a computationally efficient method to find transformed residue coefficients in intra

7/30/2019 A Computationally Efficient Method to Find Transformed Residue Coefficients in Intra

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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN

0976 6464(Print), ISSN 0976 6472(Online) Volume 3, Issue 3, October- December (2012), IAEME

84

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, [email protected], [email protected]

ABSTRACT

To achieve the best coding efficiency and video quality, H.264 encoder has to evaluate

exhaustively all the mode combinations of intra predictions for deciding coding mode. The

computational complexity and time taken for predicting for all intra modes, subtracting from

original blockand forward transforming the residues are heavy. A novel Intra 4x4 Prediction

method to reduce the computational complexity, thus enhancing the time savings is proposed

here. The experimental results demonstrate that proposed method reduces at least 40% of

computational 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 Complexity

SECTION 1: INTRODUCTION

The newest international video coding standard H.264/ advanced video coding (AVC) has

been approved by ITU-T as recommended H.264 and by ISO/IEC as the MPEG-4 part 10

AVC international Standard [1]. The emerging H.264/AVC achieves significantly better

performance in both peak signal-to-noise ratio (PSNR) and visual quality at the same bit rate

compared 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 one

important technique calledLagrangian rate-distortion optimization (RDO) performed for intraand inter mode decision. The rate-distortion optimization technique is very time consuming

and the computational complexity of H.264/AVC is drastically high using the RDO

technique.

The computational complexity refers the basic operations (e.g., Add, Shift). The method of

calculating the computational complexity of the intra prediction module was done by number

of cycles taken by basic operations by Zouch[3]. Mustafa et al [4], [5] used number of

additions and shifts performed in intra prediction, as metric for computational complexity.

INTERNATIONAL JOURNAL OF ELECTRONICS AND

COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)

ISSN 0976 6464(Print)

ISSN 0976 6472(Online)

Volume 3, Issue 3, October- December (2012), pp. 84-102

IAEME: www.iaeme.com/ijecet.asp

Journal Impact Factor (2012):3.5930 (Calculated by GISI)

www.jifactor.com

IJECET

I A E M E


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H.264 has Intra 4x4 prediction, Intra 16x16 prediction, Intra 8x8 prediction and Intra

Chroma prediction. This paper focuses on Intra 4x4 prediction only. Intra 4x4 prediction has

nine different modes and these modes have identical equations and calculating these common

equations for each mode is unnecessary. The Pixel equality based computation reduction

(PECR) technique used in [4] focussed only on pixel domain predictions. It saved

computational complexity, but it did not include the computational complexity for

comparison operation which is generally equivalent to addition operation. Still there is ascope of optimization in the data reuse techniques presented in [5] to reduce the

computational complexity.

The techniques used in [6], [7], [8], [9] and [10] reduce the amount of computations

performed by Intra prediction by trying selected intra prediction modes rather than trying all

possible 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 pixel

domain prediction and its forward transformation, (ii) to reduce the computational complexity

of Intra 4x4 Prediction of a given 4x4 sub-macroblock, and (iii)to give the transform domain

residue directly.This paper is organized in five sections. Section 2 explains the pixel domain Intra 4x4

Prediction for all modes and its computational complexity. Section 3explains the

computational complexity of finding residue and its standard forward transform. Section 4

explains the novel method to find key pixel domain predicted values, transformed

coefficients and its computational complexity. Finally,in Section 5, the comparison and the

inferences 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 in

the same slice. For a typical block of luma or chroma samples, there is a relatively high

correlation between samples in the block and samples that are immediately adjacent to theblock. Intra prediction therefore uses samples from adjacent, previously coded blocks to

predict the values in the current block [11].

