subjected to all nine prediction modes. The 4x4 sub-macroblock ispredicted by all nine different prediction techniques. The residue 4x4 sub-macroblock isfound out by subtracting the predicted 4x4 sub-macroblock from original 4x4 sub-macroblock. There are 9 set of residue 4x4 sub-macroblocks, which are forward transformedand quantized. The quantized coefficients are subjected to variable length coding, by then therate, i.e., bitlength is calculated for each prediction mode. The quantized coefficients aredequantized and inverse transformed to get reconstructed residue 4x4 sub-macroblocks. 85
  3. 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEThese reconstructed residue 4x4 sub-macroblocks are added with already predicted 4x4 sub-macroblocks to get reconstructed 4x4 sub-macroblocks. The distortions are calculatedbetween original 4x4 sub-macroblock and reconstructed 4x4 sub-macroblocks, by means ofSum of Absolute Error (SAE) or Sum of Squares of Error (SSE). For all 9 different modes,the RD-Cost are calculated by the following equation.ܴ‫ + ݊݋݅ݐݎ݋ݐݏ݅ܦ = ݐݏ݋ܥ − ܦ‬λ. ܴܽ‫݁ݐ‬ (1) The minimum RD-Cost will decide the mode for the given 4x4 sub-macroblock. The sameprocess is continued for other fifteen 4x4 submacroblocks in a Macroblock. This way offinalizing Intra 4x4 Prediction modes are followed by Joint Motion (JM) Group [12] andX264 [13]. The minimum RD-Cost among the four Intra 16x16 Prediction modes will decidethe best Intra 16x16 Prediction mode for the same Macroblock. The minimum RD-Costamong the finalized Intra 4x4 Prediction modes and Intra 16x16 Prediction mode will decidethe Macroblock type and its mode(s) to coding. The RD-Cost calculation to find best Intramode is done for all Macroblocks in all frames of a video sequence. The metric for computational complexity used here is number of additions/subtractionsand number of shifts. The intra 4x4 prediction mainly depends upon the eight pixels in theprevious row (A, B, C, D, E, F, G and H), four pixels in the previous column (I, J, K, and L)and a top-left pixel (M).Vertical Prediction (VP) mode copies down the top four pixels (A, B, C and D) as predictedblock. ܸܲሺ‫1 ,ݓ݋ݎ‬ሻ = ‫4 ≤ ݓ݋ݎ ≤ 1 ,ܣ‬ ܸܲሺ‫2 ,ݓ݋ݎ‬ሻ = ‫4 ≤ ݓ݋ݎ ≤ 1 ,ܤ‬ ܸܲሺ‫3 ,ݓ݋ݎ‬ሻ = ‫4 ≤ ݓ݋ݎ ≤ 1 ,ܥ‬ ܸܲሺ‫4 ,ݓ݋ݎ‬ሻ = ‫4 ≤ ݓ݋ݎ ≤ 1 ,ܦ‬The computational complexity of Vertical Prediction is zero, as there is only loadingoperation.Horizontal Prediction (HP) mode copies right the left four pixels (I, J, K and L) as predictedblock. ‫ ܲܪ‬ሺ1, ܿ‫ ݈݋‬ሻ = ‫4 ≤ ݈݋ܿ ≤ 1 ,ܣ‬ ‫ ܲܪ‬ሺ2, ܿ‫ ݈݋‬ሻ = ‫4 ≤ ݈݋ܿ ≤ 1 ,ܤ‬ ‫ ܲܪ‬ሺ3, ܿ‫ ݈݋‬ሻ = ‫4 ≤ ݈݋ܿ ≤ 1 ,ܥ‬ ‫ ܲܪ‬ሺ4, ܿ‫ ݈݋‬ሻ = ‫4 ≤ ݈݋ܿ ≤ 1 ,ܦ‬The computational complexity of Horizontal Prediction is zero, as there is only loadingoperation.DC Prediction mode finds the average of top four pixels (A, B, C and D) and left four pixels(I, J, K, and L), and copies the average in the entire predicted block. ‫ = ݒܣ‬ሺ‫4 + ܮ + ܭ + ܬ + ܫ + ܦ + ܥ + ܤ + ܣ‬ሻ ≫ 3If the any of top or left four pixels are not available, the ‫ ݒܣ‬is calculated by averaging theavailable four pixels. ‫ = ݒܣ‬ሺ‫2 + ܦ + ܥ + ܤ + ܣ‬ሻ ≫ 2 ‫ = ݒܣ‬ሺ‫2 + ܮ + ܭ + ܬ + ܫ‬ሻ ≫ 2 86
  4. 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEIf the current block is first in the frame, then ‫ ݒܣ‬is the predicted as half of Pixel bitwidth. ‫ ܥܦ‬ሺ‫ ݈݋ܿ ,ݓ݋ݎ‬ሻ = ‫4 ≤ ݈݋ܿ ≤ 1 ,4 ≤ ݓ݋ݎ ≤ 1 ,ݒܣ‬Considering the best case, the computational complexity is 8 additions and 1 shift operations.In Diagonal-Down-Left(DDL) Prediction, there are 7 unique pixel values calculated. Theother 9 pixels are copied from the seven unique pixel values. The 7 uniquepixels arecalculated as follows. ‫ܮܦܦ‬ሺ1,1ሻ = ሺ‫2 + ܥ + 1 ≪ ܤ + ܣ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ1,2ሻ = ‫ܮܦܦ‬ሺ2,1ሻ = ሺ‫2 + ܦ + 1 ≪ ܥ + ܤ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ1,3ሻ = ‫ܮܦܦ‬ሺ2,2ሻ = ‫ܮܦܦ‬ሺ3,1ሻ = ሺ‫2 + ܧ + 1 ≪ ܦ + ܥ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ1,4ሻ = ‫ܮܦܦ‬ሺ2,3ሻ = ‫ܮܦܦ‬ሺ3,2ሻ = ‫ܮܦܦ‬ሺ4,1ሻ = ሺ‫2 + ܨ + 1 ≪ ܧ + ܦ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ2,4ሻ = ‫ܮܦܦ‬ሺ3,3ሻ = ‫ܮܦܦ‬ሺ4,2ሻ = ሺ‫2 + ܩ + 1 ≪ ܨ + ܧ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ3,4ሻ = ‫ܮܦܦ‬ሺ4,3ሻ = ሺ‫2 + ܪ + 1 ≪ ܩ + ܨ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ4,4ሻ = ሺ‫2 + ܪ + 1 ≪ ܪ + ܩ‬ሻ ≫ 2 The computational complexity of DDL Prediction is 21 additions and 14 shifts.In Diagonal-Down-Right (DDR) Prediction, there are 7 pixel values calculated. Out of 7pixel values, five are unique and two can be derived from