In the name of Allah In the name of Allah the compassionate, the merciful the compassionate, the merciful
Digital Video Systems Digital Video Systems S. Kasaei S. Kasaei Room: CE 307 Room: CE 307 Department of Computer Engineering Department of Computer Engineering Sharif University of Technology Sharif University of Technology E- -Mail: Mail: skasaei@sharif.edu skasaei@sharif.edu E Webpage: http:// http://sharif.edu sharif.edu/~skasaei /~skasaei Webpage: Lab. Website: http:// http://ipl.ce.sharif.edu ipl.ce.sharif.edu Lab. Website:
Acknowledgment Acknowledgment Most of the slides used in this course have been provided by: Prof. of. Yao Yao Most of the slides used in this course have been provided by: Pr Wang (Polytechnic University, Brooklyn) (Polytechnic University, Brooklyn) based on the based on the book: book: Wang Video Processing & Communications Video Processing & Communications written by: Yao Yao Wang, Wang, Jom Jom Ostermann Ostermann, & , & Ya Ya- -Oin Oin Zhang Zhang written by: st edition, 2001, ISBN: 0130175471. Prentice Hall, 1 st edition, 2001, ISBN: 0130175471. Prentice Hall, 1 [SUT Code: TK 5105 .2 .W36 2001]. [SUT Code: TK 5105 .2 .W36 2001].
Chapter 8 Chapter 8 Foundation of Video Coding Part I: Overview & Binary Encoding
Outline Outline � Overview of video coding systems Overview of video coding systems � � Review of probability & information theory Review of probability & information theory � concepts concepts � Binary encoding: Binary encoding: � � Information theory bounds Information theory bounds � � Huffman coding Huffman coding � � Arithmetic coding Arithmetic coding � 6 Kasaei
Video Coding Video Coding � Video coding is an important application of video Video coding is an important application of video � processing. processing. � The goal of video coding is to The goal of video coding is to reduce the data rate reduce the data rate of a of a � video sequence (transmission, storage, & retrieval). video sequence (transmission, storage, & retrieval). � Channel bandwidth varies depending on application & Channel bandwidth varies depending on application & � transmission media (20 kbps~6 mbps). transmission media (20 kbps~6 mbps). � Two main classes of algorithms: Two main classes of algorithms: � � Waveform Waveform- -based ( based (pels pels & blocks). & blocks). � � Content Content- -dependent (objects dependent (objects’ ’ motion & behavior). motion & behavior). � � Two main types of algorithms: Two main types of algorithms: � � Lossless. Lossless. � � Lossy Lossy. . � 7 Kasaei
Video Coding Video Coding 8 Kasaei
Video Coding Video Coding Different types of redundancy redundancy to be to be Different types of � � removed/decreased in the compression algorithm removed/decreased in the compression algorithm include: include: Spatial redundancy (correlation between neighboring redundancy (correlation between neighboring Spatial 1. 1. pixel values), pixel values), Spectral redundancy (correlation between different redundancy (correlation between different Spectral 2. 2. color planes or spectral bands), color planes or spectral bands), Temporal redundancy (correlation between different redundancy (correlation between different Temporal 3. 3. frames in a video sequence), frames in a video sequence), Psychovisual redundancy (HVS), & redundancy (HVS), & Psychovisual 4. 4. Coding redundancy (entropy encoding). redundancy (entropy encoding). Coding 5. 5. 9 Kasaei
Components of a Coding System Components of a Coding System Model 10 Kasaei
Video Coding Techniques based Video Coding Techniques based on Different Source Models on Different Source Models Waveform-based techniques Content-dependent-techniques 11 Kasaei
Statistical Characterization Statistical Characterization of Random Sources of Random Sources f f n ( n ( n n - -th th sample) sample) each realization F ) . A continuous random process ( F . Fn Fn (RV) 12 Kasaei
Statistical Characterization Statistical Characterization of Random Sources of Random Sources � In statistical representation of image, each In statistical representation of image, each pixel pixel is considered is considered � as an RV RV . . as an � We think of a given We think of a given image image as a as a sample function sample function of an of an � ensemble of images . . ensemble of images Sample function, realization, or Fn Fn random image. sample sample Ensemble of images or F ). discrete random field ( F 13 Kasaei Fn (RV) (RV) Fn
