Lecture 2: Introduction to Audio, Video & Image Coding Techniques (I) -- Fundaments. Tutorial 1. Acknowledgement and References for lectures 1 to 5
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1 Lecture : Introduction to Audio, Video & Image Coding Techniques (I) -- Fundaments Dr. Jian Zhang Conjoint Associate Professor NICTA & CSE UNSW COMP959 Multimedia Systems S 006 jzhang@cse.unsw.edu.au Acknowledgement and References for lectures to 5 Special thanks should go to Prof. Henry Wu (Prof. & Director of School of ECE,RMIT) for his great support to help me draft lecture slides Special thanks should go to Prof. John Arnold and A/Prof. Michael Frater (ADFA@UNSW) for their great support during my PhD study -- video coding and communication. Reference Books: M. Ghanbari, Video coding: an introduction to standard codecs, 999. Barry G. Haskell, Digital video: an introduction to MPEG -, 997. Yun Q. Shi, Image and video compression for multimedia engineering, 000. F. Pereira, The MPEG-4 book, 00 COMP959 Multimedia Systems Lecture Slide J Zhang Tutorial.5.3 Pixel Representation Tutorial Y C C Colour Space d b r For digital component signal (CCIR Rec 60), 8-bit digital variables are used, however:. Full digital range is not used to give working margins for coding and filtering.. RGB to Yd CbCr conversion is given by Yd Rd 6 C b G d 8 = + C r B d 8 Rd Yd 6 G d Cb 8 = B d Cr 8 The positive/negative values of U and V are scaled and zero shifted in a transformation to the Cb and Cr coordinates. where digital luminance, Yd, has a rang of (6-35) with 0 levels starting at 6, and digital chrominance difference signals, Cb and Cr, have a range of (6-40) with 5 levels centered at 8. COMP959 Multimedia Systems Lecture Slide 4 J Zhang
2 .5.4 Chrominance sub-sampling Tutorial Human vision is relatively insensitive to chrominance. For this reason, chrominance is often sub-sampled. Chrominance sub-sampling is specified as a three-element ratio..5.4 Chrominance sub-sampling Tutorial In 4:4:4 format: Y, Cr & Cb 70 x 576 pixels per frame In 4:: format: Y 70 x 576 and Cr & Cb 360 x 576 pixels per frame In 4::0 format: Y 70 x 576 and Cr & Cb 360 x 88 pixels per frame A commonly used format is 4::0 which is obtained by sub-sampling each colour component of 4:: source vertically to reduce the number of lines to 88; COMP959 Multimedia Systems Lecture Slide 5 J Zhang COMP959 Multimedia Systems Lecture Slide 6 J Zhang.5.5 Digital Video Formats Tutorial Common Intermediate Format (CIF): This format was defined by CCITT (TSS) for H.6 coding standard (teleconferencing and videophone). Several size formats: SQCIF: 88x7 pixels. QCIF: 76x44 pixels. CIF: 35x88 pixels. 4CIF: 704x576 pixels. Non-interlaced (progressive), and chrominance sub-sampling using 4::0. Frame rates up to 5 frames/sec. Introduction to audio, video & image coding techniques (I).. Spatial Redundancy in Images.. Lossless & Differential Coding (Entropy coding).3 Introduction to Image.4 Summary COMP959 Multimedia Systems Lecture Slide 7 J Zhang COMP959 Multimedia Systems Lecture Slide 8 J Zhang
3 .. Spatial Statistical Redundancy Spatial redundancy is existed among pixels within a single frame of image. Especially, neighboring pixels are highly correlated... Information Measurement -- Review Information Measure Consider a symbol x with an occurrence probability p, its info. content (i.e. the amount of info contained in the symbol) I = i( x) = log[ ] = log p( x) bits - p( x) Ref: H. Wu Lena image COMP959 Multimedia Systems Lecture Slide 9 J Zhang The smaller the probability, the more info. the symbol contains The occurrence probability somewhat related to the uncertainty of the symbol A small occurrence probability means large uncertainty or the info. Content of a symbol is about the uncertainty of the symbol. Average Information per Symbol Consider a discrete memoriless information source By discreteness, the source is a countable set of symbols By memoriless, the occurrence of a symbol in the set is independent of that of its preceding symbol. COMP959 Multimedia Systems Lecture Slide 0 J Zhang.. Information Measurement -- Review Look at a source that contains m possible symbols: {si, i=,..m} The occurrence probabilities: {Pi, i=,..m} The info. content of a symbol si; = i( s) = log p bits Ii i i.. Information Measurement -- Review Information Content Consider the two blocks of binary data shown below which contains the most information? Information Entropy The Entropy is defined as the average information content per symbol of the source. The Entropy, H, can be expressed as follows: H = m i = p i log p i From this definition, the entropy of an information source is a function of occurrence probabilities. The entropy reaches the Max. when all symbols in the set are equally probable. bits COMP959 Multimedia Systems Lecture Slide J Zhang COMP959 Multimedia Systems Lecture Slide J Zhang