Diagonal-Down-Left Prediction. ‫ ܴܦܦ‬ሺ1,1ሻ = ‫ ܴܦܦ‬ሺ2,2ሻ = ‫ ܴܦܦ‬ሺ3,3ሻ = ‫ ܴܦܦ‬ሺ4,4ሻ = ሺ‫2 + ܫ + 1 ≪ ܯ + ܣ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ1,2ሻ = ‫ ܴܦܦ‬ሺ2,3ሻ = ‫ ܴܦܦ‬ሺ3,4ሻ = ሺ‫2 + ܤ + 1 ≪ ܣ + ܯ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ1,3ሻ = ‫ ܴܦܦ‬ሺ2,4ሻ = ሺ‫2 + ܥ + 1 ≪ ܤ + ܣ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ1,4ሻ = ሺ‫2 + ܦ + 1 ≪ ܥ + ܤ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ2,1ሻ = ‫ ܴܦܦ‬ሺ3,2ሻ = ‫ ܴܦܦ‬ሺ4,3ሻ = ሺ‫2 + ܬ + 1 ≪ ܫ + ܯ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ3,1ሻ = ‫ ܴܦܦ‬ሺ4,2ሻ = ሺ‫2 + ܭ + 1 ≪ ܬ + ܫ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ4,1ሻ = ሺ‫2 + ܮ + 1 ≪ ܭ + ܬ‬ሻ ≫ 2 The computational complexity of DDR Prediction is 21 additions and 14 shifts.Vertical-Right(VR) Prediction has 10 distinct pixel values. Among that, only four are uniquepixel values and the other six values can be derived from DDL and DDR Predictions. ܸܴ ሺ1,1ሻ = ܸܴሺ3,2ሻ = ሺ‫1 + ܣ + ܯ‬ሻ ≫ 1 ܸܴ ሺ1,2ሻ = ܸܴሺ3,3ሻ = ሺ‫1 + ܤ + ܣ‬ሻ ≫ 1 ܸܴ ሺ1,3ሻ = ܸܴሺ3,4ሻ = ሺ‫1 + ܥ + ܤ‬ሻ ≫ 1 ܸܴ ሺ1,4ሻ = ሺ‫1 + ܦ + ܥ‬ሻ ≫ 1 ܸܴ ሺ2,1ሻ = ܸܴሺ4,2ሻ = ሺ‫2 + ܫ + 1 ≪ ܯ + ܣ‬ሻ ≫ 2 ܸܴ ሺ2,2ሻ = ܸܴሺ4,3ሻ = ሺ‫2 + ܤ + 1 ≪ ܣ + ܯ‬ሻ ≫ 2 ܸܴ ሺ2,3ሻ = ܸܴሺ4,4ሻ = ሺ‫2 + ܥ + 1 ≪ ܤ + ܣ‬ሻ ≫ 2 ܸܴ ሺ2,4ሻ = ሺ‫2 + ܦ + 1 ≪ ܥ + ܤ‬ሻ ≫ 2 ܸܴ ሺ3,1ሻ = ሺ‫2 + ܬ + 1 ≪ ܫ + ܯ‬ሻ ≫ 2 ܸܴ ሺ4,1ሻ = ሺ‫2 + ܭ + 1 ≪ ܬ + ܫ‬ሻ ≫ 2The computational complexity of VR Prediction is 26 additions and 16 shifts.Horizontal-Down(HD) Prediction has 10 distinct pixel values. Out of those, 6 values can bederived from DDL and DDR Predictions. 87
  5. 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME ‫ ܦܪ‬ሺ1,1ሻ = ‫ ܦܪ‬ሺ2,3ሻ = ሺ‫1 + ܫ + ܯ‬ሻ ≫ 1 ‫ ܦܪ‬ሺ1,2ሻ = ‫ ܦܪ‬ሺ2,4ሻ = ሺ‫2 + ܫ + 1 ≪ ܯ + ܣ‬ሻ ≫ 2 ‫ ܦܪ‬ሺ1,3ሻ = ሺ‫2 + ܤ + 1 ≪ ܣ + ܯ‬ሻ ≫ 2 ‫ ܦܪ‬ሺ1,4ሻ = ሺ‫2 + ܥ + 1 ≪ ܤ + ܣ‬ሻ ≫ 2 ‫ ܦܪ‬ሺ2,1ሻ = ‫ ܦܪ‬ሺ3,3ሻ = ሺ‫1 + ܬ + ܫ‬ሻ ≫ 1 ‫ ܦܪ‬ሺ2,2ሻ = ‫ ܦܪ‬ሺ3,4ሻ = ሺ‫2 + ܬ + 1 ≪ ܫ + ܯ‬ሻ ≫ 2 ‫ ܦܪ‬ሺ3,1ሻ = ‫ ܦܪ‬ሺ4,3ሻ = ሺ‫1 + ܭ + ܬ‬ሻ ≫ 1 ‫ ܦܪ‬ሺ3,2ሻ = ‫ ܦܪ‬ሺ4,4ሻ = ሺ‫2 + ܭ + 1 ≪ ܬ + ܫ‬ሻ ≫ 2 ‫ ܦܪ‬ሺ4,1ሻ = ሺ‫1 + ܮ + ܭ‬ሻ ≫ 1 ‫ ܦܪ‬ሺ4,2ሻ = ሺ‫2 + ܮ + 1 ≪ ܭ + ܬ‬ሻ ≫ 2 The computational complexity of HD Prediction is 26 additions and 16 shifts.Vertical-Left (VL) Prediction has 10 distinct pixel values. Among that, only two are uniquepixel values and the other eight values can be derived from DDL and VR Predictions. ܸ‫ܮ‬ሺ1,1ሻ = ሺ‫1 + ܤ + ܣ‬ሻ ≫ 1 ܸ‫ܮ‬ሺ1,2ሻ = ܸ‫ܮ‬ሺ3,1ሻ = ሺ‫1 + ܥ + ܤ‬ሻ ≫ 1 ܸ‫ܮ‬ሺ1,3ሻ = ܸ‫ܮ‬ሺ3,2ሻ = ሺ‫1 + ܦ + ܥ‬ሻ ≫ 1 ܸ‫ܮ‬ሺ1,4ሻ = ܸ‫ܮ‬ሺ3,3ሻ = ሺ‫1 + ܧ + ܦ‬ሻ ≫ 1 ܸ‫ܮ‬ሺ2,1ሻ = ሺ‫2 + ܥ + 1 ≪ ܤ + ܣ‬ሻ ≫ 2 ܸ‫ܮ‬ሺ2,2ሻ = ܸ‫ܮ‬ሺ4,1ሻ = ሺ‫2 + ܦ + 1 ≪ ܥ + ܤ‬ሻ ≫ 2 ܸ‫ܮ‬ሺ2,3ሻ = ܸ‫ܮ‬ሺ4,2ሻ = ሺ‫2 + ܧ + 1 ≪ ܦ + ܥ‬ሻ ≫ 2 ܸ‫ܮ‬ሺ2,4ሻ = ܸ‫ܮ‬ሺ4,3ሻ = ሺ‫2 + ܨ + 1 ≪ ܧ + ܦ‬ሻ ≫ 2 ܸ‫ܮ‬ሺ3,4ሻ = ሺ‫1 + ܨ + ܧ‬ሻ ≫ 1 ܸ‫ܮ‬ሺ4,4ሻ = ሺ‫2 + ܩ + 1 ≪ ܨ + ܧ‬ሻ ≫ 2 The computational complexity of VL Prediction is 25 additions and 15 shifts.Horizontal-Up (HU) Prediction has 7 distinct pixel values. Out of those, 5pixel values can bederived from DDR and HD Predictions and one pixel value is L itself. ‫ܷܪ‬ሺ1,1ሻ = ሺ‫1 + ܬ + ܫ‬ሻ ≫ 1 ‫ܷܪ‬ሺ1,2ሻ = ሺ‫2 + ܭ + 1 ≪ ܬ + ܫ‬ሻ ≫ 2 ‫ܷܪ‬ሺ1,3ሻ = ‫ܷܪ‬ሺ2,1ሻ = ሺ‫1 + ܭ + ܬ‬ሻ ≫ 1 ‫ܷܪ‬ሺ1,4ሻ = ‫ܷܪ‬ሺ2,2ሻ = ሺ‫2 + ܮ + 1 ≪ ܭ + ܬ‬ሻ ≫ 2 ‫ܷܪ‬ሺ2,3ሻ = ‫ܷܪ‬ሺ3,1ሻ = ሺ‫1 + ܮ + ܭ‬ሻ ≫ 1 ‫ܷܪ‬ሺ2,4ሻ = ‫ܷܪ‬ሺ3,2ሻ = ሺ‫2 + ܮ + 1 ≪ ܮ + ܭ‬ሻ ≫ 2 ‫ܷܪ‬ሺ3,3ሻ = ‫ܷܪ‬ሺ3,4ሻ = ‫ܮ‬ ‫ܷܪ‬ሺ4,1ሻ = ‫ܷܪ‬ሺ4,2ሻ = ‫ܷܪ‬ሺ4,3ሻ = ‫ܷܪ‬ሺ4,4ሻ = ‫ܮ‬The computational complexity of HU Prediction is 15 additions and 9 shifts.For a 4x4 Sub-Macroblock, all possible predictions are done for all the nine modes. Thecomputational Complexity of Intra 4x4 Prediction is 142 additions and 85 shifts.SECTION 3: COMPLEXITY OF FINDING RESIDUE AND FORWARDTRANSFORMEach predicted 4x4 sub-macroblock is subtracted from the original 4x4sub-macroblockto getresidue 4x4 sub-macroblocks. The computational complexity for one 4x4 sub-macroblock is 88
  6. 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME16 subtractions and zero shift. The computational complexity of finding residue for all nineprediction modes is 9x16 subtractions, i.e., 144 addition and zero shiftoperations.The residue sub-macroblock is forward transformed using the following equation. ܴ‫ݐ݂ܥ × ݏ݁ݎ × ݂ܥ = ܵܧ‬ 1 1 1 1 ‫ݓ‬ℎ݁‫ = ݂ܥ ݁ݎ‬ቌ 2 1 −1 −2ቍ 1 −1 −1 1 1 −2 2 −1 ܽ݊݀ ‫݁ݏ݋݌ݏ݊ܽݎݐ = ݐ݂ܥ‬ሺ‫݂ܥ‬ሻThis forward transform (It is a matrix multiplication) is simplified with additions and shiftsonly as follows.for row = 1 to 4 f(row,1) = ref(row,1) + ref(row,4) f(row,2) = ref(row,2) + ref(row,3) f(row,3) = ref(row,2) - ref(row,3) f(row,4) = ref(row,1) - ref(row,4)endfor row = 1 to 4 