Performance Analysis and Implementation of Mode Dependent DCT/DST in H Performance Analysis and Implementation of Mode Dependent DCT/DST in H.264/AVC Priyadarshini Anjanappa Multimedia Processing Lab University of Texas at Arlington November 26, 2012 Advisor: Dr. K. R. Rao

Outline Motivation Overview of H.264 Overview of HEVC Mode Dependent DCT/DST Implementation Performance Analysis Conclusion Future Work

Motivation Transform coding: Basic coding tool in image and video compression to reduce spatial redundancies DCT-II used in recent video coding standards due to excellent energy compaction close to the optimal KLT Integer approximation of DCT-II used in H.264 Alternative Transforms proposed for HEVC Integer approximation of DST-VII for 4x4 luma intra prediction residuals in HEVC Revisiting Mode-Dependent DST/DCT implementation in HEVC to analyze the performance in H.264

Block Diagram of H.264 Encoder Typical H.264 encoder block diagram [1]

Block Diagram of H.264 Decoder Typical H.264 decoder block diagram [1]

Profiles and corresponding tools in H.264 [2] Profiles in H.264 Profiles and corresponding tools in H.264 [2]

Intra prediction Intra prediction samples for a 4x4 block [3] A through M are previously predicted pixels (b) Directions for intra prediction modes for 4x4 and 8x8 blocks [3]

Intra prediction modes (a) Intra prediction modes for 4x4 blocks [4] (b) Intra prediction modes for 16x16 blocks [4]

Partitions for Inter prediction Macroblock partitions for inter prediction in H.264 [4]

Integer DCT matrices in H.264 4x4 Forward Integer DCT Matrix [5] 4x4 Inverse DCT Matrix [5]

Secondary Transform for DC Coefficients in H.264 4x4 and 2x2 Hadamard Transform matrices [6] The sixteen 4x4 blocks with DC coefficients drawn as smaller blocks on upper left corner [6]

Scan order of transform coefficients [4] Scan order in H.264 DC Scan order of transform coefficients [4]

Block Diagram of HEVC Encoder Typical HEVC encoder block diagram [7]

Block Diagram of HEVC Decoder Typical HEVC decoder block diagram [8]

Unified Intra prediction in HEVC : 33 directional modes + DC + Planar Directional mode for an 8x8 block [7] Modes and angular intra prediction directions [7]

Intra prediction directions in HEVC Illustration of Intra prediction directions with mode names mapped to the angular directions [9]

Partitions for Inter prediction in HEVC

Quadtree coding structure in HEVC Subdivision of a CTB into CBs and TBs. Solid lines indicate CB boundaries and dotted lines indicate TB boundaries. Left: the CTB with its partitioning; right: the corresponding quadtree [7]

Core Transform : Integer DCT in HEVC Length-16 Integer DCT matrix in HEVC [7]

Integer DST in HEVC 4x4 Integer DST matrix used for intra prediction luma residual units in HEVC [7]

Adaptive scanning in HEVC Diagonal up-right scan (b) Horizontal scan (c) Vertical scan Scanning methods for 8x8 blocks in HEVC [7]

Mode Dependent DCT/DST Motivation for DST [10]: When prediction is performed from one-side, the energy in prediction error residuals increases as we go away from the boundary A sine transform is better adaptable to these prediction residual statistics Fast implementation of DST-VII is used in HEVC For block size of NxN with j, j as row and column indices of the 2-D DST matrix for DST-VII is given as Applied only to 4x4 luma intra prediction residuals

Mapping from intra prediction modes to DCT/DST in HM2.0 Unified Intra prediction direction Vertical Transform Horizontal Transform 0,5,6,12,13,22,23,24,25 VER to VER+8 DST DCT 1,8,9,16,17,30,31,32,33 HOR to HOR+8 2 DC 3,4,10,11,18,19,20,21 VER-8 to VER-1 7,14,15,26,27,28,29 HOR-8 to HOR-1 DCT/DST combinations applied to intra prediction modes[10]

Example of mapping a prediction mode to DCT/DST Intra prediction mode: Vertical DST in vertical direction DCT in horizontal direction

Categories of unified intra prediction modes in HEVC Category 1 oblique modes [12]: Prediction is performed from the decoded pixels from either the top row or the left column. The vertical mode 0 and the horizontal mode 1 are special cases of this oblique mode Category 2 oblique modes [12]: Prediction is performed from both the top row and the left column pixels DC mode [12]: Prediction is performed from an average of all available decoded pixels ; DCT is shown to be the optimal transform along both the directions

Category 1 oblique modes (a) Prediction from top row only [12] (b) Prediction from left-column only [12]

Category 2 Oblique modes A (dx,dy) pair denotes the horizontal and vertical distance respectively along the prediction direction for the pixel being predicted from the reference pixel [12]

Proposed Mapping from intra prediction modes to DCT/DST in H.264 Intra prediction direction Vertical Transform Horizontal Transform 0,3,7 Vertical, Diagonal Down-Left, Vertical-Right DST DCT 1,8 Horizontal, Horizontal –Up 2 DC 4,5,6 Diagonal Down-Right, Vertical-Left, Horizontal-Down