4 .. Information Measurement -- Review Definition-- Image mean Given a two-dimensional (-D) image field with pixel value, x[n.m], n=,,,n and m=,,,m, the mean of the image is defined as the spatial average of the luminance values of all pixel, i.e., N M x = N M = = n m x[ n, m] COMP959 Multimedia Systems Lecture Slide 3 J Zhang (-5) Definition--Image variance Given a two-dimensional (-D) image field with pixel value, x[n.m], n=,,,n and m=,,,m, the variance of the image is defined as the average value of the squared difference between the value of an arbitrary pixel and the image mean, i.e., N M σ = ( x[ n, m] x) N M (-6) n= m=.. Information Measurement -- Review Image quality measurement (MSE,MAE,SNR and PSNR) Assume symbol xrepresents the original image and ˆx the reconstructed image, M and N the width and the height of respectively Mean squared error (MSE): M N MSE = [ x( m, n) xˆ ( m, n)] MN m= 0 n= 0 Mean absolute error (MAE): M N MAE = x( m, n) xˆ ( m, n) MN m= 0 n= 0 Peak signal to noise ration (PSNR): PSNR = 0log 0 55 db MSE COMP959 Multimedia Systems Lecture Slide 4 J Zhang (-7) (-8) (-9) Peak pixel value is assumed 55. Lossless & Predictive Coding (Entropy Coding).. Introduction to Predictive Coding..3 Introduction to DPCM coding Application of information content to a real image COMP959 Multimedia Systems Lecture Slide 5 J Zhang COMP959 Multimedia Systems Lecture Slide 6 J Zhang
5 Image Histogram The number of bits required to represent an image can be made based on the information content using an entropy (variable length coding) approach such as a Huffman code Highly probable symbols are represented by short code-words while less probable symbols are represented by longer code-words The result is a reduction in the average number of bits per symbol Entropy = 7.63 bits/pixel COMP959 Multimedia Systems Lecture Slide 7 J Zhang COMP959 Multimedia Systems Lecture Slide 8 J Zhang Example Fixed length coding Symbol Probability Codeword Codeword Length A B C D Example Entropy (Variable Length) Coding Symbol A B C D Probability Codeword Codeword Length 3 3 Average bits/symbol = 0.75* + 0.5* * * =.0 bits/pixel Average bits/symbol = 0.75* + 0.5* * *3 =.375 bits/pixel (A 30% saving with no loss) COMP959 Multimedia Systems Lecture Slide 9 J Zhang COMP959 Multimedia Systems Lecture Slide 0 J Zhang
6 Generation of Huffman Codewords If the symbol probabilities are known, Huffman codewords can be automatically generated. From Right to Left,. Two bottom-most branches are formed a node 3. Reorder probabilities into descending order Details are introduced in next two slides Note on Merging (left to right). Reorder in decreasing order of probability at each step. Merge the two lowest probability symbols at each step Note on Splitting (right to left). Split the symbol merged at that step into two symbols Tree Construction process COMP959 Multimedia Systems Lecture Slide J Zhang COMP959 Multimedia Systems Lecture Slide J Zhang ) Re-arrange the tree to eliminate crossovers, ) The coding proceeds from left to right, 3) 0 step up and step down. Code generation Truncated and Modified Huffman Coding Given the size of the code book is L, the longest codeword will reach L bits For a large quantities of symbols, the size of the code book will be restricted Truncated Huffman coding For a suitable selected L<L, the first L symbols are Huffman coded and the remaining symbols are coded by a prefix code, following by a suitable fixed-length code Second Order Entropy Instead of find the entropy of individual symbols, they can be grouped in pairs and the entropy of the symbol pairs calculated. This is called the SECOND ORDER ENTROPY. For correlated data, this will lead to an entropy closer to the source entropy. COMP959 Multimedia Systems Lecture Slide 3 J Zhang COMP959 Multimedia Systems Lecture Slide 4 J Zhang
