Repetition 1st lecture


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1 Repetition 1st lecture Human Senses in Relation to Technical Parameters Multimedia  what is it? Human senses (overview) Historical remarks Color models RGB Y, Cr, Cb Data rates Text, Graphic Picture, Audio, Video
2 Overview Focus MuMeSy
3 History 1980: Media and Computer technique separate Record Transmit Play Computer 1 Network Computer 2
4 History (5) 2000: Complete digital processing Computer 1 Network Computer 2 => Technical basis for a Multimediacommunication
5 Color spectrum Red, Blue, Green (Spectrum)
6 Colors RGB curves to generate all colors 0,05B + 0,06G 0,09R ~ 500nm source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
7 Color models (RGB) color cube (diagonal: complementary colors) R:(FF,00,00) complement (difference to (FF,FF,FF)) (FF,FF,00) G:(00,FF,00) (FF,00,FF) B:(00,00,FF) 3 x 8 = 24 Bit 2^24 = colors True Color (just to remember : Human can differ: !) => 3 x 6 = 18 Bit => 2^18 = (00,FF,FF)
8 color models (RGB CMY) Monitor: Addition Printer: Subtraction RGB CMY to a dark area light is added Light colors Prism from a white area light is subtracted Corpus colors also in photography
9 Transformation RGB => YCbCr Y = 0.299R G B U = α (B Y) Cb = (B  Y) / V = β (R Y) Cr = (R  Y) / YUV used in PAL (α β depends on implementation) CbCr used in JPEG and MPEG H.D. Wuttke 2007
10 Examples of Graphic  Formats Vector Graphic  PS, EPS, WMF geometrical figures, exact calculation to a needed resolution Raster Graphic  BMP, GIF, JPEG, PNG fixed number of pixels (ppi) reproduction via interpolation (dpi) Problem: Macdesign (Vector) => PC (GIF)
11 Summary Color: Resolution: overlapping of colors RGB additive CMY subtractive Y Cb Cr Luminance + 2 Crominance compromise between quality and required memory ppi dpi picture in memory in/output device
12 Information ways CPU Memory Keyboard/ Mouse BUS  System Network external memory and interfaces Graphic / Video / Audio
13 Continuous Media Movement Audio and Movie encoding (MPEG1) (Moving Audio rate: between kbit/s Picture Experts constant data rate: Bit/s Group) 1,77 MBit/s Remark: M in Relation to Hz : (10 6 ) M in Relation to Byte: ( 2 20 ) M in Relation to Bit: k in Relation to Hz: (10 3 ) k in Relation to Byte: ( 2 10 ) k in Relation to Bit: M 3 : MultiMediaMogelfaktor
14 Day 2: October 3, 16:0019:15 Compression Methods Lossless Compression Entropy encoding Source encoding Hybrid Compression Lossy Compression JPEG encoding
15 Compression classes Quelle: Steinmetz, Ralf: MultimediaTechnologie: Einführung and Grundlagen, Springer, Verlag
16 Entropy encoding compression algorithms RLC Huffman Adaptive Huffman encoding Arithmetic encoding LZW
17 Entropy vs. Source Entropy Ignoring the kind of data Removing of repetitions Statistical basis Lossless and exact reproducible Low compression Source Properties of the source and/ or drain are important (e.g. Human senses as drain) Lossless possible Lossy if high compression (MP3)
18 RLC: Run Length Code Special sign (in the example #) outside of the Alphabet shows that the next sign is a number, followed by the sign that has to be repeated e.g. eaaaabaaabb 11 signs e#4abaaabb 10 signs Makes sense only for many equal signs
19 Huffman encoding Information of a sign (entropy H) is indirect proportional to the probability of its occurrence and its code length Seldom signs: higher information => longer code words their absence is more difficult to reconstruct => entropy H ~ length of the code => algorithm?
