Performance analysis of Integer DCT of different block sizes used in H 264 AVS China and WMV9 Aim To investigate performance analysis of integer DCT of block sizes 8X8 16X16 and 32X32 used in H 264 AVS China and WMV9 Abstract Discrete cosine transform DCT has been serving as the main component of video coding systems The integer discrete cosine transform Int DCT 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 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 For example order 16 integer transform is simple low computational complexity transform but has high coding efficiency This project discusses how the use of larger transforms especially in high resolution videos can provide higher coding gain The DCT based systems have huge advantage to image applications because they provide a high compression ratio However their coding systems are limited to operating in only lossy coding because distortion of decoded image is unavoidable with these lossy algorithms On the other hand the integer transform is becoming popular as a key technique to lossless and lossy unified waveform coding Especially the integer DCT is attractive as the unified coding comparable to the conventional DCT based algorithms Submitted by Suvinda Mudigere Srikantaiah UTA ID 1000646539 Email Suvinda mudigeresrikantaiah mavs uta edu Introduction In digital image processing data compression is necessary to improve efficiency in storage and transmission Transformation is one popular technique for data compression By first transforming correlated pixels into weakly correlated ones and after a ranking in their energy contents for example and retaining only the most significant components high compression ratio is possible Since inverse transformation is needed to reproduce the original image from the compressed data it is important that the transform process be simple and fast The family of orthogonal transforms is well suited for this application because the inverse of an orthogonal matrix is its transpose The discrete cosine transform DCT is widely accepted as having a high efficiency 1 The 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 transform Using the principle of dyadic symmetry 2 order 8 integer cosine transform ICT which has zero truncation errors was introduced This requires a small number as little as 2 bit representation and comparable efficiency to the DCT 3 Briefly an ICT matrix is in the form I KJ where I is the orthogonal ICT matrix and 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 Integer cosine transforms ICT can be generated from DCT II by replacing the real numbered elements of the DCT II matrix with integers keeping the relative magnitudes and orthogonal relationship among the matrix elements 6 The integer transform coefficients result in a computationally less intense procedure that implements similar energy concentration like DCT II It can be implemented using integer arithmetic without mismatch between encoder and decoder The orthogonality of ICT depends on the elements of the transform matrix for orders greater than four Due to this constraint the magnitudes of elements tend to be quite large for large ICTs 8 This led to the development of ICTs that are mutually orthogonal by using the principle of dyadic symmetry 5 Thus the elements in transform matrices can be selected without orthogonality constraint Transforms used in some standards 4 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 4 WMV 9 17 and AVS China 16 Insight into the project As part of an image compression system the role of the ICT is to de correlate the picture elements of image blocks for subsequent quantization and entropy encoding The order 8 ICT was derived using the principle of dyadic symmetry This concept gives a different development that leads to the order 16 ICT 5 Equations relating the elements of the ICT matrix so as to satisfy the orthogonality conditions among the columns of the ICT matrix are first written Then a search method is proposed to find integer solutions for these elements It is noticed that the coding performance of the Int DCT is similar to that of the conventional lossy DCT in a low bitrate but it is slightly worse than that of the conventional lossy DCT in a high bit rate because of rounding errors The aim of this project is to analyze performance of order 8 order 16 and order 32 integer transforms in H 264 AVS China and WMV9 It is essential to get a good understanding of the three technologies before moving ahead with the analysis It is also necessary for one to get a good grasp of discrete cosine transform on which integer transform is based So in the first section a brief description of the same is presented The next section an overview of the coding standards is given The third section deals with the extension of order 8 transform matrix to order 16 and order 32 transform matrices The last section discusses performance analysis of order 8 order 16 and order 32 integer transforms in H 264 AVS China and WMV9 I DCT In images videos the DCT II which represents a signal image as the sum of cosine functions with different frequencies is primarily used for transform coding DCT II is basically a tool that strives to achieve maximum compression efficiency without compromising
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