7 Limitations of Huffman Coding Huffman codewords have to be an integer number of bits long. If the probability of a symbol is /3, the optimum number of bits to encode that symbol is -log (/3) =.6. Assigning either one or two bits leads to a longer code message than is the theoretically necessary The symbol probabilities must be known in the decoder size. If not, they must be generated and transmitted to the decoder with the Huffman coded data A larger of number of symbols results in a large codebook Dynamic Huffman coding scheme exists where the code words are adaptively adjusted during encoding and decoding, but it is complex for implementation. Arithmetic Coding It overcomes limitation of Huffman coding: non-integer length coding, and probability distribution can be derived in real-time It operates by replacing a stream of input symbols with a single floating point output number. Consider the following symbols with probabilities A sub-interval cab be defined by its lower end point and its width or lower and upper end points The sum of preceding Probabilities known as Cumulative Probability CP( s i ) = p( s ) i i j= Where CP(S)=0 is defined COMP959 Multimedia Systems Lecture Slide 5 J Zhang COMP959 Multimedia Systems Lecture Slide 6 J Zhang Arithmetic Coding Suppose we wish to encode the string: S; S; S3; S4; S5; S6; We start with the interval [L,H) and set to [0,) for 6 symbols. Since the first symbol is S, we pick up its subinterval [L,H) = [0.0,0.3), and any real symbols can be considered as disjoint to be divided in the same way. To encode the S, we use the same procedure as used in above to divide the interval [0,0.3) into six sub-intervals. We pick up the S subinterval [0.09,0.) The subinterval recursion is equivalent to the two recursions End point recursion and width recursion L new = Lcurrent + Wcurrent CPnew Low end point recursion W new = Wcurrent P( S ) i The width recursion COMP959 Multimedia Systems Lecture Slide 7 J Zhang COMP959 Multimedia Systems Lecture Slide 8 J Zhang
8 Arithmetic Decoding For encoding, the input is a source symbol string and the output is a subinterval (called the final subinterval). For our case, it is [ , ). Decoding sort of reverses what encoding has done. The decoder knows the encoding procedure and therefore has the information contained in the following figure The lower end falls into the subinterval associated with the symbol S which is first decoded. After the first symbol is decoded, 0.09< <0.!!!. The lower end is contained in the subinterval covers the S Repeat the process until the symbols S4; S5; S6 are subsequently decoded. Using Huffman coding to encode the same symbols It compares the lower end point of the final subinterval with all the end points in the above figure 0< <0.3!!! COMP959 Multimedia Systems Lecture Slide 9 J Zhang COMP959 Multimedia Systems Lecture Slide 30 J Zhang Human coding converts each source symbol into a fixed codeword (but variable length). The output of S; S; S3; S4; S5; S6 are: 00,0,,00,000,0 which is a 7-bit code string Arithmetic coding converts a source symbol to a code symbol string = ~ [ , ). Which is 5- bit code string This is a simple example about the arithmetic coding is more efficient than Human coding It is obvious that the width of the final subinterval becomes smaller when the length of the source symbol string become larger and larger. This was a big problem to widely apply the arithmetic coding Run-length Coding Ref: H.Wu In run-length coding, a run of consecutive identical symbols is combined together and represented by a single codeword. The coding of facsimile information is one application of run length coding. The various run-lengths are then represented by a variable length (e.g. Huffman) codeword. In the case of facsimile transmission, separate VLCs are defined for white and black Use an escape code (out side of symbol set or 0 ), followed by the run-length coded symbol and number of repetitions of symbol. Arithmetic coding now becomes an increasingly important coding COMP959 Multimedia Systems Lecture Slide 3 J Zhang COMP959 Multimedia Systems Lecture Slide 3 J Zhang