There are four different Intra prediction types based on block size and components. They

are Intra 16x16, Intra 8x8 and Intra 4x4 for Luma components and Intra Chroma for Chroma

components. Intra 16x16 Prediction has 4 different ways of prediction, namely, Vertical,

Horizontal, DC and Plane Prediction. There are 9 different Intra 4x4 Prediction modes

namely, 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 followed

by Intra 8x8 Prediction. Intra Chroma modes are DC, Horizontal, Vertical and Plane

Prediction. 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, each

4x4 sub-macroblock is subjected to all nine prediction modes. The 4x4 sub-macroblock is

predicted by all nine different prediction techniques. The residue 4x4 sub-macroblock is

found 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 transformed

and quantized. The quantized coefficients are subjected to variable length coding, by then the

rate, i.e., bitlength is calculated for each prediction mode. The quantized coefficients are

dequantized and inverse transformed to get reconstructed residue 4x4 sub-macroblocks.


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These reconstructed residue 4x4 sub-macroblocks are added with already predicted 4x4 sub-

macroblocks to get reconstructed 4x4 sub-macroblocks. The distortions are calculated

between original 4x4 sub-macroblock and reconstructed 4x4 sub-macroblocks, by means of

Sum 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.

= + . (1)The minimum RD-Cost will decide the mode for the given 4x4 sub-macroblock. The same

process is continued for other fifteen 4x4 submacroblocks in a Macroblock. This way of

finalizing Intra 4x4 Prediction modes are followed by Joint Motion (JM) Group [12] and

X264 [13]. The minimum RD-Cost among the four Intra 16x16 Prediction modes will decide

the best Intra 16x16 Prediction mode for the same Macroblock. The minimum RD-Cost

among the finalized Intra 4x4 Prediction modes and Intra 16x16 Prediction mode will decide

the Macroblock type and its mode(s) to coding. The RD-Cost calculation to find best Intra

mode is done for all Macroblocks in all frames of a video sequence.

The metric for computational complexity used here is number of additions/subtractions

and number of shifts. The intra 4x4 prediction mainly depends upon the eight pixels in the

previous 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 predicted

block.

, 1 = , 1 4 , 2 = , 1 4 , 3 = , 1 4 , 4 = , 1 4The computational complexity of Vertical Prediction is zero, as there is only loading

operation.Horizontal Prediction (HP) mode copies right the left four pixels (I, J, K and L) as predicted

block.

1, = , 1 42, = , 1 43, = , 1 44, = , 1 4The computational complexity of Horizontal Prediction is zero, as there is only loading

operation.

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.

= + + + + + + + + 4 3If the any of top or left four pixels are not available, the is calculated by averaging the

available four pixels.

= + + + + 2 2= + + + + 2 2


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If the current block is first in the frame, then is the predicted as half of Pixel bitwidth.

, = , 1 4, 1 4Considering 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. The

other 9 pixels are copied from the seven unique pixel values. The 7 uniquepixels are

calculated as follows.

1,1 = + 1 + + 2 21,2 = 2,1 = + 1 + + 2 21,3 = 2,2 = 3,1 = + 1 + + 2 21,4 = 2,3 = 3,2 = 4,1 = + 1 + + 2 22,4 = 3,3 = 4,2 = + 1 + + 2 23,4 = 4,3 = + 1 + + 2 24,4 = + 1 + + 2 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.

1,1 = 2,2 = 3,3 = 4,4 = + 1 + + 2 21,2 = 2,3 = 3,4 = + 1 + + 2 21,3 = 2,4 = + 1 + + 2 21,4 = + 1+ +2 22,1 = 3,2 = 4,3 = + 1 + + 2 23,1 = 4,2 = + 1 + + 2 24,1 = + 1 + + 2 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.

1,1 = 3,2 = + + 1 11,2 = 3,3 = + + 1 11,3 = 3,4 = + + 1 11,4 = + + 1 12,1 = 4,2 = + 1+ + 2 22,2 = 4,3 = + 1+ + 2 22,3 = 4,4 = + 1+ + 2 2

2,4 = + 1 + + 2 23,1 = + 1 + + 2 2

4,1 = + 1 + + 2 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 be

derived from DDL and DDR Predictions.