g(row,1) = f(row,1) + f(row,2) g(row,2) = f(row,3) + f(row,4)<< 1 g(row,3) = f(row,1) - f(row,2) g(row,4) = f(row,4) - f(row,3)<< 1endfor col = 1 to 4 h(1,col) = g(1,col) + g(4,col) h(2,col) = g(2,col) + g(3,col) h(3,col) = g(2,col) - g(3,col) h(4,col) = g(1,col) - g(4,col)endfor col = 1 to 4 RES(1,col) = h(1,col) + h(2,col) RES(2,col) = h(3,col) + h(4,col) << 1 RES(3,col) = h(1,col) - h(2,col) RES(4,col) = h(4,col) - h(3,col) << 1endThe computational complexity of forward transform of one residue 4x4 sub-macroblock is 64additions and 16 shifts. For all nine modes, the computational complexity is 9x64 additionsand 9x16 shifts, i.e., 576 addition and 144 shift operations.SECTION 4: PROPOSED METHOD WITH COMPUTATIONAL COMPLEXITY There are 24 unique equations to find predicted values of all nine intra 4x4 modes. ‫ ܥܦ‬ሺ1,1ሻ = ሺ‫4 + ܪ + ܩ + ܨ + ܧ + ܦ + ܥ + ܤ + ܣ‬ሻ ≫ 3 89
  7. 7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME ‫ܮܦܦ‬ሺ1,1ሻ = ሺ‫2 + ܥ + 1 ≪ ܤ + ܣ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ1,2ሻ = ሺ‫2 + ܦ + 1 ≪ ܥ + ܤ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ1,3ሻ = ሺ‫2 + ܧ + 1 ≪ ܦ + ܥ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ1,4ሻ = ሺ‫2 + ܨ + 1 ≪ ܧ + ܦ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ2,4ሻ = ሺ‫2 + ܩ + 1 ≪ ܨ + ܧ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ3,4ሻ = ሺ‫2 + ܪ + 1 ≪ ܩ + ܨ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ4,4ሻ = ሺ‫2 + ܪ + 1 ≪ ܪ + ܩ‬ሻ ≫ 2 ‫ܴܦܦ‬ሺ1,1ሻ = ሺ‫2 + ܫ + 1 ≪ ܯ + ܣ‬ሻ ≫ 2 ‫ܴܦܦ‬ሺ1,2ሻ = ሺ‫2 + ܤ + 1 ≪ ܣ + ܯ‬ሻ ≫ 2 ‫ܴܦܦ‬ሺ2,1ሻ = ሺ‫2 + ܬ + 1 ≪ ܫ + ܯ‬ሻ ≫ 2 ‫ܴܦܦ‬ሺ3,1ሻ = ሺ‫2 + ܭ + 1 ≪ ܬ + ܫ‬ሻ ≫ 2 ‫ܴܦܦ‬ሺ4,1ሻ = ሺ‫2 + ܮ + 1 ≪ ܭ + ܬ‬ሻ ≫ 2 ‫ܷܪ‬ሺ2,4ሻ = ሺ‫2 + ܮ + 1 ≪ ܮ + ܭ‬ሻ ≫ 2 ܸܴ ሺ1,1ሻ = ሺ‫1 + ܣ + ܯ‬ሻ ≫ 1 ܸܴሺ1,2ሻ = ሺ‫1 + ܤ + ܣ‬ሻ ≫ 1 ܸܴሺ1,3ሻ = ሺ‫1 + ܥ + ܤ‬ሻ ≫ 1 ܸܴሺ1,4ሻ = ሺ‫1 + ܦ + ܥ‬ሻ ≫ 1 ܸ‫ܮ‬ሺ1,4ሻ = ሺ‫1 + ܧ + ܦ‬ሻ ≫ 1 ܸ‫ܮ‬ሺ3,4ሻ = ሺ‫1 + ܨ + ܧ‬ሻ ≫ 1 ‫ܦܪ‬ሺ1,1ሻ = ሺ‫1 + ܫ + ܯ‬ሻ ≫ 1 ‫ܦܪ‬ሺ2,1ሻ = ሺ‫1 + ܬ + ܫ‬ሻ ≫ 1 ‫ܦܪ‬ሺ3,1ሻ = ሺ‫1 + ܭ + ܬ‬ሻ ≫ 1 ‫ܦܪ‬ሺ4,1ሻ = ሺ‫1 + ܮ + ܭ‬ሻ ≫ 1 The DC Prediction has only one unique equation, the Diagonal-Down-Left Prediction has 7equations, the Diagonal-Down-Right Prediction has 5 equations, the Vertical-RightPrediction has 4 equations, the Horizontal-Down Prediction has 4 equations, the Vertical-LeftPrediction has 2 equations and the Horizontal-Up Prediction has 1 equation. The other pixelvalues are copied from the already calculated pixel values by the above-said 24equations.Thus reduces the computational complexity to 67 addition and 37 shiftoperations.But those 24 equations are split intelligently and modified as follows. ‫ 1 + ܤ + ܣ = ܤܣ‬ ‫ 1 + ܥ + ܤ = ܥܤ‬ ‫ 1 + ܦ + ܥ = ܦܥ‬ ‫ 1 + ܧ + ܦ = ܧܦ‬ ‫ 1 + ܨ + ܧ = ܨܧ‬ ‫ 1 + ܩ + ܨ = ܩܨ‬ ‫ 1 + ܪ + ܩ = ܪܩ‬ ‫ 1 + ܯ + ܣ = ܯܣ‬ ‫ 1 + ܫ + ܯ = ܫܯ‬ ‫ 1 + ܬ + ܫ = ܬܫ‬ ‫ 1 + ܭ + ܬ = ܭܬ‬ ‫1 + ܮ + ܭ = ܮܭ‬ ܸܴ ሺ1,2ሻ = ‫ 1 ≫ ܤܣ‬ ܸܴ ሺ1,3ሻ = ‫ 1 ≫ ܥܤ‬ ܸܴ ሺ1,4ሻ = ‫ 1 ≫ ܦܥ‬ ܸܴ ሺ1,1ሻ = ‫ 1 ≫ ܯܣ‬ 90
  8. 8. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME ܸ‫ܮ‬ሺ1,4ሻ = ‫ 1 ≫ ܧܦ‬ ܸ‫ܮ‬ሺ3,4ሻ = ‫ 1 ≫ ܨܧ‬ ‫ ܦܪ‬ሺ1,1ሻ = ‫ 1 ≫ ܫܯ‬ ‫ ܦܪ‬ሺ2,1ሻ = ‫ 1 ≫ ܬܫ‬ ‫ ܦܪ‬ሺ3,1ሻ = ‫ 1 ≫ ܭܬ‬ ‫ ܦܪ‬ሺ4,1ሻ = ‫ 1 ≫ ܮܭ‬ ‫ ܥܦ‬ሺ1,1ሻ = ሺ‫ܪܩ + ܨܧ + ܦܥ + ܤܣ‬ሻ ≫ 3 ‫ܮܦܦ‬ሺ1,1ሻ = ሺ‫ ܥܤ + ܤܣ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ1,2ሻ = ሺ‫ܦܥ + ܥܤ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ1,3ሻ = ሺ‫ ܧܦ + ܦܥ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ1,4ሻ = ሺ‫ ܨܧ + ܧܦ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ2,4ሻ = ሺ‫ ܩܨ + ܨܧ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ3,4ሻ = ሺ‫ܪܩ + ܩܨ‬ሻ ≫ 2 ‫ܮܦܦ‬ሺ4,4ሻ = ሺ‫1 + 1 ≪ ܪ + ܪܩ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ1,1ሻ = ሺ‫ ܫܯ + ܯܣ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ1,2ሻ = ሺ‫ܤܣ + ܯܣ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ2,1ሻ = ሺ‫ܬܫ + ܫܯ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ3,1ሻ = ሺ‫ ܭܬ + ܬܫ‬ሻ ≫ 2 ‫ ܴܦܦ‬ሺ4,1ሻ = ሺ‫ܮܭ + ܭܬ‬ሻ ≫ 2 ‫ܷܪ‬ሺ2,4ሻ = ሺ‫1 + 1 ≪ ܮ + ܮܭ‬ሻ ≫ 2 Now, computational complexity of finding pixel domain predictions for all nine modes is 42addition and 26 shift operations.The novel approach of finding transform domain residue 4x4 sub-macroblocks is explainedhereafter. The facts of transform domain coefficients are given below. 1) The pixel domain predicted 4x4 sub-macroblock of each mode has spatial redundancy. When predicted sub-macroblock is subtracted from original sub- macroblock to form residue sub-macroblock, this spatial redundancy is not utilized/exploited. Instead, the pixel domain predicted values are forward transform to exploit the spatial redundancy. ܶ‫ ݔ‬ሺ‫݀݁ݎ݌ – ݃ݎ݋‬ሻ = ܶ‫ݔ‬ሺ‫݃ݎ݋‬ሻ − ܶ‫ݔ‬ሺ‫݀݁ݎ݌‬ሻ 2) The additive property of Forward Transform is shown below. 3) Using the above-said equation and the spatial redundancy of pixel domain predicted sub-macroblock, certain selected transform domain predicted sub-macroblock coefficients are directly calculated. TRANSFORM OF ORIGINALThe original 4x4 sub-macroblock is forward transformed and its computational complexity is64 additions and 16 shifts. ܱܴ‫ݐ݂ܥ × ݃ݎ݋ × ݂ܥ = ܩ‬ ‫ݓ‬ℎ݁‫݈ܽ݊݅݃݅ݎ݋ ݀݁݉ݎ݋݂ݏ݊ܽݎݐ ݀ݎܽݓݎ݋݂ ݏ݅ ܩܴܱ ݁ݎ‬ 91
