PROJECT PERFORMANCE ANALYSIS OF INTEGER DCT OF DIFFERENT BLOCK SIZES Guided by Dr K R Rao Presented by Suvinda Mudigere Srikantaiah UTA ID 1000646539 Introduction to IntDCT Discrete cosine transform has been serving as the basic elements of video coding systems The integer discrete cosine transform is an integer approximation of the discrete cosine transform It can be implemented exclusively with integer arithmetic It proves to be highly advantageous in cost and speed for hardware implementations 1 Definition ICT matrix is in the form 2 3 I KJ where I is the orthogonal ICT matrix K is a diagonal matrix whose elements take on values that serve to scale the rows of the matrix J so that the relative magnitudes of elements of the ICT matrix I are similar to those in the DCT matrix The matrix J is orthogonal with elements that are all integers Transforms used in some standards Standard Transform 1 MPEG 4 part 10 H 264 2 WMV 9 8 X 8 4 X 4 integer DCT 4 X 4 2 X 2 Hadamard 8 X 8 8 X 4 4 X 8 4 X 4 integer DCT 3 AVS China Asymmetric 8 X 8 integer DCT Table no 1 Transforms used in standards H 264 WMV 9 and AVS china 4 I DCT The forward Discrete Cosine Transform DCT of N samples is formulated by 11 for u 0 1 N 1 where The function f x represents the value of the xth sample of the input signal F u represents a Discrete Cosine Transformed coefficient for u 0 1 N 1 First of all we apply this transformation to the rows then to the columns of image data ma IDCT The Inverse Discrete Cosine Transform IDCT of N samples is formulated by for x 0 1 N 1 where The function f x represents the value of the xth sample of the input signal F u represents a Discrete Cosine Transformed coefficient for u 0 1 N 1 For image decompression we use this DCT DCT II The DCT II is probably the most commonly used form and is often simply referred to as the DCT 6 Given an input function f i j over two integer variables i and j a piece of an image the 2D DCT transforms it into a new function F u v with integer u and v running over the same range as i and j The general definition of the transform is where i u 0 1 M 1 j v 0 1 N 1 and the constants C u or C v are determined by where l u v Taking the example of the standard H 264 H 264 4 uses an adaptive transform block size 4 X 4 and 8 X 8 high profiles only For improved compression efficiency H 264 also employs a hierarchical transform structure The DC coefficients of neighboring 4 X 4 transforms for the luma signals are grouped into 4 X 4 blocks and transformed again by the Hadamard transform For blocks with mostly flat pel values there is significant correlation among transform DC coefficients of neighboring blocks Therefore the standard specifies the 4 X 4 Hadamard transform for luma DC coefficients for 16 X 16 Intra mode only and 2 X 2 Hadamard transform for chroma DC coefficients II ORDER 4 INTEGER TRANSFORM The 4X4 IntDCT matrix is obtained using matrix H The varables a b c are as follows Thus Order 4 Integer transform III ORDER 8 INTEGER TRANSFORM Consider the ICT of a one dimensional data vector X of size 8 7 This ICT is implemented by premultiplying X by the orthogonal matrix C given by IV ORDER 16 INTEGER TRANSFORM Order 16 ICT has been shown to be very close to order 16 DCT 8 A simple integer transform for video coding is considered and its test is based on a set of CIF sequences The order 16 transform considered is an extended version of the order 8 ICT adopted in AVS As shown in 1 T8 is the order 8 transform matrix Without significant increase in complexity T8 can be extended to order 16 transform T16 as shown in 2 The normalized basis vectors of T16 have the waveforms similar to that of DCT 1 Order 8 transform matrix 1 T8 Order 8 transform matrix 5 2 Order 16 transform matrix derived from order 8 transform matrix 2 2 T16 Order 16 transform matrix 5 Performance Evaluation The efficiency of a transform is generally defined as its ability to decorrelate a vector or random elements In finding efficiency of integer DCT standard images are applied as an input signal Transforms considered will be DCT Integer DCT of different block sizes The following operations are performed a Variance distribution for I order Markov process 0 9 Plot and Tabulate b Normalized basis restriction error vs of basis function Plot and Tabulate c Obtain transform coding gains d Plot fractional correlation 0 1 References 1 2 3 4 5 6 7 N Ahmed T Natarajan and K R Rao Discrete Cosine Transform IEEE Trans Computers vol C 32 pp 90 93 Jan 1974 W K Cham and Y T Chan An Order 16 Integer Cosine Transform IEEE Trans Signal proc vol 39 issue no 5 pp 1205 1208 May 1991 W K Cham Development of integer cosine transforms by the principle of dyadic symmetry in Proc Inst Electr Eng I Commun Speech Vis vol 136 no 4 pp 276 282 Aug 1989 S Kwon A Tamhankar K R Rao Overview of H 264 MPEG 4 part 10 Special issue on Emerging H 264 AVC video coding standard J Visual Communication and Image Representation vol 17 pp 183 552 Apr 2006 W Cham and C Fong Simple order 16 integer transform for video coding IEEE ICIP 2010 Hong Kong Sept 2010 R Joshi Y A Reznik and M Karczewicz Efficient large size transforms for high performance video coding SPIE 0ptics Photonics vol 7798 paper 7798 31 San Diego CA Aug 2010 M Costa and K Tong A simplified integer cosine transform and its application in image compression Communications Systems Research Section TDA Progress Report pp 42 119 Nov 1994 8 9 10 11 12 13 14 15 A T Hinds Design of high performance fixed point transforms using the common factor method SPIE 0ptics Photonics vol 7798 paper 7798 29 San Diego CA Aug 2010 S Chokchaitam M Iwahashi and N Kambayashi Optimum word length allocation of integer DCT and its error analysis Elsevier Signal Processing Image Communication vol 19 pp 465 478 July 2004 C Wei P Hao Q Shi Integer DCT based Image Coding National Lab on Machine Perception Peking University Beijing 100871 China P C Yip and K R Rao The transform and data compression handbook Boca Raton FL CRC Press 2001 Y Zeng et al Integer DCTs and Fast Algorithms IEEE Trans Signal proc vol 49 No 11 Nov 2001 P Chen Y Ye and M Karczewicz Video Coding Using Extended Block Sizes ITU T Q 6 SG16 T09 SG16 C 0123 Geneva Jan 2009 B Lee et al A 16 16 Transform Kernel with …
View Full Document
Unlocking...