EE 5359: MULTIMEDIA PROCESSING PROJECT PERFORMANCE ANALYSIS OF INTEGER DCT OF DIFFERENT BLOCK SIZES USED IN H.264, AVS CHINA AND WMV9. Guided by Dr. K.R. Rao Presented by: Suvinda Mudigere Srikantaiah UTA ID: 1000646539Aim and Abstract Aim: To investigate performance analysis of integer DCT of block sizes 8X8, 16X16 and 32X32 used in H.264, AVS China and WMV9. Abstract: This project discusses how the use of larger transforms, especially in high resolution videos, can provide better performance. In particular, transforms of sizes larger than 4x4 or 8x8, especially 16x16 and 32x32 are proposed because of their increased applicability to the de-correlation of high resolution video signals.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].DCT to IntDCT DCT matrix elements are real numbers and for a 16-order DCT, 8 bits are needed to represent these numbers in order to ensure perfectly negligible image reconstruction errors due to finite-length number representation If the transform matrix elements are integers, then it may be possible to have a smaller number of bit representation and at the same time zero truncation errors. Moreover, the resultant cosine values are difficult to approximate in fixed precision integers, thus producing rounding errors in practical applications. Rounding errors can introduce enough error into the computations and alter the orthogonality property of the transformDefinition: 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 8 X 8, 4 X 4 integer DCT 2. WMV-9 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].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 matrixIDCT 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,vOVERVIEW OF CODING STANDARDS H.264, AVS CHINA AND WMV9Int DCT in H.264: H.264 video coding standard uses a transform for reduction of spatial correlation, quantization for bitrate control, motion compensated prediction for reduction of temporal correlation, and entropy encoding for reduction of statistical correlation. One of the important changes in H.264 to fulfill better coding performance was the introduction of Integer transform. It is multiplier free and reduces implementation complexity. In general, transform and quantization require several multiplications resulting in high complexity for implementation. So, for simple implementation, the exact transform process is modified to avoid the multiplications. Then the transform and quantization are combined by the modified integer forward transform, quantization, scaling.Int DCT in AVS China Audio Video Coding Standard (AVS) is the national standard of China. Its Enhanced Profile (EP) targets at high definition video coding. It is expected that the use of larger transform, especially in high resolution videos, can provide higher coding gain. The order-16 and order-32 transform proposed is an extended version of the order-8 ICT adopted in AVS. Without significant increase in complexity, order-8 transform matrix can be extended to order-16 and order-32 transform matrixInt DCT in WMV9 Windows Media 9 Series includes a variety of audio and video codecs, which are key components for authoring and playback of digital media. Floating point arithmetic is ruled out on the decoder side in wmv9 for several reasons, the important ones being the need to minimize decoder complexity, and the need to implement decoders that precisely match the specification so as to avoid mismatch. Floating point operations are not very portable across processors—their definitions usually involve some measure of tolerance, making them unsuitable for perfectly matching implementations. It is largely accepted that low-precision integer arithmetic is a desirable feature.EXTENDING ORDER 8 INTEGER TRANSFORM TO ORDER 16 AND ORDER 32Dyadic symmetry(1) Order-8 transform matrix (1) T8: Order 8 transform matrix [5].Extending order 8 to order 16 Denoting even symmetry with ‗E‘ and odd symmetry with ‗O‘ about the solid line represents mirror image and negative mirror image.(2) Order-16 transform matrix derived from order-8 transform matrix (2) T16: Order 16 transform matrix [5]. (2)H.264 The transform matrices of order 8, 16 and 32 for H.264 are shown below. Note the Orthogonality in all three cases:AVS China The transform matrices of order 8, 16 and 32 for AVS China are shown below. Note the Orthogonality in all three cases:WMV9 The transform matrices of order 8, 16 and 32 for WMV9 are shown below. Note the Orthogonality in all
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