  9. 9. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEVERTICAL PREDICTIONcoefficients ሺܸܲ_ܶ‫ݔ‬ሻand they are calculated using these values as follows.The unique pixel predicted values are A, B, C and D. There are four unique transform ‫ܦ + ܣ = ܦܣ‬ ‫ ܦ − ܣ = 1ܦܣ‬ ‫ܥ + ܤ = ܥܤ‬ ‫ܥ − ܤ = 1ܥܤ‬ ܸܲ_ܶ‫ݔ‬ሺ1,1ሻ = ሺ‫ܥܤ + ܦܣ‬ሻ ≪ 2 ܸܲ_ܶ‫ݔ‬ሺ1,2ሻ = ሺ‫1ܥܤ + 1 ≪ 1ܦܣ‬ሻ ≪ 2 ܸܲ_ܶ‫ݔ‬ሺ1,3ሻ = ሺ‫ܥܤ − ܦܣ‬ሻ ≪ 2 ܸܲ_ܶ‫ݔ‬ሺ1,4ሻ = ሺ‫1 ≪ 1ܥܤ − 1ܦܣ‬ሻ ≪ 2 ܸܲ_ܶ‫ݔ‬ሺ2,1ሻ = ܸܲ_ܶ‫ݔ‬ሺ2,2ሻ = ܸܲ_ܶ‫ݔ‬ሺ2,3ሻ = ܸܲ_ܶ‫ݔ‬ሺ2,4ሻ = 0 ܸܲ_ܶ‫ݔ‬ሺ3,1ሻ = ܸܲ_ܶ‫ݔ‬ሺ3,2ሻ = ܸܲ_ܶ‫ݔ‬ሺ3,3ሻ = ܸܲ_ܶ‫ݔ‬ሺ3,4ሻ = 0 ܸܲ_ܶ‫ݔ‬ሺ4,1ሻ = ܸܲ_ܶ‫ݔ‬ሺ4,2ሻ = ܸܲ_ܶ‫ݔ‬ሺ4,3ሻ = ܸܲ_ܶ‫ݔ‬ሺ4,4ሻ = 0 The computational complexity to find transform domain Vertical Prediction modecoefficients is 8 additions and 6 shifts.The transform domain residue for Vertical PredictionMode is calculated by subtracting these four transform coefficients from original transformcoefficients. ܸܲ_ܴ‫ܵܧ‬ሺ1,1ሻ = ܱܴ‫ܩ‬ሺ1,1ሻ − ܸܲ_ܶ‫ݔ‬ሺ1,1ሻ ܸܲ_ܴ‫ܵܧ‬ሺ1,2ሻ = ܱܴ‫ܩ‬ሺ1,2ሻ − ܸܲ_ܶ‫ݔ‬ሺ1,2ሻ ܸܲ_ܴ‫ܵܧ‬ሺ1,3ሻ = ܱܴ‫ܩ‬ሺ1,3ሻ − ܸܲ_ܶ‫ݔ‬ሺ1,3ሻ ܸܲ_ܴ‫ܵܧ‬ሺ1,4ሻ = ܱܴ‫ܩ‬ሺ1,4ሻ − ܸܲ_ܶ‫ݔ‬ሺ1,4ሻ The other values of ܸ‫ ܵܧܴ_ܴܧ‬is copied from respective ܱܴ‫ ܩ‬values.The computationalcomplexity to find transform domain residue coefficients of Vertical Prediction mode is 4additions and zero shifts.HORIZONTAL PREDICTIONcoefficients ሺ‫ݔܶ_ܲܪ‬ሻand they are calculated using these values as follows.The unique pixel predicted values are I, J, K and L. There are four unique transform ‫ܮ + ܫ = ܮܫ‬ ‫ ܮ − ܫ = 1ܮܫ‬ ‫ܭ + ܬ = ܭܬ‬ ‫ܭ − ܬ = 1ܭܬ‬ ‫ݔܶ_ܲܪ‬ሺ1,1ሻ = ሺ‫ܭܬ + ܮܫ‬ሻ ≪ 2 ‫ݔܶ_ܲܪ‬ሺ2,1ሻ = ሺ‫1ܭܬ + 1 ≪ 1ܮܫ‬ሻ ≪ 2 ‫ݔܶ_ܲܪ‬ሺ3,1ሻ = ሺ‫ܭܬ − ܮܫ‬ሻ ≪ 2 ‫ݔܶ_ܲܪ‬ሺ4,1ሻ = ሺ‫1 ≪ 1ܭܬ − 1ܮܫ‬ሻ ≪ 2 ‫ݔܶ_ܲܪ‬ሺ1,2ሻ = ‫ݔܶ_ܲܪ‬ሺ2,2ሻ = ‫ݔܶ_ܲܪ‬ሺ3,2ሻ = ‫ݔܶ_ܲܪ‬ሺ4,2ሻ = 0 ‫ݔܶ_ܲܪ‬ሺ1,3ሻ = ‫ݔܶ_ܲܪ‬ሺ2,3ሻ = ‫ݔܶ_ܲܪ‬ሺ3,3ሻ = ‫ݔܶ_ܲܪ‬ሺ4,3ሻ = 0 ‫ݔܶ_ܲܪ‬ሺ1,4ሻ = ‫ݔܶ_ܲܪ‬ሺ2,4ሻ = ‫ݔܶ_ܲܪ‬ሺ3,4ሻ = ‫ݔܶ_ܲܪ‬ሺ4,4ሻ = 0 92
  10. 10. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEThe computational complexity to find transform domain Horizontal Prediction modecoefficients is 8 additions and 6 shifts.The transform domain residue for HorizontalPrediction Mode is calculated by subtracting these four transform coefficients from originaltransform coefficients. ‫ܵܧܴ_ܲܪ‬ሺ1,1ሻ = ܱܴ‫ܩ‬ሺ1,1ሻ − ‫ݔܶ_ܲܪ‬ሺ1,1ሻ ‫ܵܧܴ_ܲܪ‬ሺ2,1ሻ = ܱܴ‫ܩ‬ሺ2,1ሻ − ‫ݔܶ_ܲܪ‬ሺ2,1ሻ ‫ܵܧܴ_ܲܪ‬ሺ3,1ሻ = ܱܴ‫ܩ‬ሺ3,1ሻ − ‫ݔܶ_ܲܪ‬ሺ3,1ሻ ‫ܵܧܴ_ܲܪ‬ሺ4,1ሻ = ܱܴ‫ܩ‬ሺ4,1ሻ − ‫ݔܶ_ܲܪ‬ሺ4,1ሻ The other values of ‫ ܵܧܴ_ܲܪ‬is copied from respective ܱܴ‫ ܩ‬values.The computationalcomplexity to find transform domain residue coefficients of Horizontal Prediction mode is 4additions and zero shifts.DC PREDICTIONThere is one unique transform coefficient ሺ‫ݔܶ_ܥܦ‬ሻcalculated as follows. ‫ݔܶ_ܥܦ‬ሺ1,1ሻ = ‫ܥܦ‬ሺ1,1ሻ ≪ 4 The computational complexity to find transform domain DC Prediction mode coefficients iszero additions and 1 shift. The transform domain residue for DC Prediction Mode iscalculated by subtracting this one transform coefficient from original transform coefficient. ‫ܵܧܴ_ܥܦ‬ሺ1,1ሻ = ܱܴ‫ܩ‬ሺ1,1ሻ − ‫ݔܶ_ܥܦ‬ሺ1,1ሻ The other values of ‫ ܵܧܴ_ܥܦ‬is copied from respective ܱܴ‫ ܩ‬values.The computationalcomplexity to find transform domain residue coefficients of Vertical Prediction mode is 4additions and zero shifts.DIAGONAL-DOWN-LEFT PREDICTIONThere are ten unique transform coefficients ሺ‫ݔܶ_ܮܦܦ‬ሻcalculated as follows. ‫ܮܦܦ = 00_ܮܦܦ‬ሺ1,1ሻ + ‫ܮܦܦ‬ሺ4,4ሻ ‫ܮܦܦ = 10_ܮܦܦ‬ሺ1,1ሻ − ‫ܮܦܦ‬ሺ4,4ሻ ‫ܮܦܦ = 20_ܮܦܦ‬ሺ1,3ሻ + ‫ܮܦܦ‬ሺ2,4ሻ ‫ܮܦܦ = 30_ܮܦܦ‬ሺ1,3ሻ − ‫ܮܦܦ‬ሺ2,4ሻ ‫ܮܦܦ = 40_ܮܦܦ‬ሺ1,2ሻ + ‫ܮܦܦ‬ሺ3,4ሻ ‫ܮܦܦ = 50_ܮܦܦ‬ሺ1,2ሻ − ‫ܮܦܦ‬ሺ3,4ሻ ‫ܮܦܦ = 60_ܮܦܦ‬ሺ1,4ሻ ≪ 2 ‫ܮܦܦ = 70_ܮܦܦ‬ሺ1,4ሻ ≪ 3 + ‫ܮܦܦ‬ሺ1,4ሻ ≪ 1 ‫ 20_ܮܦܦ + 1 ≪ 20_ܮܦܦ = 80_ܮܦܦ‬ ‫ 50_ܮܦܦ + 1 ≪ 50_ܮܦܦ = 90_ܮܦܦ‬ ‫ 1 ≪ 40_ܮܦܦ = 01_ܮܦܦ‬ ‫ 60_ܮܦܦ + 00_ܮܦܦ = 11_ܮܦܦ‬ ‫ 30_ܮܦܦ + 10_ܮܦܦ = 21_ܮܦܦ‬ ‫ 1 ≪ 30_ܮܦܦ = 31_ܮܦܦ‬ 93