9 Run-length Coding (Example) [Ref: H. Wu].. Introduction to Differential Coding Strong correlation exists between adjacent pixel spatially Spatial redundancy is existed among pixels within a single frame of image. Especially, neighboring pixels are highly correlated. A pixel is coded based on the difference between its value and a predicted value. Run-length (using 0 as the escape code) coding DCT Coefficients Ref: H. Wu Lena image.3. Spatial Statistical Redundancy COMP959 Multimedia Systems Lecture Slide 33 J Zhang COMP959 Multimedia Systems Lecture Slide 34 J Zhang.. Introduction to Differential Coding By exploring spatial/temporal inter-pixel correlation, prediction and quantization coding scheme achieve efficiency and yet computationally simple coding technique. When the prediction error (difference error) is quantized, the differential coding is called Differential Pulse Code Modulation (DPCM) Where zi is current input pixel Where zi = n ai zi j= j is a linear prediction function of N previously reconstructed samples (Summation) = z f ( z,... ) z z n.. Introduction to Differential Coding In this approach, the preceding pixel on the video/image line is used to predict the next pixel. The prediction error is then transmitted Example (+7) 0 (+8) 03 (+) 96 (-3) 97 (-4) 04 (+) This approach achieves compression because the entropy of the prediction error is less than the entropy of the original image. The better the prediction, the lower the entropy of the prediction error. COMP959 Multimedia Systems Lecture Slide 35 J Zhang COMP959 Multimedia Systems Lecture Slide 36 J Zhang
10 .. Introduction to Differential Coding Lena image.. Introduction to Differential Coding This approach can be applied to a two dimensional predictor by taking advantage of vertical correlation as well. Example -D prediction error of Lena image Entropy = 3.06 bits/pixel COMP959 Multimedia Systems Lecture Slide 37 J Zhang -D prediction error of Lena image Entropy =.44. bits/pixel COMP959 Multimedia Systems Lecture Slide 38 J Zhang.. Introduction to Differential Coding Ref: H, Wu Coding efficiently Code assigner is a strategy to code the symbols of coefficients after the transform. Improve accuracy.3 Introduction to Image The major mechanism for loss in image/video codecs (encoder/decoder) is as a result of quantization However, when quantization is performed carefully in frequency domain, it is difficulty for a viewer to notice any degradation. Prediction error: e( n) = s( n) sˆ ( n) Where Reconstruction: sˆ( n) = f [ s '( n ), s '( n ), s '( n 3),...] s '( n) = sˆ ( n) + e'( n) COMP959 Multimedia Systems Lecture Slide 39 J Zhang Original JPEG (compressed 70%) COMP959 Multimedia Systems Lecture Slide 40 J Zhang
11 .3 Introduction to Image Linear The simplest form of quantize is a linear quantize where the quantize step is constant.3 Introduction to Image Linear/Non-linear For the case of the linear quantizer, a simple relationship exits between the number of symbols after quantization and the error introduced by quantization This approach is sensible for a signal with a uniform distribution of values such as an original image However, it makes very little sense for difference image where the differences are non-uniformly distributed about zero, For these types of signals, a non-linear quantization is needed. Maximum error = ± Half quantize step size COMP959 Multimedia Systems Lecture Slide 4 J Zhang COMP959 Multimedia Systems Lecture Slide 4 J Zhang.3 Introduction to Image Linear Quantizer Applied to a Difference Image.3 Introduction to Image Non-Linear Quantizer Applied to a Difference Image COMP959 Multimedia Systems Lecture Slide 43 J Zhang COMP959 Multimedia Systems Lecture Slide 44 J Zhang
12 .3 Introduction to Image Non-Linear Quantizer Transfer Function.3 Introduction to Image and HVS In most of the codecs, the quantization stepsize is controlled in such a way that distortion is as imperceptible as possible Much study has been conducted for the characteristics of the HVS (human visual system). It is well known that various features in video/image tend to mask the visibility of errors introduced by coding. These include: Edges, Motion and high luminance values Codec try to focus quantization errors in these regions. COMP959 Multimedia Systems Lecture Slide 45 J Zhang COMP959 Multimedia Systems Lecture Slide 46 J Zhang
Lecture 2: Introduction to Audio, Video & Image Coding Techniques (I) -- Fundaments
Lecture 2: Introduction to Audio, Video & Image Coding Techniques (I) -- Fundaments Dr. Jian Zhang Conjoint Associate Professor NICTA & CSE UNSW COMP9519 Multimedia Systems S2 2006 jzhang@cse.unsw.edu.au
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