Forward Integer DCT matrix in H.264 Norms of the basis vectors along rows : Row 1: 2 Row 2: 10 (3.1623) Row 3: 2 Row 4: 10 (3.1623)

Inverse DCT matrix in H.264 Inverse Integer DCT matrix = 1 1 1 1 1 1/2 −1/2 −1 1 −1 −1 1 1/2 −1 1 −1/2 Norms of the basis vectors along rows : Row 1: 2 Row 2: 5/2 (1.5811) Row 3: 2 Row 4: 5/2 (1.5811)

Integer DST matrix in HEVC Norms of the basis vectors along rows : Row 1: 16398 (128.0547) Row 2: 16428 (128.1718) Row 3: 16398 (128.0547) Row 4: 16398 (128.0547)

Obtaining DST matrices for H.264 To implement the same DST matrix in H.264, the norm along each row of the DST matrix is made equal to the norm of the corresponding row of the DCT matrices. Divide rows of the DST matrix by the factor : Norm of row ′x′ of DST Norm of row ′x′ of DCT

Forward DST matrix in H.264 Forward Integer DST matrix = 0.4529 0.8590 1.1558 1.3119 1.8257 1.8257 0 −1.8257 1.3119 −0.4529 −1.1558 0.8590 1.3582 −2.0744 1.8274 −0.7161 Norms of the basis vectors along rows : Row 1: 2 Row 2: 3.1622 Row 3: 2 Row 4: 3.1623

Inverse DST matrix in H.264 Inverse Integer DST matrix = 0.4529 0.8590 1.1558 1.3119 0.9129 0.9129 0 −0.9129 0.4529 −0. 8590 −1.1558 1.3119 0.6791 −1.0372 0.9137 −0.3581 Norms of the basis vectors along rows : Row 1: 2 Row 2: 1.5812 Row 3: 2 Row 4: 1.5812

Implementation of Mode Dependent DCT/DST in H.264 Mode dependent DCT/DST is implemented in the H.264 Reference Software JM 18.4 [13] in the Main profile Matrix multiplication is implemented instead of fast implementation as the new transform matrices obtained are non-integer values It is verified that the default fast DCT implementation in H.264 reference software and DCT matrix multiplication give the same results Simulations are run on an i7 quad 4, 2.0 GHz processor, 8 GB RAM Performance of default fast DST implementation in HEVC is also analyzed using HEVC reference software HM 8.0 [14] in the Intra Main profile

BD PSNR gives the absolute PSNR gain at the same bitrate and BD Bitrate gives the percentage bitrate savings at the same PSNR BD PSNR and BD Rate [16] [17] are used to analyze the performance of the RD-curves Video sequences[15] belonging to HD (1920x1080, 1280x720), WVGA (832x480) and WQVGA (416x240) are used for evaluating the performance WVGA: Wide Video Graphics Array (Touch screen mobile phones support this resolution) [18] WQVGA: Wide Quarter Video Graphics Array (Hand-held internet- enabled devices support this resolution) [18] Only the first frame ( I frame) of the video sequences are considered for the analysis

Calculation of BD PSNR and BD Rate BD PSNR and BD Rate represent the average PSNR and bitrate differences respectively between two rate distortion (RD) curves [16] Fit a curve through four data points corresponding to QP = 16, 20, 24, 28 The data points are Y-PSNR values for BD PSNR and bitrate values for BD Rate A good interpolation curve through the four data points can be obtained by a third order polynomial of the form: SNR = a + b*bit + c*bit2 + d*bit3 where a, b, c, d are determined such that the curve passes through all the data points The difference between the RD curves is dominated by high bitrates. Hence logarithmic value of bitrate is considered for calculating BD Rate In the same way, we can do interpolation as a function of SNR as follows: SNR = a + b*SNR + c*SNR2 + d*SNR3 Based on the interpolation , find an expression for the integral of the curve The average difference is the difference between the integrals divided by the integration interval

Comparing Default H.264 and Default HEVC BD PSNR: 2.0212 dB BD Rate: -17.735% Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: -0.4913 dB BD Rate: 4.775%

Comparing Default H.264 and Default HEVC BD PSNR: 1.4722 dB BD Rate: -14.2433% Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: -0.4852 dB BD Rate: 5.1894%

Comparing Default H.264 and Default HEVC BD PSNR: 1.8785 dB BD Rate: -14.6427 % Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: -0.7315 dB BD Rate: 6.2691 %

Comparing Default H.264 and Default HEVC BD PSNR: 1.4754 dB BD Rate: -17.985 % Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: -0.3462 dB BD Rate: 4.6475 %

Comparing Default H.264 and Default HEVC BD PSNR: 1.3704 dB BD Rate: -20.3635 Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: 0.0665 dB BD Rate: -1.1473 %

Comparing Default H.264 and Default HEVC BD PSNR: 1.2773 dB BD Rate: -10.2026 % Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: -0.6996 dB BD Rate: 6.0669 %

Comparing Default H.264 and Default HEVC BD PSNR: 2.1567 dB BD Rate: -21.9681 % Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: -0.6369 dB BD Rate: 7.2692 %