  11. 11. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME ‫ݔܶ_ܮܦܦ‬ሺ1,1ሻ = ‫ 01_ܮܦܦ + 80_ܮܦܦ + 11_ܮܦܦ‬ ‫ݔܶ_ܮܦܦ‬ሺ1,2ሻ = ‫ 90_ܮܦܦ + 1 ≪ 21_ܮܦܦ‬ ‫ݔܶ_ܮܦܦ‬ሺ1,3ሻ = ‫ 20_ܮܦܦ − 00_ܮܦܦ‬ ‫ݔܶ_ܮܦܦ‬ሺ1,4ሻ = ‫ 50_ܮܦܦ − 21_ܮܦܦ‬ ‫ݔܶ_ܮܦܦ‬ሺ2,2ሻ = ሺ‫40_ܮܦܦ + 00_ܮܦܦ‬ሻ ≪ 2 − ‫ 70_ܮܦܦ − 80_ܮܦܦ‬ ‫ݔܶ_ܮܦܦ‬ሺ2,3ሻ = ሺ‫31_ܮܦܦ − 10_ܮܦܦ‬ሻ ≪ 1 − ‫ 50_ܮܦܦ‬ ‫ݔܶ_ܮܦܦ‬ሺ2,4ሻ = ሺ‫40_ܮܦܦ − 00_ܮܦܦ‬ሻ ≪ 1 + ‫ 40_ܮܦܦ − 20_ܮܦܦ‬ ‫ݔܶ_ܮܦܦ‬ሺ3,3ሻ = ‫ 01_ܮܦܦ − 20_ܮܦܦ − 11_ܮܦܦ‬ ‫ݔܶ_ܮܦܦ‬ሺ3,4ሻ = ‫ 90_ܮܦܦ − 31_ܮܦܦ + 21_ܮܦܦ‬ ‫ݔܶ_ܮܦܦ‬ሺ4,4ሻ = ‫ 70_ܮܦܦ − 2 ≪ 40_ܮܦܦ − 3 ≪ 20_ܮܦܦ + 00_ܮܦܦ‬ The other coefficients are copied from those 10 unique coefficients. ‫ݔܶ_ܮܦܦ‬ሺ2,1ሻ = ‫ݔܶ_ܮܦܦ‬ሺ1,2ሻ ‫ݔܶ_ܮܦܦ‬ሺ3,1ሻ = ‫ݔܶ_ܮܦܦ‬ሺ1,3ሻ ‫ݔܶ_ܮܦܦ‬ሺ4,1ሻ = ‫ݔܶ_ܮܦܦ‬ሺ1,4ሻ ‫ݔܶ_ܮܦܦ‬ሺ3,2ሻ = ‫ݔܶ_ܮܦܦ‬ሺ2,3ሻ ‫ݔܶ_ܮܦܦ‬ሺ4,2ሻ = ‫ݔܶ_ܮܦܦ‬ሺ2,4ሻ ‫ݔܶ_ܮܦܦ‬ሺ4,3ሻ = ‫ݔܶ_ܮܦܦ‬ሺ3,4ሻ The computational complexity to find transform domain coefficients of Diagonal-Down-LeftPrediction mode is 31 additions and 13 shifts. The transform domain residue for Diagonal-Down-Left Prediction Mode is calculated by subtracting these transform coefficients fromoriginal transform coefficient. The computational complexity to find transform domainresidue coefficients of Diagonal-Down-Left Prediction mode is 16 additions and zero shifts.DIAGONAL-DOWN-RIGHT PREDICTIONThere are ten unique transform coefficients ሺ‫ݔܶ_ܴܦܦ‬ሻ calculated as follows. ‫ܮܦܦ = 00_ܴܦܦ‬ሺ1,1ሻ + ‫ܴܦܦ‬ሺ3,1ሻ ‫ܮܦܦ = 10_ܴܦܦ‬ሺ1,2ሻ + ‫ܴܦܦ‬ሺ4,1ሻ ‫ܮܦܦ = 20_ܴܦܦ‬ሺ1,1ሻ − ‫ܴܦܦ‬ሺ3,1ሻ ‫ 20_ܴܦܦ + 1 ≪ 20_ܴܦܦ = 30_ܴܦܦ‬ ‫ܴܦܦ = 40_ܴܦܦ‬ሺ1,2ሻ + ‫ܴܦܦ‬ሺ2,1ሻ ‫ 40_ܴܦܦ + 1 ≪ 40_ܴܦܦ = 50_ܴܦܦ‬ ‫ܴܦܦ = 60_ܴܦܦ‬ሺ1,2ሻ − ‫ܴܦܦ‬ሺ2,1ሻ ‫ܮܦܦ = 70_ܴܦܦ‬ሺ1,2ሻ − ‫ܴܦܦ‬ሺ4,1ሻ ‫ 70_ܴܦܦ + 60_ܴܦܦ = 80_ܴܦܦ‬ ‫ܴܦܦ = 90_ܴܦܦ‬ሺ1,1,5ሻ ≪ 2 ‫ = 01_ܴܦܦ‬ሺ‫ܴܦܦ‬ሺ1,1ሻ + ‫90_ܴܦܦ‬ሻ ≪ 1 ‫ 1 ≪ 00_ܴܦܦ = 11_ܴܦܦ‬ ‫ 90_ܴܦܦ + 10_ܴܦܦ = 21_ܴܦܦ‬ ‫ 1 ≪ 10_ܴܦܦ = 31_ܴܦܦ‬ ‫ 1 ≪ 11_ܴܦܦ = 41_ܴܦܦ‬ ‫ 1 ≪ 60_ܴܦܦ = 51_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ1,1ሻ = ‫ 21_ܴܦܦ + 11_ܴܦܦ + 50_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ1,2ሻ = − ‫ 1 ≪ 80_ܴܦܦ − 30_ܴܦܦ‬ 94
  12. 12. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME ‫ݔܶ_ܴܦܦ‬ሺ1,3ሻ = ‫ 40_ܴܦܦ − 10_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ1,4ሻ = ‫ 80_ܴܦܦ − 20_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ2,2ሻ = ‫ 1 ≪ 31_ܴܦܦ − 41_ܴܦܦ − 01_ܴܦܦ + 50_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ2,3ሻ = ሺ‫51_ܴܦܦ − 70_ܴܦܦ‬ሻ ≪ 1 − ‫ 20_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ2,4ሻ = ‫ 31_ܴܦܦ − 11_ܴܦܦ + 40_ܴܦܦ − 00_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ3,3ሻ = ‫ 40_ܴܦܦ − 11_ܴܦܦ − 21_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ3,4ሻ = ‫ 51_ܴܦܦ − 70_ܴܦܦ − 60_ܴܦܦ − 30_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ4,4ሻ = ‫ 01_ܴܦܦ + 3 ≪ 40_ܴܦܦ − 10_ܴܦܦ − 41_ܴܦܦ‬ ‫ݔܶ_ܴܦܦ‬ሺ2,1ሻ = −‫ݔܶ_ܴܦܦ‬ሺ1,2ሻ ‫ݔܶ_ܴܦܦ‬ሺ3,1ሻ = ‫ݔܶ_ܴܦܦ‬ሺ1,3ሻ ‫ݔܶ_ܴܦܦ‬ሺ4,1ሻ = −‫ݔܶ_ܴܦܦ‬ሺ1,4ሻ ‫ݔܶ_ܴܦܦ‬ሺ3,2ሻ = −‫ݔܶ_ܴܦܦ‬ሺ2,3ሻ ‫ݔܶ_ܴܦܦ‬ሺ4,2ሻ = ‫ݔܶ_ܴܦܦ‬ሺ2,4ሻ ‫ݔܶ_ܴܦܦ‬ሺ4,3ሻ = −‫ݔܶ_ܴܦܦ‬ሺ3,4ሻ The computational complexity to find transform domain coefficients of Diagonal-Down-Right Prediction mode is 32 additions and 12 shifts. The transform domain residue forDiagonal-Down-Right Prediction Mode is calculated by subtracting these transformcoefficients from original transform coefficient. The computational complexity to findtransform domain residue coefficients of Diagonal-Down-Right Prediction mode is 16additions and zero shifts.VERTICAL-RIGHT PREDICTION All the transform coefficients ሺܸܴ_ܶ‫ݔ‬ሻ calculated as follows. ‫ܴܸ = 00_݌ݐ‬ሺ1,4ሻ + ‫ܴܦܦ‬ሺ3,1ሻ ‫ܴܸ = 10_݌ݐ‬ሺ1,4ሻ − ‫ܴܦܦ‬ሺ3,1ሻ ‫ܴܦܦ = 20_݌ݐ‬ሺ2,1ሻ + ‫ܮܦܦ‬ሺ1,2ሻ ‫ܴܦܦ = 30_݌ݐ‬ሺ2,1ሻ − ‫ܮܦܦ‬ሺ1,2ሻ ‫ܴܸ = 40_݌ݐ‬ሺ1,1ሻ + ‫ܮܦܦ‬ሺ1,1ሻ ‫ܴܸ = 50_݌ݐ‬ሺ1,1ሻ − ‫ܮܦܦ‬ሺ1,1ሻ ‫ܴܸ = 60_݌ݐ‬ሺ1,3ሻ − ‫ܴܦܦ‬ሺ1,1ሻ ‫ 1 << 40_݌ݐ = 70_݌ݐ‬ ܸܴ_00 = ‫ 20_݌ݐ − 00_݌ݐ‬ ܸܴ_01 = ܸܴ_00 − ‫ 20_݌ݐ‬ ܸܴ_02 = ‫ 20_݌ݐ + 00_݌ݐ‬ ܸܴ_03 = ‫ 20_ܴܸ + 00_݌ݐ‬ ܸܴ_04 = ܸܴሺ1,3ሻ + ‫ܴܦܦ‬ሺ1,1ሻ ܸܴ_05 = ‫ 1 ≪ 40_ܴܸ + 70_݌ݐ‬ ܸܴ_06 = ‫ 1 ≪ 40_ܴܸ − 70_݌ݐ‬ ܸܴ_07 = ܸܴሺ1,2ሻ + ‫ܴܦܦ‬ሺ1,2ሻ ܸܴ_08 = ܸܴ_07 ≪ 1 ܸܴ_09 = ܸܴ_08 + ܸܴ_07 ܸܴ_10 = ‫ 30_݌ݐ − 10_݌ݐ‬ ܸܴ_11 = ‫ 01_ܴܸ + 10_݌ݐ‬ ܸܴ_12 = ‫ 60_݌ݐ − 50_݌ݐ‬ ܸܴ_13 = ܸܴ_12 ≪ 1 + ܸܴ_12 95
  13. 13. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME ܸܴ_14 = ‫ 30_݌ݐ + 10_݌ݐ‬ ܸܴ_15 = ܸܴ_14 + ‫ 30_݌ݐ‬ ܸܴ_16 = ‫ 60_݌ݐ + 50_݌ݐ‬ ܸܴ_17 = ܸܴ_16 ≪ 1 + ܸܴ_16 ܸܴ_18 = ܸܴሺ1,2ሻ − ‫ܴܦܦ‬ሺ1,2ሻ ܸܴ_19 = ܸܴ_18 ≪ 1 + ܸܴ_18 ܸܴ_20 = ‫ 70_݌ݐ + 40_݌ݐ‬ ܸܴ_ܶ‫ݔ‬ሺ1,1ሻ = ܸܴ_02 + ܸܴ_05 + ܸܴ_08 ܸܴ_ܶ‫ݔ‬ሺ1,2ሻ = ܸܴ_13 − ܸܴ_10 ≪ 1 ܸܴ_ܶ‫ݔ‬ሺ1,3ሻ = ܸܴ_02 − ܸܴ_08 ܸܴ_ܶ‫ݔ‬ሺ1,4ሻ = −ܸܴ_10 − ܸܴ_12 ܸܴ_ܶ‫ݔ‬ሺ2,1ሻ = ܸܴ_11 + ܸܴ_16 + ܸܴ_18 ܸܴ_ܶ‫ݔ‬ሺ2,2ሻ = ܸܴ_20 − ܸܴ_03 ≪ 1 + ܸܴ_09 ܸܴ_ܶ‫ݔ‬ሺ2,3ሻ = ܸܴ_11 + ܸܴ_13 − ܸܴ_18 ܸܴ_ܶ‫ݔ‬ሺ2,4ሻ = ܸܴ_04 − ܸܴ_03 + ሺܸܴ_05 − ܸܴ_09ሻ ≪ 1 ܸܴ_ܶ‫ݔ‬ሺ3,1ሻ = ܸܴ_00 ܸܴ_ܶ‫ݔ‬ሺ3,2ሻ = ሺܸܴ_18 − ܸܴ_14ሻ ≪ 1 + ܸܴ_16 ܸܴ_ܶ‫ݔ‬ሺ3,3ሻ = ܸܴ_00 + ܸܴ_06 ܸܴ_ܶ‫ݔ‬ሺ3,4ሻ = ܸܴ_17 − ܸܴ_14 − ܸܴ_18 ≪ 2 ܸܴ_ܶ‫ݔ‬ሺ4,1ሻ = ܸܴ_15 + ܸܴ_17 + ܸܴ_19 