Compression. Compression. Compression. This part of the course... Ifi, UiO Norsk Regnesentral Vårsemester 2005 Wolfgang Leister

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1 Kurs INF5080 Ifi, UiO Norsk Rgnsntrl Vårsmstr 2005 Wolfgng Listr This prt of th ours is hl t Ifi, UiO... (Wolfgng Listr) n t ontins mtril from Univrsity Collg Krlsruh (Ptr Ol, Clmns Knorzr)

2 Informtion Thory Dt Contnt Prviw Img Formts JPEG / JIFF Wvlt Frtl Vio Formts MJPEG MPEG

3 Imgs Grphis Multimi t typs Vio / Img squns Auio 3D-Dt Txt / Doumnts othrs Imgs Grphis Multimi t typs Vio / Img squns Auio 3D-Dt Txt / Doumnts othrs

4 Lossy Coing Applil only for t typs lik: Imgs Films (img squns) Auio Us physiologil pilitis n limittions of th snss to sign omprssion mthos Ey Cpilitis of th snss Ey rogniss frqunis Brightnss is ttr rognis thn olours. Movmnt n flikr is rognis vry strongly! Er - Dnsly situt frqunis ovr h othr. - Frqunis hrtristis of th r

5 Informtion Thory Symols: A = 0, 1,... N-1 Coing: C = 0, 1,... N-1 trivil Coing (onstnt Co Lngth) i = i0, i1,... im-1 ij {0,1} M = log 2 N for i [0,N-1] (inry) (Co lngth, numr of its) Distriution: P = p 0,p 1,... p N-1 proility for symols H Informtion Thory Informtion ontnt: (Entropy) N 1 0 = p i logpi i= 0 Exmpl: Uniform istriution (Bsis = 2 it/owor) 1 p i = N N H0 = N log N= log N= logn i= 0

6 Informtion thory Coing: C = 0, 1,... N-1 i = i0, i1,... ili -1 i [0,N-1] ij {0,1} l i = lngth of o wor i vrg o lngth: N 1 L = pl ii H 0 i= 0 Informtion Thory Whn is L = H 0? li = l p i 1 1 p i = l = 2 i 2 k Wht if p 1 i for ll i? 2 k not uniform istriution i..: vrg o Lngth = Entropy uniform istriution

7 Informtion Thory Wht if? p 1 i 2 k non uniform istriution Huffmn Coing Group vnts into on o wor: ( i1,..., in ) i Evry ( i )-omintion must vill: N n o wors Arithmti oing oftn ttr suitl Intrmzzo... Why Dt omprssion? An img sys mor thn thousn wors An img ns mor sp thn thousn wors Dt r ontin runny... Humns lov runny

8 thniqus losslss run lngth noing thniqus losslss run lngth noing: run lngth noing (4x0)(3x1)(8x0)(2x1)(4x0)(1x1)(1x0)(6x1)(10x0) 4,3,8,2,4,1,1,6,10 Exmpls: PCX Fx JPEG

9 thniqus losslss run lngth noing optiml Cos thniqus losslss run lngth noing optiml Cos Co wors hv iffrnt lngths Lngth of o wor pnnt on proility: (high proility short Cowort) (low proility long Cowort) Glol n fix o wor tl Co wor tl is prt of oing

10 thniqus Exmpl: Huffmn-Coing: losslss run lngth noing optiml Cos 1.Stp: Evnts to o r sort y proilitis (rising orr). 2.Stp: Th vnts with lst proilitis r rmov from list, unit to on vnt, n sort into list with sum of oth proilitis. 3.Stp: Rpt Stp 2 until only on lmnt is ontin in list. 4.Stp: Co wors r gnrt y mrking th gs in th inry tr y 0 n 1. R th o wor from top to ottom. thniqus Exmpl Huffmn-Coing: losslss run lngth noing optiml Cos

11 thniqus Exmpl: Huffmn-Coing: losslss run lngth noing optiml Cos thniqus Exmpl: Huffmn-Coing: losslss run lngth noing optiml Cos

12 thniqus Exmpl: Huffmn-Coing: losslss 0.6 run lngth noing optiml Cos thniqus Exmpl: Huffmn-Coing: losslss run lngth noing optiml Cos

13 thniqus Exmpl: Huffmn-Coing: losslss run lngth noing optiml Cos thniqus Exmpl: Huffmn-Coing: losslss with loss run lngth noing optiml Cos

14 thniqus losslss run lngth noing optiml Cos ptiv Cos thniqus losslss Mtho y Ziv n Lmpl run lngth noing optiml Cos ptiv Cos Co tll is gnrt whil oing No n to trnsfr o tll

15 thniqus losslss Exmpl: run lngth noing optiml Cos ptiv Cos 1 2 w: 3 4 Output: thniqus losslss Exmpl: run lngth noing optiml Cos ptiv Cos Output: w: 12

16 thniqus losslss Exmpl: run lngth noing optiml Cos ptiv Cos w: Output: 123 thniqus losslss Exmpl: run lngth noing optiml Cos ptiv Cos w: Output: 1234

17 thniqus losslss Exmpl: run lngth noing optiml Cos ptiv Cos w: Output: Arithmti Coing Symols r rprsnt y proility intrvls Symol hins r rprsnt y ontntion of thir proility intrvls

18 Arithmti Coing # A P # 0.35 # = [0.95, 1.0) = [0.75, 0.95) = [0.7, 0.75) = [0.35, 0.7) = [, 0.35) = [0.0, ) Arithmti Coing # A # P 0.35 #

19 Arithmti Coing # 0.35 # A # P Arithmti Coing # # 0.35 # # #

20 Arithmti Coing # # Huffmn: (0000) # # thniqus losslss Quntising: run lngth noing optiml Cos ptiv Cos Anlogu Digitl 8 Bit 4 Bit RGB Colour pltt Clustring Quntisirung Clustring

21 thniqus losslss run lngth noing optiml Cos ptiv Cos Quntising Clustring thniqus losslss run lngth noing optiml Cos ptiv Cos Quntising Clustring Dsriptiv Trnsformtion

22 Img Dt formts losslss PBM+ GIF? PNG (JPEG) JPEG Wvlt Compr. Wvlt Compr. Th En of Ltur

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