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1,1 = 2,3 = + + 1 11,2 = 2,4 = + 1 + + 2 21,3 = + 1 + + 2 21,4 = + 1 + + 2 22,1=

3,3=+ + 1

12,2 = 3,4 = + 1 + + 2 23,1 = 4,3 = + + 1 13,2 = 4,4 = + 1 + + 2 24,1 = + + 1 14,2 = + 1 + + 2 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 unique

pixel values and the other eight values can be derived from DDL and VR Predictions.

1,1 = + + 1 11,2 = 3,1 = + + 1 11,3 = 3,2 = + + 1 11,4 = 3,3 = + + 1 12,1 = + 1 + + 2 22,2 = 4,1 = + 1 + + 2 22,3 = 4,2 = + 1 + + 2 22,4 = 4,3 = + 1+ + 2 23,4 = + + 1 14,4 = + 1 + + 2 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 be

derived from DDR and HD Predictions and one pixel value is L itself.

1,1 = + + 1 11,2 = + 1 + + 2 21,3 = 2,1 = + + 1 11,4 = 2,2 = + 1 + + 2 22,3 = 3,1 = + + 1 12,4 = 3,2 = + 1 + + 2 23,3 = 3,4 = 4,1 = 4,2 = 4,3 = 4,4 = The 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. The

computational Complexity of Intra 4x4 Prediction is 142 additions and 85 shifts.

SECTION 3: COMPLEXITY OF FINDING RESIDUE AND FORWARD

TRANSFORM

Each predicted 4x4 sub-macroblock is subtracted from the original 4x4sub-macroblockto get

residue 4x4 sub-macroblocks. The computational complexity for one 4x4 sub-macroblock is


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16 subtractions and zero shift. The computational complexity of finding residue for all nine

prediction modes is 9x16 subtractions, i.e., 144 addition and zero shiftoperations.

The residue sub-macroblock is forward transformed using the following equation.

= = 1 12 1 1 11 21 11 2 1 12 1 =

This forward transform (It is a matrix multiplication) is simplified with additions and shifts

only 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)

end

for row = 1 to 4

g(row,1) = f(row,1) + f(row,2)

g(row,2) = f(row,3) + f(row,4)


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1,1 = + 1 + + 2 21,2 = + 1 + + 2 21,3 = + 1 + + 2 21,4 = + 1 + + 2 2

2,4 = + 1 + + 2 23,4 = + 1 + + 2 24,4 = + 1 + + 2 21,1 = + 1 + + 2 21,2 = + 1 + + 2 22,1 = + 1 + + 2 23,1 = + 1 + + 2 24,1 = + 1 + + 2 22,4 = + 1 + + 2 21,1 = + + 1 11,2 = + + 1 11,3 = + + 1 11,4 = + + 1 11,4 = + + 1 13,4 = + + 1 11,1 = + + 1 12,1 = + + 1 13,1 = + + 1 14,1 = + + 1 1

The DC Prediction has only one unique equation, the Diagonal-Down-Left Prediction has 7

equations, the Diagonal-Down-Right Prediction has 5 equations, the Vertical-Right

Prediction has 4 equations, the Horizontal-Down Prediction has 4 equations, the Vertical-Left

Prediction has 2 equations and the Horizontal-Up Prediction has 1 equation. The other pixel

values are copied from the already calculated pixel values by the above-said 24

equations.Thus reduces the computational complexity to 67 addition and 37 shiftoperations.But those 24 equations are split intelligently and modified as follows.

= + + 1= + + 1= + + 1= + + 1= + + 1= + + 1= + + 1

= + + 1= + + 1= + + 1= + + 1= + + 11,2 = 11,3 = 11,4 = 11,1 = 1


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1,4 = 13,4 = 11,1 = 12,1 = 13,1= 14,1 = 11,1 = + + + 31,1 = + 21,2 = + 21,3 = + 21,4 = + 22,4 = + 23,4 = + 24,4 = + 1 + 1 21,1 = + 21,2 = + 2

2,1 = + 23,1 = + 24,1 = + 22,4 = + 1 + 1 2Now, computational complexity of finding pixel domain predictions for all nine modes is 42

addition and 26 shift operations.