ܸܴ_ܶ‫ݔ‬ሺ4,2ሻ = ሺܸܴ_06 − ܸܴ_01ሻ ≪ 1 − ܸܴ_04 − ܸܴ_07 ܸܴ_ܶ‫ݔ‬ሺ4,3ሻ = ܸܴ_15 − ܸܴ_12 − ܸܴ_19 ܸܴ_ܶ‫ݔ‬ሺ4,4ሻ = ܸܴ_08 − ܸܴ_01 − ܸܴ_20 The computational complexity to find transform domain coefficients of Vertical-RightPrediction mode is 55 additions and 12 shifts. The transform domain residue for Vertical-Right Prediction Mode is calculated by subtracting these transform coefficients from originaltransform coefficient. The computational complexity to find transform domain residuecoefficients of Vertical-Right Prediction mode is 16 additions and zero shifts.HORIZONTAL-DOWN PREDICTION All the transform coefficients ሺ‫ݔܶ_ܦܪ‬ሻ calculated as follows. ‫ܴܦܦ = 00_ܦܪ‬ሺ1,2ሻ + ‫ܴܦܦ‬ሺ4,1ሻ ‫ܴܦܦ = 10_ܦܪ‬ሺ1,2ሻ − ‫ܴܦܦ‬ሺ4,1ሻ ‫ܮܦܦ = 20_ܦܪ‬ሺ1,1ሻ + ‫ܦܪ‬ሺ4,1ሻ ‫ܮܦܦ = 30_ܦܪ‬ሺ1,1ሻ − ‫ܦܪ‬ሺ4,1ሻ ‫ܦܪ = 40_ܦܪ‬ሺ1,1ሻ + ‫ܴܦܦ‬ሺ3,1ሻ ‫ܦܪ = 50_ܦܪ‬ሺ1,1ሻ − ‫ܴܦܦ‬ሺ3,1ሻ ‫ܴܦܦ = 60_ܦܪ‬ሺ1,1ሻ + ‫ܦܪ‬ሺ3,1ሻ ‫ܴܦܦ = 70_ܦܪ‬ሺ1,1ሻ − ‫ܦܪ‬ሺ3,1ሻ ‫ܦܪ = 80_ܦܪ‬ሺ2,1ሻ + ‫ܴܦܦ‬ሺ2,1ሻ ‫ܦܪ = 90_ܦܪ‬ሺ2,1ሻ − ‫ܴܦܦ‬ሺ2,1ሻ ‫ 70_ܦܪ + 50_ܦܪ = 01_ܦܪ‬ ‫ 70_ܦܪ − 50_ܦܪ = 11_ܦܪ‬ ‫ 20_ܦܪ + 00_ܦܪ = 21_ܦܪ‬ ‫ 20_ܦܪ − 00_ܦܪ = 31_ܦܪ‬ 96
  14. 14. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME ‫ 00_ܦܪ + 31_ܦܪ = 41_ܦܪ‬ ‫ 20_ܦܪ + 21_ܦܪ = 51_ܦܪ‬ ‫ 30_ܦܪ + 10_ܦܪ = 61_ܦܪ‬ ‫ 30_ܦܪ − 10_ܦܪ = 71_ܦܪ‬ ‫ 30_ܦܪ + 61_ܦܪ = 81_ܦܪ‬ ‫ 10_ܦܪ + 71_ܦܪ = 91_ܦܪ‬ ‫ 40_ܦܪ + 1 ≪ 40_ܦܪ = 02_ܦܪ‬ ‫ 1 ≪ 80_ܦܪ = 12_ܦܪ‬ ‫ 80_ܦܪ + 12_ܦܪ = 22_ܦܪ‬ ‫ = 32_ܦܪ‬ሺ‫60_ܦܪ + 40_ܦܪ‬ሻ ≪ 1 ‫ = 42_ܦܪ‬ሺ‫60_ܦܪ − 40_ܦܪ‬ሻ ≪ 1 ‫ 90_ܦܪ + 11_ܦܪ = 52_ܦܪ‬ ‫ 90_ܦܪ − 11_ܦܪ = 62_ܦܪ‬ ‫ 01_ܦܪ + 1 ≪ 01_ܦܪ = 72_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ1,1ሻ = ‫ 12_ܦܪ + 32_ܦܪ + 21_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ1,2ሻ = ‫ 81_ܦܪ − 52_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ1,3ሻ = −‫ 31_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ1,4ሻ = ‫ 52_ܦܪ + 1 ≪ 52_ܦܪ + 91_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ2,1ሻ = ‫ 72_ܦܪ + 1 ≪ 61_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ2,2ሻ = ‫ 22_ܦܪ + 1 ≪ 51_ܦܪ − 02_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ2,3ሻ = ‫ 52_ܦܪ + 1 ≪ 71_ܦܪ − 90_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ2,4ሻ = ሺ‫42_ܦܪ + 41_ܦܪ‬ሻ ≪ 1 − ‫ 80_ܦܪ − 60_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ3,1ሻ = ‫ 12_ܦܪ − 21_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ3,2ሻ = ‫ 90_ܦܪ − 81_ܦܪ − 72_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ3,3ሻ = ‫ 31_ܦܪ − 42_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ3,4ሻ = ‫ 90_ܦܪ − 1 ≪ 90_ܦܪ − 01_ܦܪ − 91_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ4,1ሻ = ‫ 01_ܦܪ − 61_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ4,2ሻ = ‫ − 51_ܦܪ − 60_ܦܪ‬ሺ‫32_ܦܪ − 22_ܦܪ‬ሻ ≪ 1 ‫ݔܶ_ܦܪ‬ሺ4,3ሻ = ‫ 1 ≪ 62_ܦܪ + 90_ܦܪ − 71_ܦܪ − 62_ܦܪ‬ ‫ݔܶ_ܦܪ‬ሺ4,4ሻ = ‫ 12_ܦܪ + 02_ܦܪ − 41_ܦܪ‬The computational complexity to find transform domain coefficients of Horizontal-DownPrediction mode is 56 additions and 12 shifts. The transform domain residue for Horizontal-Down Prediction Mode is calculated by subtracting these transform coefficients from originaltransform coefficient. The computational complexity to find transform domain residuecoefficients of Horizontal-Down Prediction mode is 16 additions and zero shifts.VERTICAL-LEFT PREDICTION All the transform coefficients ሺܸ‫ݔܶ_ܮ‬ሻ calculated as follows. ܸ‫ܴܸ = 00_ܮ‬ሺ1,2ሻ + ‫ܮܦܦ‬ሺ2,4ሻ ܸ‫ܴܸ = 10_ܮ‬ሺ1,2ሻ − ‫ܮܦܦ‬ሺ2,4ሻ ܸ‫ܮܦܦ = 20_ܮ‬ሺ1,1ሻ + ܸ‫ܮ‬ሺ3,4ሻ ܸ‫ܮܦܦ = 30_ܮ‬ሺ1,1ሻ − ܸ‫ܮ‬ሺ3,4ሻ ܸ‫ܴܸ = 40_ܮ‬ሺ1,3ሻ + ‫ܮܦܦ‬ሺ1,4ሻ ܸ‫ܴܸ = 50_ܮ‬ሺ1,3ሻ − ‫ܮܦܦ‬ሺ1,4ሻ ܸ‫ܴܸ = 60_ܮ‬ሺ1,4ሻ + ‫ܮܦܦ‬ሺ1,3ሻ 97
  15. 15. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME ܸ‫ܴܸ = 70_ܮ‬ሺ1,4ሻ − ‫ܮܦܦ‬ሺ1,3ሻ ܸ‫ܮܸ = 80_ܮ‬ሺ1,4ሻ + ‫ܮܦܦ‬ሺ1,2ሻ ܸ‫ܮܸ = 90_ܮ‬ሺ1,4ሻ − ‫ܮܦܦ‬ሺ1,2ሻ ܸ‫ 20_ܮܸ + 00_ܮܸ = 01_ܮ‬ ܸ‫ 20_ܮܸ − 00_ܮܸ = 11_ܮ‬ ܸ‫ 00_ܮܸ + 01_ܮܸ = 21_ܮ‬ ܸ‫ 20_ܮܸ − 11_ܮܸ = 31_ܮ‬ ܸ‫ 30_ܮܸ + 10_ܮܸ = 41_ܮ‬ ܸ‫ 30_ܮܸ − 10_ܮܸ = 51_ܮ‬ ܸ‫ 41_ܮܸ + 10_ܮܸ = 61_ܮ‬ ܸ‫ 30_ܮܸ − 51_ܮܸ = 71_ܮ‬ ܸ‫ 50_ܮܸ + 90_ܮܸ = 81_ܮ‬ ܸ‫ 50_ܮܸ − 90_ܮܸ = 91_ܮ‬ ܸ‫ 80_ܮܸ + 1 ≪ 80_ܮܸ = 02_ܮ‬ ܸ‫ 1 ≪ 60_ܮܸ = 12_ܮ‬ ܸ‫ = 22_ܮ‬ሺܸ‫80_ܮܸ + 40_ܮ‬ሻ ≪ 1 ܸ‫ = 32_ܮ‬ሺܸ‫80_ܮܸ − 40_ܮ‬ሻ ≪ 1 ܸ‫ 70_ܮܸ + 1 ≪ 70_ܮܸ = 42_ܮ‬ ܸ‫ 81_ܮܸ + 1 ≪ 81_ܮܸ = 52_ܮ‬ ܸ‫ 91_ܮܸ + 1 ≪ 91_ܮܸ = 62_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ1,1ሻ = ܸ‫ 22_ܮܸ + 12_ܮܸ + 01_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ1,2ሻ = ܸ‫ 62_ܮܸ − 1 ≪ 41_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ1,3ሻ = ܸ‫ 12_ܮܸ − 01_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ1,4ሻ = ܸ‫ 91_ܮܸ + 41_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ2,1ሻ = ܸ‫ 81_ܮܸ + 61_ܮܸ + 