20 Huffman encoding Formula: (Shannon) n signs with probabilities p i Information source S: generates binary signs S i p i: probability that S i occurs in S entropy H(S) =  i p i ld(p i ) i= 1... n
21 Huffman encoding Entropy H(S) =  i p i ld(p i ) i= 1... n e.g. picture with an homogenous greypart with 8Bitcode: i= n=256 grey values, each grey value has the same probability p i = 1/256 => ld(p i ) = ld(1/256) = ld(1)ld(256) = 8 H(S) =  (1/256 * (8) /256 *(8) ) = * 1/256 *(8) = 8 => ld(1/p i ) is the ideal number of bits for encoding
22 Shannon Fano algorithm Top Down S = AEABADDABADACADABADACABABABECADABCECECE 1. Sort on occurrence Symbol A B C D E Occurrence source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
23 Shannon Fano algorithm 2. Divide iteratively into two sets so that the sum in each of them is nearly the same Symbol A B C D E Anzahl Bit (0 1) Bit (0 1) Bit (0 1) 3. Encoding: A B C D E
24 Calculation of the needed Bits Symbol S Number S: 39 ld(1/p i ) Code Sum Bits: 89 A *) B C D E source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada *) p(a)=15/39 => ld(39/15)=1,38 Relative to a 3bitencoding: 3bit/S x 39S = 117bit89bit= 28 bits
25 Huffman algorithm BottomUp 1. Start with an open list. [A,B,C,D,E] Keep it always sorted by the number of occurrences Symbol A B C D E Number of occurrences source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
26 Huffman algorithm 2. Take always the two elements with the lowest the occurrence and calculate their Sum s, [A(15),B(7),C(6),D(6),E(5)] [A(15),B(7),C(6),D(6),E(5)], s =11 replace them by a new element (knode) Wi(s) (W1(11)) in the list: [A(15),B(7),C(6),W1(11)] and sort: [A(15),W1(11),B(7),C(6)] further: [A(15),W1(11),B(7),C(6)] [A(15),W1(11),W2(13)] [A(15),W2(13),W1(11)] [A(15),W3(24)] [W3(24),A(15)] [W4(39)] until 1 element left over => binary tree E(5) D(6) C(6) B(7) W1(11) 1 W3(24) 1 W2(13) W4(39) A(15) source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada 0 0 0
27 Calculation of the needed Bits, entropy Symbol number 39 log 2 (1/p i ) code Sum of Bits 87 A B C D E Relative to a 3bitencoding: 87 to 3 x 39 = 117: 30 bits source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
28 Huffman  encoding entropy H(S) =  i p i ld(p i ) i= 1... n entropy of the sequence of signs (p(a)=15/39, p(b)=7/39...) (15 x x x x x 2.96) / 39 = / 39 = 2.19 (ideal value for encoding) Bits / signs for the Huffman encoding: 87 / 39 = 2.23 ~ entropy 2,19!
29 Encoding properties + Optimal encoding (entropy) + prefix unique + => no separator necessary  Code table must be known  => to be transmitted together with message,  Overhead  Not suitable for live video or audio => Adaptive Huffman encoding
30 Adaptive Huffman  encoding Idea: same InitialTable same actualization routine for encoder and decoder Actualization routine update model : count the occurrence update the Huffman tree, if necessary (if the Huffmantree is not valid => swapping) => encoding of a sign is changing!
31 Adaptive Huffman  encoding ENCODER Initialize_model(); while ((c = getc(input))!=eof) { encode (c, output); update_model (c); } DECODER Initialize_model(); while ((c = decode(input))!= eof) { putc (c, output); update_model (c); }
32 Adaptive Huffman  encoding After 17 signs: A(1),B(2),C(2),D(2),E(10) encoding A: source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
33 Adaptive Huffman  encoding After next 2 A: A(3),B(2),C(2),D(2),E(10) encoding A: source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
34 Adaptive Huffman  encoding after next two A: A(5),B(2),C(2),D(2),E(10) encoding A:
35 Encoding properties + Optimal encoding (entropy) + prefix unique + => no need of a separation sign, even if the codes of the signs have a different length + probability must not be known  Huge effort in encoding / decoding  Increases with the number of signs  Exact synchronism is needed
36 Arithmetic encoding 1. Occurrences are normalized into an interval between First sign of the sequence defines the 1.interval, which again will be divided proportional to the occurrence of the signs 3. The second sign defines the part in between the former defined interval and so on. 4. End at the end of the sequence of signs 5. The number in the last interval, that has the lowest number of digits is the encoding
37 Arithmetic encoding
38 k Arithmetic encoding 0,7 0,5 0,1
39 Arithmetische encoding
40 Encoding properties + only one number for the whole string  occurrences must be known  => has to be sent with the message  Overhead  Not possible for live video or audio  Limited accuracy of floating point numbers in computers => limited Length
41 LempelZivWelch algorithm (LZW) Sources: LZ77, LZ78 Terry A. Welch: "A Technique for High Performance Data Compression", IEEE Computer, Vol. 17, No. 6, 1984, pp Used in the compressinstruction of Unix und picturecompressionformat TIFF Idea: successive build a dictionary