The novel approach of finding transform domain residue 4x4 sub-macroblocks is explained

hereafter. The facts of transform domain coefficients are given below.

1) The pixel domain predicted 4x4 sub-macroblock of each mode has spatialredundancy. 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 toexploit the spatial redundancy.

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 ORIGINAL

The original 4x4 sub-macroblock is forward transformed and its computational complexity is

64 additions and 16 shifts.

=


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VERTICAL PREDICTION

The unique pixel predicted values are A, B, C and D. There are four unique transform

coefficients _ and they are calculated using these values as follows.

= +

1 = = + 1 = _ 1,1 = + 2_ 1,2 = 1 1+ 1 2_ 1,3 = 2_ 1,4 = 1 1 1 2_ 2,1 = _ 2,2 = _ 2,3 = _ 2,4 = 0_ 3,1 = _ 3,2 = _ 3,3 = _ 3,4 = 0_ 4,1 = _ 4,2 = _ 4,3 = _ 4,4 = 0The computational complexity to find transform domain Vertical Prediction modecoefficients is 8 additions and 6 shifts.The transform domain residue for Vertical Prediction

Mode is calculated by subtracting these four transform coefficients from original transform

coefficients.

_ 1,1 = 1,1 _ 1,1_ 1,2 = 1,2 _ 1,2_ 1,3 = 1,3 _ 1,3_ 1,4 = 1,4 _ 1,4The other values of _ is copied from respective values.The computationalcomplexity to find transform domain residue coefficients of Vertical Prediction mode is 4

additions and zero shifts.

HORIZONTAL PREDICTION

The unique pixel predicted values are I, J, K and L. There are four unique transform

coefficients _ and they are calculated using these values as follows.= + 1 = = +

1 =

_ 1,1 = + 2_ 2,1 = 1 1 + 1 2_ 3,1 = 2_ 4,1 = 1 1 1 2_ 1,2 = _ 2,2 = _ 3,2 = _ 4,2 = 0_ 1,3 = _ 2,3 = _ 3,3 = _ 4,3 = 0_ 1,4 = _ 2,4 = _ 3,4 = _ 4,4 = 0


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The computational complexity to find transform domain Horizontal Prediction mode

coefficients is 8 additions and 6 shifts.The transform domain residue for Horizontal

Prediction Mode is calculated by subtracting these four transform coefficients from original

transform coefficients.

_ 1,1 = 1,1 _ 1,1_ 2,1 = 2,1 _ 2,1_ 3,1 = 3,1 _ 3,1_ 4,1 = 4,1 _ 4,1The other values of _ is copied from respective values.The computationalcomplexity to find transform domain residue coefficients of Horizontal Prediction mode is 4


DC PREDICTION

There is one unique transform coefficient

_ calculated as follows.

_ 1,1 = 1,1 4The computational complexity to find transform domain DC Prediction mode coefficients is

zero additions and 1 shift. The transform domain residue for DC Prediction Mode is

calculated by subtracting this one transform coefficient from original transform coefficient.