70_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ2,2ሻ = ሺܸ‫60_ܮܸ − 21_ܮ‬ሻ ≪ 1 − ܸ‫ 02_ܮܸ − 60_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ2,3ሻ = ܸ‫ 62_ܮܸ + 70_ܮܸ − 61_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ2,4ሻ = ܸ‫ + 12_ܮܸ + 40_ܮܸ − 21_ܮ‬ሺܸ‫22_ܮܸ − 12_ܮ‬ሻ ≪ 1 ܸ‫ݔܶ_ܮ‬ሺ3,1ሻ = ܸ‫ 11_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ3,2ሻ = ሺܸ‫70_ܮܸ − 51_ܮ‬ሻ ≪ 1 − ܸ‫ 81_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ3,3ሻ = ܸ‫ 32_ܮܸ − 11_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ3,4ሻ = ܸ‫ 52_ܮܸ − 51_ܮܸ + 2 ≪ 70_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ4,1ሻ = ܸ‫ 52_ܮܸ + 71_ܮܸ + 42_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ4,2ሻ = ܸ‫ + 60_ܮܸ + 40_ܮ‬ሺܸ‫32_ܮܸ + 31_ܮ‬ሻ ≪ 1 ܸ‫ݔܶ_ܮ‬ሺ4,3ሻ = ܸ‫ 91_ܮܸ − 42_ܮܸ − 71_ܮ‬ ܸ‫ݔܶ_ܮ‬ሺ4,4ሻ = ܸ‫ 12_ܮܸ − 02_ܮܸ + 31_ܮ‬The computational complexity to find transform domain coefficients of Vertical-LeftPrediction mode is 56 additions and 14 shifts. The transform domain residue for Vertical-LeftPrediction Mode is calculated by subtracting these transform coefficients from originaltransform coefficient. The computational complexity to find transform domain residuecoefficients of Vertical-Left Prediction mode is 16 additions and zero shifts. 98
  16. 16. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEHORIZONTAL-UP PREDICTION All the transform coefficients ሺ‫ݔܶ_ܷܪ‬ሻ calculated as follows. ‫ܦܪ = 00_ܷܪ‬ሺ2,1ሻ + ‫ܴܦܦ‬ሺ3,1ሻ ‫ܦܪ = 10_ܷܪ‬ሺ2,1ሻ − ‫ܴܦܦ‬ሺ3,1ሻ ‫ܦܪ = 20_ܷܪ‬ሺ3,1ሻ + ‫ܴܦܦ‬ሺ4,1ሻ ‫ܦܪ = 30_ܷܪ‬ሺ3,1ሻ − ‫ܴܦܦ‬ሺ4,1ሻ ‫ܦܪ = 40_ܷܪ‬ሺ4,1ሻ + ‫ܷܪ‬ሺ2,4ሻ ‫ܦܪ = 50_ܷܪ‬ሺ4,1ሻ − ‫ܷܪ‬ሺ2,4ሻ ‫ܦܪ = 60_ܷܪ‬ሺ2,1ሻ + ‫ 00_ܷܪ‬ ‫ܴܦܦ − 10_ܷܪ = 70_ܷܪ‬ሺ3,1ሻ ‫ ܮ − 40_ܷܪ = 80_ܷܪ‬ ‫ ܮ + 1 ≪ ܮ = 90_ܷܪ‬ ‫ ܮ + 50_ܷܪ + 1 ≪ 50_ܷܪ = 01_ܷܪ‬ ‫ 90_ܷܪ − 50_ܷܪ = 11_ܷܪ‬ ‫ܴܦܦ = 21_ܷܪ‬ሺ4,1ሻ + ‫ 80_ܷܪ‬ ‫ܴܦܦ = 31_ܷܪ‬ሺ4,1ሻ − ‫ 80_ܷܪ‬ ‫30_ܷܪ + 1 ≪ 30_ܷܪ + 70_ܷܪ = 41_ܷܪ‬ ‫ 80_ܷܪ − 20_ܷܪ = 51_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ1,1ሻ = ‫ + 00_ܷܪ‬ሺ‫90_ܷܪ + 40_ܷܪ + 20_ܷܪ‬ሻ ≪ 1 ‫ݔܶ_ܷܪ‬ሺ1,2ሻ = ‫ 11_ܷܪ + 30_ܷܪ + 60_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ1,3ሻ = ‫ 10_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ1,4ሻ = ‫ 01_ܷܪ + 41_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ2,1ሻ = ሺ‫ܮ − 20_ܷܪ + 00_ܷܪ‬ሻ ≪ 1 + ‫ 3 ≪ ܮ − 20_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ2,2ሻ = ሺ‫21_ܷܪ − 60_ܷܪ‬ሻ ≪ 1 − ‫ 21_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ2,3ሻ = ሺ‫50_ܷܪ − 10_ܷܪ‬ሻ ≪ 1 − ‫ 30_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ2,4ሻ = ‫ 21_ܷܪ + 30_ܷܪ − 1 ≪ 41_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ3,1ሻ = ‫ 80_ܷܪ − 1 ≪ 80_ܷܪ − 00_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ3,2ሻ = ‫ 11_ܷܪ − 20_ܷܪ − 1 ≪ 20_ܷܪ − 60_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ3,3ሻ = ‫ 1 ≪ 30_ܷܪ − 10_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ3,4ሻ = ‫ 01_ܷܪ − 20_ܷܪ + 70_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ4,1ሻ = ‫ 20_ܷܪ − 00_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ4,2ሻ = ‫ 21_ܷܪ + 51_ܷܪ − 2 ≪ 51_ܷܪ − 60_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ4,3ሻ = ‫ − 10_ܷܪ‬ሺ‫50_ܷܪ − 30_ܷܪ‬ሻ ≪ 2 + ‫ 30_ܷܪ‬ ‫ݔܶ_ܷܪ‬ሺ4,4ሻ = ‫31_ܷܪ + 1 ≪ 31_ܷܪ + 80_ܷܪ + 70_ܷܪ‬The computational complexity to find transform domain coefficients of Horizontal-UpPrediction mode is 51 additions and 16 shifts. The transform domain residue for Horizontal-Up Prediction Mode is calculated by subtracting these transform coefficients from originaltransform coefficient. The computational complexity to find transform domain residuecoefficients of Horizontal-Up Prediction mode is 16 additions and zero shifts. SECTION 5: COMPARISON ANDINFERENCES OF THE PROPOSED METHOD The computational complexity of reference software and the proposed method arecompared here. The computational complexity of Pixel domain Intra 4x4 Prediction for all 99
  17. 17. