Implementation and Performance Analysis of 2 D Order 16 Integer Transforms in H 264 AVC and AVS video for HD video coding Madhu Peringassery Krishnan Multimedia Processing Lab University of Texas at Arlington TX USA Advisor Dr K R Rao Outline Discrete Cosine Transform DCT II Development of Integer Cosine Transform ICT ICT in H 264 AVC ICT in AVS video Order 16 ICT 2 D order 16 ICT and HD video coding Simple order 16 ICT SICT Modified order 16 ICT SICT binDCT L Implementation Performance Analysis Conclusions References Discrete Cosine Transforms ICT Discrete Cosine Transform DCT II 1 k n 0 1 2 N 1 2 D transform is separable into two 1 D transforms evaluated along rows followed by columns 2 Pros and Cons DCT II Pro Good energy compaction capability Fast algorithms for implementation Con Involves floating point arithmetic Mismatch between forward and inverse transform ICT 3 Pro Integer arithmetic implementation Avoid mismatch between forward and inverse transform Good energy compaction capability if well designed Fast algorithms can be developed Con Orthogonality depends on the elements of transform matrix Development of ICT Approximation of DCT II 3 where k is scaling factor and T is ICT Elements of T 3 Maintain relative magnitude and signs Posses dyadic symmetry 4 Orthogonality H 264 AVC encoder Typical block diagram of a H 264 AVC encoder 5 H 264 AVC decoder Typical block diagram of a H 264 AVC decoder 5 ICT in H 264 AVC ICT Order 4 ICT 6 Order 8 ICT 7 Other transforms 4 4 Hadamard transform applied to the DC coefficients of 4 4 integer transforms intra predicted 16 x 16 macroblocks Additional 2 2 Hadamard transform applied to DC coefficients of 4 4 integer transforms for chroma components ICT in H 264 AVC 4 x 4 ICT matrix 4 x 4 2 x 2 Hadamard matrix ICT in H 264 AVC 8 x 8 ICT matrix Non normalized Fast implementation 8 ICT in H 264 AVC Flow diagram for 8 x 8 ICT 9 ICT in H 264 AVC Sparse matrix factors where AVS video encoder Typical block diagram of AVS video encoder 10 AVS video decoder Typical block diagram of AVS video decoder 10 ICT in AVS video Order 8 ICT 11 Order 16 ICT extended from order 8 ICT Fast implementation ICT in AVS video Flow diagram for 8 x 8 ICT 9 ICT in AVS video Sparse matrix factors where Order 16 ICT Approximated from order 16 DCT II 12 General transform matrix 13 E denotes even symmetry and O denotes odd symmetry about the solid line mirror image and negative of mirror image Order 16 ICT and HD video coding Spatial correlation of HD videos are higher 14 where E is the ensemble average operator x n1 and x n2 intensity values of n1 n2 1 2 mean 1 2 standard deviation Better coding efficiency using higher order transforms Order 16 ICT and HD video coding Prediction error Difference between original and intra or inter predicted macroblocks r 1 Test sequences Resolution r 2 Mean Standard Deviation Mean Standard Deviation 0 8673 0 1284 0 7311 0 1434 0 7431 0 1820 0 6695 0 1967 Cactus 0 8542 0 1692 0 7483 0 1245 Vidyo1 0 7539 0 2401 0 4073 0 1842 0 6643 0 1982 0 3060 0 1569 Vidyo3 0 5474 0 1125 0 3221 0 2923 PartyScene 0 4953 0 1598 0 2019 0 1757 0 4517 0 2145 0 1966 0 2450 BasketballDrill 0 5594 0 1183 0 2301 0 1032 BQSquare 0 3543 0 2935 0 0964 0 1722 0 2879 0 1515 0 0473 0 1906 0 2177 0 1784 0 0355 0 2098 Kimono Parkscene Vidyo2 BQMall BlowingBubbles BaketballPass 1920 1080 HD 1280 720 HD 832 480 WVGA 416 240 WQVGA Table showing spatial correlation of prediction error Simple order 16 ICT SICT Extension of order 8 ICT 15 Low complexity Comparable transform coding gain with DCT II Plot 1 Transform matrix of order 16 SICT for AVS video Requires 24 shifts and 88 additions Simple order 16 ICT SICT Transform matrix of order 16 SICT for H 264 AVC Requires 20 shifts and 80 additions Simple order 16 ICT Flow diagram 16 x 16 SICT 15 Simple order 16 ICT Sparse matrix factors H 264 AVC where AVS video where where and order of input as shown in flow diagram Modified order 16 ICT Low complexity more complex than SICT Comparable transform coding gain better than SICT Steps involved in development 9 Order 8 ICT of H 264 AVC or AVS video is borrowed as the even part T8e Modified dyadic symmetry of odd part of order 16 DCT II symmetry M8o 9 Modified order 16 ICT Transform matrix of order 16 MICT for H 264 AVC Modified order 16 ICT Transform matrix of order 16 MICT for AVS video Modified order 16 ICT Elements x1 x3 x15 are 11 11 11 9 8 6 4 1 M8o is implemented in three stages M8o M1 M2 M3 Constraints for M1 M2 M3 Contain integers Small magnitude Sparse Orthogonality Requires 32 shifts and 150 additions Modified order 16 ICT Flow diagram 16 x 16 MICT shifts for M8o not shown for clarity 9 Modified order 16 ICT Sparse matrix factors H 264 AVC where AVS video where where and order of input as shown in flow diagram Order 16 binDCT L Based on Loeffler et al factorization 16 Planar rotation in DCT II represented as lifting steps shears 17 where Order 16 binDCT L Rotation needing 4 multiplications and 2 additions implemented using 3 multiplications and 3 additions Irrational parameters represented as dyadic rational coefficients Coding efficiency improved by tuning the approximations Involves 51 shifts and 107 additions Order 16 binDCT L Flow diagram for 16 x 16 binDCT L 18 Implementation in H 264 AVC JM 17 2 reference software 19 H 264 high profile Integration of SICT MICT and binDCT L Defining a parameter for selecting them tLCT Simulations run on an i7 quad 4 2 60 GHz processor 6GB RAM Group of pictures GOP size 8 GOP structure IBBBBBBP Intra frame period 0 5 s R D optimization on QP 22 27 32 37 Reference frames 2 Fast motion estimation on Search range 32 Deblocking filter on Entropy coding CABAC Configuration parameters I Intra predicted frames P Predicted frames B Bidirectionally predicted Implementation in AVS video RM 52e reference software 20 AVS video enhanced profile Integration of SICT MICT and binDCT L Defining a parameter for selecting them tLCT Simulations run on an i7 quad 4 2 60 GHz processor 6GB RAM Group of pictures GOP size 8 GOP structure IBBBBBBP Intra frame period 0 5 s R D optimization on QP 22 27 32 37 Reference frames 2 Fast motion estimation on Search range 32 Deblocking filter on Entropy coding CABAC Configuration parameters Transform Coding gain Measures energy compaction efficiency of transforms Source 1 D zero mean unit variance first order Markov process Transform coding gain where domain 21 is the covariance of the coefficients in transform Transform
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