_ 1,1 = 1,1 _ 1,1The other values of _ is copied from respective values.The computationalcomplexity to find transform domain residue coefficients of Vertical Prediction mode is 4


DIAGONAL-DOWN-LEFT PREDICTION

There are ten unique transform coefficients _ calculated as follows._00 = 1,1 + 4,4_01 = 1,1 4,4_02 = 1,3 + 2,4_03 = 1,3 2,4_04 = 1,2 + 3,4_05 = 1,2 3,4_06 = 1,4 2_07 = 1,4 3 + 1,4 1_08 = _02 1 + _02_09 = _05 1 + _05_10 = _04 1_11 = _00 + _06_12 = _01 + _03_13 = _03 1


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_ 1,1 = _11 + _08 + _10_ 1,2 = _12 1 + _09_ 1,3 = _00 _02_ 1,4 = _12 _05

_ 2,2 = _00 + _04 2 _08 _07_ 2,3 = _01 _13 1 _05_ 2,4 = _00 _04 1 + _02 _04_ 3,3 = _11 _02 _10_ 3,4 = _12 + _13 _09_ 4,4 = _00 + _02 3 _04 2 _07The other coefficients are copied from those 10 unique coefficients.

_ 2,1 = _ 1,2_ 3,1 = _ 1,3_ 4,1 = _ 1,4_ 3,2 = _ 2,3_ 4,2 = _ 2,4_ 4,3 = _ 3,4

The computational complexity to find transform domain coefficients of Diagonal-Down-Left

Prediction mode is 31 additions and 13 shifts. The transform domain residue for Diagonal-

Down-Left Prediction Mode is calculated by subtracting these transform coefficients from

original transform coefficient. The computational complexity to find transform domain

residue coefficients of Diagonal-Down-Left Prediction mode is 16 additions and zero shifts.

DIAGONAL-DOWN-RIGHT PREDICTION

There are ten unique transform coefficients

_ calculated as follows.

_00 = 1,1 + 3,1_01 = 1,2 + 4,1_02 = 1,1 3,1_03 = _02 1 + _02_04 = 1,2 + 2,1_05 = _04 1 + _04_06 = 1,2 2,1_07 = 1,2 4,1_08 = _06 + _07

_09 = 1,1,5 2_10 = 1,1 + _09 1_11 = _00 1_12 = _01 + _09_13 = _01 1_14 = _11 1_15 = _06 1_ 1,1 = _05 + _11 + _12_ 1,2 = _03 _08 1


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_ 1,3 = _01 _04_ 1,4 = _02 _08_ 2,2 = _05 + _10 _14 _13 1_ 2,3 = _07 _15 1 _02

_ 2,4 = _00 _04 + _11 _13_ 3,3 = _12 _11 _04_ 3,4 = _03 _06 _07 _15_ 4,4 = _14 _01 _04 3 + _10_ 2,1 = _ 1,2_ 3,1 = _ 1,3_ 4,1 = _ 1,4_ 3,2 = _ 2,3_ 4,2 = _ 2,4_ 4,3 = _ 3,4

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 transform

coefficients from original transform coefficient. The computational complexity to find

transform domain residue coefficients of Diagonal-Down-Right Prediction mode is 16


VERTICAL-RIGHT PREDICTION

All the transform coefficients _ calculated as follows._00 = 1,4 + 3,1_01 = 1,4 3,1_02 = 2,1 + 1,2_03 = 2,1 1,2_04 = 1,1 + 1,1_05 = 1,1 1,1_06 = 1,3 1,1_07 = _04


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_14 = _01 + _03_15 = _14 + _03_16 = _05 + _06_17 = _16 1 + _16

_18 = 1,2 1,2_19 = _18 1 + _18_20 = _04 + _07_ 1,1 = _02 + _05 + _08_ 1,2 = _13 _10 1_ 1,3 = _02 _08_ 1,4 = _10 _12_ 2,1 = _11 + _16 + _18_ 2,2 = _20 _03 1 + _09_ 2,3 = _11 + _13 _18_ 2,4 = _04 _03 + _05 _09 1_ 3,1 = _00_ 3,2 = _18 _14 1 + _16_ 3,3 = _00 + _06_ 3,4 = _17 _14 _18 2_ 4,1 = _15 + _17 + _19_ 4,2 = _06 _01 1 _04 _07_ 4,3 = _15 _12 _19_ 4,4 = _08 _01 _20

The computational complexity to find transform domain coefficients of Vertical-Right

Prediction mode is 55 additions and 12 shifts. The transform domain residue for Vertical-

Right Prediction Mode is calculated by subtracting these transform coefficients from original

transform coefficient. The computational complexity to find transform domain residue

coefficients of Vertical-Right Prediction mode is 16 additions and zero shifts.

