Fundamentals. Relative data redundancy of the set. C.E., NCU, Taiwan Angela Chih-Wei Tang,

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1 Image Compressio Agela Chih-Wei Tag ( 唐之瑋 ) Departmet of Commuicatio Egieerig Natioal Cetral Uiversity JhogLi, Taiwa 2012 Sprig

2 Fudametals Compressio ratio C R / 2, 1 : origial, 2 1 : compressed Relative data redudacy of the set R 11/ D C R 1 C.E., NCU, Taiwa Agela Chih-Wei Tag,

3 Autocorrelatio coefficiet Autocorrelatio coefficiet N y x f y x f A A A 1 ) ( ) ( 1 ) ( (0) ) / ( ) ( Solutio: VLC y y x f y x f N A 0 ), ( ), ( ) ( Solutio: VLC 1. The adjacet pixels are highly correlated. 2 Periodically 2. Periodically high correlatio 3

4 Data Redudacy Codig Redudacy More code symbols are used tha absolutely ecessary The statistical redudacy associated with codig techiques C.E., NCU, Taiwa Agela Chih-Wei Tag,

5 Data Redudacy Iterpixel Redudacy The pixels of a image frame ad pixels of a group of successive image or video frames are ot statistically idepedet The value of ay give pixel ca be reasoably predicted from the value of its eighbors, the iformatio carried by idividual pixels is relatively small. C.E., NCU, Taiwa Agela Chih-Wei Tag,

6 Data Redudacy Psychovisual Redudacy d Quatizatio The eye does ot respod with equal sesitivity to all visual iformatio If we apply fewer data to represet less importat visual iformatio, perceptio will ot be affected C.E., NCU, Taiwa Agela Chih-Wei Tag,

7 Fidelity Criteria Objective fidelity criterio Root-mea-square error e rms 1/ 2 M 1N MN x0 y0 [ fˆ( x, y) f ( x, y)] Recostructed sigals Mea-square sigal-to-oise ratio SNR ms M 1 N 1 2 x0 y0 M1N1 x0 y0 [ fˆ( x, Subjective fidelity criterio fˆ( x, y ) y ) f ( x, y )] PSNR? C.E., NCU, Taiwa Agela Chih-Wei Tag,

8 A Geeral Compressio System Model Error free? Lossy? C.E., NCU, Taiwa Agela Chih-Wei Tag,

9 Source Ecoder & Source Decoder Model (Reversible) Iterpixel 2. Psychovisual 3. Codig Redudacy Redudacy Redudacy 9

10 Elemets of Iformatio Theory Self-iformatio of a radom evet E I( E) log(1/ P( E)) log P( E) Etropy/ucertaity/the average iformatio per source output J H ( z) P ( a j )log P ( a j ) j1 [ ( a1), P( a2 P ),..., P( a J )] SourcalphabetA{ a:1, a2,..., aj } The etropy z is maximized if the source symbols are equally eare probable T C.E., NCU, Taiwa Agela Chih-Wei Tag,

11 Error-Free Compressio Variable-Legth Codig (1/2) Huffma Codig L avg 2.2 bits/symbol H ( z ) bits/symbol New! 11

12 Error-Free Compressio Variable-Legth Codig (2/2) Arithmetic codig: ot itegral bits/symbol To ecode a1, a2, a3, a3, a4 Ex Decoder? Agela Chih-Wei Tag,

13 Error-Free Compressio Lempel-Ziv-Welch l (LZW) Codig As the ecoder sequetially examies the image s pixels, gray-level sequeces that are ot i the dictioary are placed i algorithmically determied locatios A example: 4x4, 8-bit image Dictioary Etry Locatio

14 Error-Free Compressio LZW Codig Example New! GIF, TIFF, PDF, COMPRESS (Uix), wizip 14

15 Error-Free Compressio Lossless Predictive Codig To elimiate iterpixel redudacy, ad ecode oly the differece/ew iformatio! VLC C.E., NCU, Taiwa Agela Chih-Wei Tag,

16 Lossy Compressio Lossy Predictive Codig 2 1 Lossy Ecoder Predictor miimize ii i E { e 2 }, miimize ii i 1 2 E 2 subject to f e e fˆ m i1 i f si s i 1 ( s t i ) p( s) ds ad fˆ f where i 1,2,..., L/2 i 0, 16

17 Lossy Compressio Trasform Codig The goal of the trasformatio process To decorrelate the pixels of each subimage/pack as much iformatio as possible ito the smallest umber of trasform coefficiets C.E., NCU, Taiwa Agela Chih-Wei Tag,

18 Trasform Codig Trasform Selectio Spatial domai KLT (optimal): pack the most iformatio ito the fewest coefficiets DFT: cause blockig effect DCT 18

19 Image Compressio Stadards C.E., NCU, Taiwa Agela Chih-Wei Tag,

20 A Example of JPEG (1/2) Level shiftig (-128) Agela Chih-Wei Tag,

21 A Example of JPEG (2/2) DCT Coefficiets roud[-415/16] Quatizatio 21

22 Quatizatio Matrix for JPEG Baselie Stadard C.E., NCU, Taiwa Agela Chih-Wei Tag,

23 JPEG (3/3) Zigzag orderig patter [ EOB] Ecode DC coefficiet: DPCM (differetial pulse code modulatio) magitude category ad K LSBs of 2 s complemet! positive differece egative differece [-26-(-17)]= DC coefficiet of the left block Ecode AC coefficiet The umber of zero-valued coefficiets precedig the ozero coefficiet to be coded, magitude category ad LSBs -3:

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26 C.E., NCU, Taiwa Agela Chih-Wei Tag,

27 JPEG2000 Why JPEG 2000? R' G' B' Y'C b C ' ' r 27

28 Embedded Block Codig with Optimized Trucatio (EBCOT) Partitio of Tiled Compoets ito Coded d Blocks & Precicts To be coded idepedetly Sigificat propagatio pass Magitude refiemet pass Clea-up pass 28

29 Coceptual Correspodece betwee The Spatial & The Bit Stream Represetatios 29