42 LempelZivWelch algorithm (LZW) w k wk = actually processed actual sign (word) = actual sign = actual sign of w and k Initial dictionary : 8 Bit ASCII => 1. free encoding: 256
43 LempelZivWelch algorithm (LZW) w = NIL; while ( read a character k ) { if wk exists in the dictionary w = wk; else add wk to the dictionary; output the code for w; w = k; }
44 LempelZivWelch algorithm (LZW) ^WED^WE^WEE^WEB^WET w k Output Index Symbol NIL ^ ^ W ^ 256 ^W W E W 257 WE E D E 258 ED D ^ D 259 D^ ^ W ^W E ^WE E ^ E 261 E^ ^ W source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
45 w k Output Index Symbol ^ ^W W E LempelZivWelch algorithm (LZW) ^WE E ^WEE E ^ E^ W E^W W E WE B WEB B ^ B 265 B^ ^ W ^W E ^WE T ^WET T EOF T
46 LZW Decompression Algorithm read a character k; output k; w = k; while ( read a character k ) /* k could be a character or a code. */ { entry = dictionary entry for k; output entry; add w + entry[0] to dictionary; w = entry; }
47 LZW Decompression Algorithm w k Output Index Symbol ^ ^ ^ W W 256 ^W W E E 257 WE E D D 258 ED D <256> ^W 259 D^ <256> E E 260 ^WE E <260> ^WE 261 E^ <260> <261> E^ 262 ^WEE <261> <257> WE 263 E^W <257> B B 264 WEB B <260> ^WE 265 B^ <260> T T 266 ^WET source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
48 Compression classes Quelle: Steinmetz, Ralf: MultimediaTechnologie: Einführung and Grundlagen, Springer, Verlag
49 Compression classes Quelle: Steinmetz, Ralf: MultimediaTechnologie: Einführung and Grundlagen, Springer, Verlag
50 Source encoding compression algorithms Where information is getting lost? Why can we accept this? Which side effects occur? Which advantages bring transformations? What are asymmetric algorithms?
51 DPCM Differential Pulse Code Modulation Prediction coding High compression rate by an optimal respect to the properties of the source / drain Specialized for each class of information (Audio, Video, Picture, Text)
52 DPCM source:
53 Transformation Examples
54 DCT Discrete Cosine Transform (DCT): Inverse Discrete Cosine Transform (IDCT): source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
55 FFT vs. DCT source: ZeNian Li : Script Multimedia Systems, Sin theon Fraser University, Canada
56 Wavelet Examples Source: Amara Graph, Introduction to Wavelets
57 Sub sampling
58 JPEG Steps 1. Color model transformation 2. Discrete Cosine Transformation (DCT) 3. Quantization 4. Zigzagscan 5. DPCM, RLE 6. Huffman
59 JPEG  Overview source: ZeNian Li : Script Multimedia Systems, Simon Fraser University, Canada
60 Transformation RGB => YCbCr Y = 0.299R G B U = α (B Y) Cb = (B  Y) / V = β (R Y) Cr = (R  Y) / YUV used in PAL (α β depends on implementation) CbCr used in JPEG and MPEG
61 Components Y U V source: ZeNian Li : Script Multimedia Systems, Simon Fraser University, Canada
62 Discrete Cosine Transform (DCT) Basic functions for 8x8 constant 1/2 vertical cosine period 7/2 vertical cosine periods 1/2 horizontal cosine period source: ZeNian Li : Script Multimedia Systems, Simon Fraser University, Canada
63 Discrete Cosine Transformation (DCT) source: ZeNian Li : Script Multimedia Systems, Simon Fraser University, Canada
64 DCT Factorized Discrete Cosine Transform (DCT): Inverse Discrete Cosine Transform (IDCT): source: ZeNian Li : Script Multimedia Systems, Simon Fraser University, Canada
65 Vertical Line
66 Horizontal line
67 Corner
68 Quantization Luminance Quantization Table q(u, v) Chrominance Quantization Table q(u, v) Scalable for different levels of quality and compression rate source: ZeNian Li : Script Multimedia Systems, Simon Fraser University, Canada
69 Zig Zag Scan most important values first most reduced values (many to 0 ) at the end as a sequence source: ZeNian Li : Script Multimedia Systems, Simon Fraser University, Canada
70 DPCM RLC DC component is large and varied, often close to the previous value. Encode the difference from previous 8 x 8 blocks  DPCM AC vector has lots of zeros in it RLC for those values special method: zeros are skipped and replaced by the number of zeros, other signs are non zeros
71 Huffman Entropy encoding of the whole result from former steps finished the algorithm. source: ZeNian Li : Script Multimedia Systems, Simon Fraser University, Canada
72 Summary JPEG source: ZeNian Li : Script Multimedia Systems, Simon Fraser University, Canada
73 Compression classes Quelle: Steinmetz, Ralf: MultimediaTechnologie: Einführung and Grundlagen, Springer, Verlag
74 Day 2: October 3, 16:0019:15 Compression Methods Lossless Compression Entropy encoding Source encoding Hybrid Compression Lossy Compression JPEG encoding Thanks again for your attention! Hope to see you next Thursday Oct. 9 th Room VI201
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