HORIZONTAL-DOWN PREDICTION

All the transform coefficients _ calculated as follows._00 = 1,2 + 4,1_01 = 1,2 4,1_02 = 1,1 + 4,1_03 = 1,1 4,1

_04 = 1,1 + 3,1_05 = 1,1 3,1_06 = 1,1 + 3,1_07 = 1,1 3,1_08 = 2,1 + 2,1_09 = 2,1 2,1_10 = _05 + _07_11 = _05 _07_12 = _00 + _02_13 = _00 _02


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_14 = _13 + _00_15 = _12 + _02_16 = _01 + _03_17 = _01 _03

_18 = _16 + _03_19 = _17 + _01_20 = _04 1 + _04_21 = _08 1_22 = _21 + _08_23 = _04 + _06 1_24 = _04 _06 1_25 = _11 + _09_26 = _11 _09_27 = _10 1 + _10_ 1,1 = _12 + _23 + _21_ 1,2 = _25 _18_ 1,3 = _13_ 1,4 = _19 + _25 1 + _25_ 2,1 = _16 1 + _27_ 2,2 = _20 _15 1 + _22_ 2,3 = _09 _17 1 + _25_ 2,4 = _14 + _24 1 _06 _08_ 3,1 = _12 _21_ 3,2 = _27 _18 _09_ 3,3 = _24 _13_ 3,4 = _19 _10 _09 1 _09_ 4,1 = _16 _10_ 4,2 = _06 _15 _22 _23 1_ 4,3 = _26 _17 _09 + _26 1_ 4,4 = _14 _20 + _21

The computational complexity to find transform domain coefficients of Horizontal-Down

Prediction mode is 56 additions and 12 shifts. The transform domain residue for Horizontal-

Down Prediction Mode is calculated by subtracting these transform coefficients from original


coefficients of Horizontal-Down Prediction mode is 16 additions and zero shifts.

VERTICAL-LEFT PREDICTION

All the transform coefficients _ calculated as follows._00 = 1,2 + 2,4_01 = 1,2 2,4_02 = 1,1 + 3,4_03 = 1,1 3,4_04 = 1,3 + 1,4_05 = 1,3 1,4_06 = 1,4 + 1,3


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_07 = 1,4 1,3_08 = 1,4 + 1,2_09 = 1,4 1,2_10 = _00 + _02_11 = _00 _02_12 = _10 + _00_13 = _11 _02_14 = _01 + _03_15 = _01 _03_16 = _01 + _14_17 = _15 _03_18 = _09 + _05_19 = _09 _05_20 = _08 1 + _08_21 = _06 1_22 = _04 + _08 1_23 = _04 _08 1_24 = _07 1 + _07_25 = _18 1 + _18_26 = _19 1 + _19_ 1,1 = _10 + _21 + _22_ 1,2 = _14 1 _26_ 1,3 = _10 _21_ 1,4 = _14 + _19_ 2,1 = _07 + _16 + _18_ 2,2 = _12 _06 1 _06 _20_ 2,3 = _16 _07 + _26_ 2,4 = _12 _04 + _21 + _21 _22 1_ 3,1 = _11_ 3,2 = _15 _07 1 _18_ 3,3 = _11 _23_ 3,4 = _07 2 + _15 _25_ 4,1 = _24 + _17 + _25_ 4,2 = _04 + _06 + _13 + _23 1_ 4,3 = _17 _24 _19_ 4,4 = _13 + _20 _21

The computational complexity to find transform domain coefficients of Vertical-Left

Prediction mode is 56 additions and 14 shifts. The transform domain residue for Vertical-LeftPrediction Mode is calculated by subtracting these transform coefficients from original


coefficients of Vertical-Left Prediction mode is 16 additions and zero shifts.