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEthe nine prediction modes in the reference softwares[12] and [13] tabulatedin the table 1below. Table 1 Complexity of Pixel domain Intra 4x4 prediction in reference software Reference Prediction Type Software Addition Shifts Vertical 0 0 Horizontal 0 0 DC 8 1 Diagonal-Down- 21 14 Left Diagonal-Down- 21 14 Right Vertical-Right 26 16 Horizontal-Down 26 16 Vertical-Left 25 15 Horizontal-Up 15 9 Total 142 85The reference software does the pixel domain prediction first, and then finds the residue andlast it does the forward transform for all nine modes. In that order, the computationalcomplexity of the existing reference software is listed in the table 2.The proposed method does the selective pixel domain prediction, calculates the selectivetransform domain coefficients and finds the transform domain residue coefficients. Thecomputational complexity of the proposed method is listed in table 3. Table 2 Complexity of Reference software during Intra 4x4 prediction Reference Process Software Addition Shift Pixel domain 142 85 Prediction Finding Residue 144 0 Forward Transform 576 144 Total 862 229 Table 3 Complexity of Proposed method during Intra 4x4 prediction Proposed Method Process Addition Shift Pixel domain 42 26 Prediction Forward Transform 361 108 Finding Residue 105 0 Total 508 134 100
  18. 18. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME The transform domain residue sub-macroblocks for all the nine modes are available by508 additions and 134 shifts only, where as the existing reference software can produce thesame by 862 additions and 229 shifts. After finalizing mode, the corresponding pixel domainprediction values can be generated just by copying from available 24 unique pixel values.CONCLUSION The process of predicting the intra 4x4 prediction for all the nine modes, finding theresidue and forward transforming will take more complexity in terms of addition and shifts.Every macroblock in the frame of the sequence is subjected to do this process repeatedly forall its sixteen sub-macroblocks. The proposed method used (i) the unique equations forprediction, (ii) the additive property of core forward transform and (iii) the spatialredundancy of pixel domain predicted values, and reduced the computational complexity into59% addition and 59% shift operations, thus saved 41% computational complexity. But theproposed method did not compromise the accuracy of the results, thus maintaining the samequality and bitrate. The same method can be extended to Intra 16x16 Prediction, Intra 8x8Prediction and Intra Chroma Predictions also in H.264 Encoder.ACKNOWLEDGMENT The author thanks RiverSilica Technologies Private Limited, INDIA for theirencouragement and support.REFERENCES[1] T. Wiegand, G. J. Sullivan, G. Bjontegaard, and A. Luthra, “Overview of the H.264/AVCvideo coding standard,” IEEE Transactions on Circuits and Systems for Video Technology.,Vol. 13, No. 7, pp. 560–576, Jul. 2003.[2] A. Joch, F. Kossentini, H. Schwarz, T. Wiegand, and G. J. Sullivan, “Performancecomparison of video standards using Lagrangian control,” in Proc. IEEE Int. Conf. ImageProcess., pp. 501–504, 2002.[3] W. Zouch, A. Samet, M. A. Ben Ayed, F Kossentini, N. Masmoudi, “ComplexityAnalysis of Intra Prediction in H.264/AVC”, Micro Electronics, 2004. ICM 2004Proceedings, 16th International Conference on Dec 6-8, 2004[4] Mustafa Parlak, Yusuf Adibelli, and IlkerHamzaoglu, “A Novel ComputationalComplexity and Power Reduction Technique for H.264 Intra Prediction”, IEEE Transactionson Consumer Electronics, Vol. 54, No. 4, Nov’2008[5] Yusuf Adibelli, Mustafa Parlak, and IlkerHamzaoglu, “A Computation and PowerReduction Technique for H.264 Intra Prediction”, 13thEuromicro Conference on DigitalSystem Design: Architecture, Methods and Tools, 2010[6] E. Sahin, I. Hamzaoglu, “An Efficient Hardware Architecture for H.264 Intra PredictionAlgorithm”, DATE Conference, Apr’2007[7] Y. Lai, T. Liu, Y. Li, C. Lee, “Design of An Intra Predictor with Data Reuse for High-Profile H.264 Applications”, IEEE ISCAS, May 2009[8] F. Pan, X. Lin, S. Rahardja, K. Lim, Z. Li, S. Dajun Wu, “Fast Mode Decision Algorithmfor Intra Prediction in H.264/AVC Video Coding”, IEEE Transactions on CAS for VideoTechnology, Vol. 15, No. 7.,pp 813 – 822, Jul’2005[9] I. Choi, J. Lee, B. Jeon, “Fast Coding Mode Selection With Rate-Distortion Optimizationfor MPEG-4 Part 10 AVC/H.264”, IEEE Transactions on CAS for Video Technology, Vol.16, No. 12, pp 1557 – 1561, Dec’2006 101
  19. 19. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME[10] A. Elyousfi, A. A. Tamtaoui, and E. Bouyakhf, “A New Fast Intra Prediction ModeDecision Algorithm for H.264/AVC Encoders”, World Academy of Science, Engineering andTechnology, 2007[11] The H.264 – Advanced Video Compression Standard – Second Edition – Iain E.Richardson – A John Wiley and Sons, Ltd., Publication, 2010[12] Joint Video Team, JM Reference Software V17.1 - iphome.hhi.de/suehring/tml/[13] X264 Encoder Open Source - http://www.videolan.org/developers/x264.html 102

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