Comparing Default H.264 and Default HEVC BD PSNR: 1.3025 dB BD Rate: -19.1702 % Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: -0.2102 dB BD Rate: 3.5532 %

Comparing Default H.264 and Default HEVC BD PSNR: 1.4856 dB BD Rate: -33.1268 % Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: -0.029 dB BD Rate: -0.4242 %

Comparing Default H.264 and Default HEVC BD PSNR: 2.053 dB BD Rate: -33.5926 % Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: 0.0216 dB BD Rate: -0.5157 %

Comparing Default H.264 and Default HEVC BD PSNR: 1.9721 dB BD Rate: -33.2696 % Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: 0.0851 dB BD Rate: -1.8388 %

Comparing Default H.264 and Default HEVC BD PSNR: 2.0659 dB BD Rate: -33.2327 % Comparing Default H.264 and Mode Dependent DCT/DST BD PSNR: 0.0422 dB BD Rate: -0.8327 %

Case BD PSNR (dB) BD Rate (%) 1 0.0192 -0.1817 2 -0.0277 0.2627 3 0.0239 -0.2468 4 0.0678 -0.7543 5 -0.0844 0.7942 6 -0.1595 1.4838 7 -0.0236 0.1937 8 -0.4913 4.775 9 -6.3851 82.9101 Input sequence: RaceHorses_416x240_30.yuv

Conclusions HEVC shows almost 1.5 – 2 dB performance improvement in quality over default H.264 Four out of 12 input sequences showed some performance improvement for Mode Dependent DCT/DST in H.264 The performance drop in most cases could be due to many reasons: Use of non-integer transform coefficients which results in the decrease in accuracy of reconstructed output The number of prediction modes is just 9 in case of H.264 and 33 in case of HEVC. The DCT/DST combinations are used for less number of prediction directions in the former case Selection of the best prediction mode and the corresponding mode dependent DCT/DST is not considered here

Future Work The scan order of the transformed coefficients can be modified to obtain better performance depending upon the intra prediction direction for each block Rate distortion optimization could be used to apply Mode Dependent DCT/DST only to the best performing modes Higher resolution video sequences can be used for analysis by using the High profiles in H.264 Analysis can be extended to block sizes other than 4x4 luma and also for chroma intra prediction residuals

References [1] S. -K. Kwon et al, "Overview of h.264/MPEG-4 part 10", Journal of Visual Communication and Image Representation, vol. 17, no. 2, pp. 186-216, April 2006 [2] D. Marpe et al, “The H.264/MPEG-4 AVC standard and its applications”, IEEE Communications Magazine, vol. 44, pp. 134- 143, Aug. 2006 [3] H.Kalva, “The H.264 video coding standard,” IEEE Multimedia, vol. 13, no. 4, pp.86-90, Oct. 2006 [4] I.E.Richardson, “The H.264 advanced video compression standard”, Wiley, Second edition, 2010 [5] Whitepaper: 4x4 Transform and Quantization in H.264/AVC:http://www.vcodex.com/files/H264_4x4_transform _whitepaper_Nov10.pdf [6] A. Puri et al, "Video coding using the H.264/MPEG-4 AVC compression standard", Signal Processing: Image Communication, vol. 19, pp. 793-849, Oct. 2004

[7] G. J. Sullivan et al, “Overview of high efficiency video coding (HEVC) standard”, Pre-publication draft, to appear in IEEE Trans. Circuits and Systems for Video Technology, Dec. 2012 [8] C. Fogg, “Suggested figures for the HEVC specification”, ITU-T / ISO-IEC Document: JCTVC-J0292r1, July 2012 [9] Analysis of coding tools in HEVC Test model (HM 1.0) - Intra Prediction: http://www.h265.net/2010/12/analysis-of- coding-tools-in-hevc-test-model-hm-intra-prediction.html [10] A. Saxena and F. Fernanades, "CE7: Mode-dependent DCT/DST for intra prediction in video coding”, ITU-T / ISO-IEC Document: JCTVC-D033, Jan. 2011 [11] V. Britanak et al, "Discrete cosine and sine transforms: General properties, fast algorithms and integer approximations", Academic Press - Elsevier, Oxford, UK, 2007

[12] A. Saxena and F. Fernandes, "Mode dependent DCT/DST for intra prediction in block-based image/video coding", IEEE ICIP, pp. 1685-1688, Sep. 2011 [13] H.264 Reference Software JM 18.4: http://iphome.hhi.de/suehring/tml/download/ [14] HEVC Reference Software HM 8.0 : http://hevc.kw.bbc.co.uk/trac/browser/tags/HM-8.0 [15] Test video sequences: ftp://ftp.tnt.uni- hannover.de/testsequences/ [16] G. Bjontegaard, "Calculation of average PSNR differences between RD curves", VCEG-M33, April 2001 [17] MATLAB source code for BD PSNR and BD Rate: http://www.mathworks.com/matlabcentral/fileexchange/27798- bjontegaard-metric/content/bjontegaard.m [18] Graphics Display Resolution: http://en.wikipedia.org/wiki/Graphics_display_resolution

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