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HORIZONTAL-UP PREDICTION

All the transform coefficients _ calculated as follows._00 = 2,1 + 3,1_01 = 2,1 3,1_02 = 3,1 + 4,1_03 = 3,1 4,1_04 = 4,1 + 2,4_05 = 4,1 2,4_06 = 2,1 + _00_07 = _01 3,1_08 = _04 _09 = 1 + _10 = _05 1 + _05 + _11 = _05 _09_12 = 4,1 + _08_13 = 4,1 _08_14 = _07 + _03 1+ _03_15 = _02 _08 _ 1,1 = _00 + _02 + _04 + _09 1_ 1,2 = _06 + _03 + _11_ 1,3 = _01_ 1,4 = _14 + _10_ 2,1 = _00 + _02 1 + _02 3_ 2,2 = _06 _12 1 _12_ 2,3 = _01 _05 1 _03_ 2,4 = _14 1 _03 + _12_ 3,1 = _00 _08 1 _08_ 3,2 = _06 _02 1 _02 _11_ 3,3 = _01 _03 1_ 3,4 = _07 + _02 _10_ 4,1 = _00 _02_ 4,2 = _06 _15 2 _15 + _12_ 4,3 = _01 _03 _05 2 + _03_ 4,4 = _07 + _08 + _13 1 + _13

The computational complexity to find transform domain coefficients of Horizontal-Up

Prediction 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 residue

coefficients 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 are

compared here. The computational complexity of Pixel domain Intra 4x4 Prediction for all


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the nine prediction modes in the reference softwares[12] and [13] tabulatedin the table 1

below.

Table 1 Complexity of Pixel domain Intra 4x4 prediction in reference software

Prediction Type

Reference

Software

Addition Shifts

Vertical 0 0

Horizontal 0 0

DC 8 1

Diagonal-Down-

Left21 14

Diagonal-Down-

Right21 14

Vertical-Right 26 16

Horizontal-Down 26 16

Vertical-Left 25 15Horizontal-Up 15 9

Total 142 85

The reference software does the pixel domain prediction first, and then finds the residue and

last it does the forward transform for all nine modes. In that order, the computational

complexity of the existing reference software is listed in the table 2.

The proposed method does the selective pixel domain prediction, calculates the selective

transform domain coefficients and finds the transform domain residue coefficients. The

computational complexity of the proposed method is listed in table 3.

Table 2 Complexity of Reference software during Intra 4x4 prediction

Process

Reference

Software

Addition Shift

Pixel domain

Prediction142 85

Finding Residue 144 0

Forward Transform 576 144

Total 862 229

Table 3 Complexity of Proposed method during Intra 4x4 prediction

ProcessProposed Method

Addition Shift

Pixel domain

Prediction42 26

Forward Transform 361 108

Finding Residue 105 0

Total 508 134


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The transform domain residue sub-macroblocks for all the nine modes are available by

508 additions and 134 shifts only, where as the existing reference software can produce the

same by 862 additions and 229 shifts. After finalizing mode, the corresponding pixel domain

prediction 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 the

residue 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 for

all its sixteen sub-macroblocks. The proposed method used (i) the unique equations for

prediction, (ii) the additive property of core forward transform and (iii) the spatial

redundancy of pixel domain predicted values, and reduced the computational complexity into

59% addition and 59% shift operations, thus saved 41% computational complexity. But the

proposed method did not compromise the accuracy of the results, thus maintaining the same

quality and bitrate. The same method can be extended to Intra 16x16 Prediction, Intra 8x8Prediction and Intra Chroma Predictions also in H.264 Encoder.

ACKNOWLEDGMENTThe author thanks RiverSilica Technologies Private Limited, INDIA for their

encouragement and support.

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a computationally efficient method to find transformed residue coefficients in intra

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