Statistical Characterization Statistical Characterization of Random Sources of Random Sources � Source: A random sequence (discrete Source: A random sequence (discrete- -time random process), time random process), � � Ex 1: An Ex 1: An image image that follows a certain statistics: that follows a certain statistics: � � F F n represents the possible value possible value ( ( random value random value ) ) of the of the n n - -th th pixel of the image, pixel of the image, n represents the � n =( n =(m,n m,n). ). � f f n represents the actual value actual value taken. taken. n represents the � � Ex 2: A Ex 2: A video video that follows a certain statistics: that follows a certain statistics: � pixel of a video, n n =( � F F n represents the possible value possible value of the of the n n - -th th pixel of a video, =(k,m,n k,m,n). ). n represents the � � f f n represents the actual value taken. n represents the actual value taken. � � Continuous Continuous- -source source : F : F n n takes continuous values (analog image). takes continuous values (analog image). � � Discrete Discrete- -source: source: F F n takes discrete values (digital image). n takes discrete values (digital image). � 14 Kasaei
Statistical Characterization Statistical Characterization of Random Sources of Random Sources � Stationary source Stationary source: statistical distribution is : statistical distribution is invariant to time invariant to time � (space) shift. (space) shift. � Probability distribution Probability distribution: : � � Probability mass function Probability mass function ( (pmf pmf) for discrete sources & ) for discrete sources & probability density function probability density function � (pdf pdf) for continuous sources: ) for continuous sources: ( or or � Joint Joint pmf pmf or or pdf pdf: : � or or � Conditional Conditional pmf pmf or or pdf pdf: : � or r o 15 Kasaei
Statistical Characterization Statistical Characterization of Random Sources of Random Sources � Independent & identically distributed Independent & identically distributed ( (i.i.d i.i.d.) source .) source ( (memoryless memoryless): ): � = p f ( , f ,..., f ) p f ( ) ( p f )... ( p f ) 1 2 N 1 2 N & & = p f ( | f , f ,..., f ) p f ( ) + − + M 1 M M 1 1 M 1 � Markov process Markov process: : � = p f ( | f , f ,..., f ) p f ( | f ) + − + M 1 M M 1 1 M 1 M � More generally, an More generally, an M M - -th th order Markov process is one in which a sample order Markov process is one in which a sample � depends only on its previous M M samples. samples. depends only on its previous � A Gaussian process is Markov ( A Gaussian process is Markov (Gauss Gauss- -Markov process Markov process), if the covariance ), if the covariance � F F between two samples & has the form of: between two samples & has the form of: n m = δ ρ − − 2 ( n m ) C F F ( , ) n m 16 Kasaei
Information Content Information Content Characterization of Discrete RVs Characterization of Discrete RVs Entropy of a discrete RV: of a discrete RV: Entropy � � (bits) � Entropy is a measure of Entropy is a measure of uncertainty uncertainty or or information information content. content. � � Very uncertain (uniform distribution) Very uncertain (uniform distribution) � � low information content (max low information content (max � entropy). entropy). Joint entropy of two discrete RVs: of two discrete RVs: Joint entropy � � � Uncertainty of two RVs together: Uncertainty of two RVs together: � 17 Kasaei
Information Content Information Content Characterization of Discrete RVs Characterization of Discrete RVs � Conditional entropy Conditional entropy between two RVs: between two RVs: � � Uncertainty of one RV given the other RV: Uncertainty of one RV given the other RV: � � Mutual information Mutual information between two RVs : between two RVs : � � Information provided by Information provided by G G about about F F (reduction in required (reduction in required bitrate bitrate to specify to specify F F ): ): � 18 Kasaei
Information Content Characterization Information Content Characterization of Discrete Sources of Discrete Sources � N N - -th th order entropy of a discrete stationary source: order entropy of a discrete stationary source: � N -fold Cartesian product of A A � M M - -th th order order conditional conditional entropy of a discrete stationary source : entropy of a discrete stationary source : � 19 Kasaei
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