Lossy Image Compression Methods. CSEP 590 Data Compression Autumn Barbara. JPEG Standard JPEG. DCT Compression JPEG

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1 ossy Imge Compresson ethods CSEP 59 Dt Compresson Autumn 7 ossy Imge Compresson rnsform Codng DC Compresson Slr quntzton (SQ). Vetor quntzton (). Wvelet Compresson SPIH UWIC (Unversty of Wshngton Imge Coder) EBCO CSEP 59 - eture 7 - Autumn 7 Stndrd Brbr - Jont Photogrph Eperts Group Current mge ompresson stndrd. Uses dsrete osne trnsform, slr quntzton, nd Huffmn odng. uses to wvelet ompresson. orgnl 3: ompresson rto.5 bts/pel (8 bts) CSEP 59 - eture 7 - Autumn 7 3 Wvelet-SPIH CSEP 59 - eture 7 - Autumn 7 4 CSEP 59 - eture 7 - Autumn 7 5 CSEP 59 - eture 7 - Autumn 7 6

2 SPIH Orgnl CSEP 59 - eture 7 - Autumn 7 7 CSEP 59 - eture 7 - Autumn 7 8 Imges nd the Eye Imges re ment to be vewed by the humn eye (usully). he eye s very good t nterpolton, tht s, the eye n tolerte some dstorton. So lossy ompresson s not neessrly bd. he eye hs more uty for lumnne (gry sle) thn hromnne (olor). Gry sle s more mportnt thn olor. Compresson s usully done n the YUV olor oordntes, Y for lumnne nd U,V for olor. U nd V should be ompressed more thn Y hs s why we wll onentrte on ompressng gry sle (8 bts per pel) mges. CSEP 59 - eture 7 - Autumn 7 9 orgnl Enoder Dstorton ompressed y ˆ Deoder deompressed ossy ompresson: ˆ esure of dstorton s ommonly men squred error (SE). Assume hs n rel omponents (pels). n SE ( ˆ ) n CSEP 59 - eture 7 - Autumn 7 PSNR Rte-Fdelty Curve Pek Sgnl to Nose Rto (PSNR) s the stndrd wy to mesure fdelty. m PSNR log ( ) SE where m s the mmum vlue of pel possble. For gry sle mges (8 bts per pel) m 55. PSNR s mesured n debels (db)..5 to db s sd to be pereptble dfferene. Deent mges strt t bout 3 db PSNR bts per pel SPIH oded Brbr Propertes: - Inresng - Slope deresng CSEP 59 - eture 7 - Autumn 7 CSEP 59 - eture 7 - Autumn 7

3 PSNR s not Everythng PSNR Reflets Fdelty () PSNR bpp.8 : PSNR 5.8 db PSNR 5.8 db CSEP 59 - eture 7 - Autumn 7 3 CSEP 59 - eture 7 - Autumn 7 4 PSNR Reflets Fdelty () PSNR Reflets Fdelty (3) PSNR 4..3 bpp 5.6 : PSNR 3..6 bpp 5. : CSEP 59 - eture 7 - Autumn 7 5 CSEP 59 - eture 7 - Autumn 7 6 Ide of rnsform Codng rnsform the nput pels,,..., N- nto oeffents,,..., N- (rel vlues) he oeffents hve the property tht most of them re ner zero ost of the energy s ompted nto few oeffents Quntze the oeffents hs s where there s loss, sne oeffents re only ppromted Importnt oeffents re kept t hgher preson Entropy enode the quntzton symbols Deodng Entropy deode the quntzed symbols Compute ppromte oeffents,,..., N- from the quntzed symbols. Inverse trnsform,,..., N- to,,..., N- whh s good ppromton of the orgnl,,..., N-. CSEP 59 - eture 7 - Autumn 7 7 CSEP 59 - eture 7 - Autumn 7 8 3

4 ε nput Blok Dgrm of rnsform Codng Enoder oeffents symbols quntzton s trnsform bt lloton entropy deodng symbols s deode symbols entropy odng bt strem b output nverse trnsform oeffents themtl Propertes of rnsforms ner rnsformton - Defned by rel nn mtr A ( ) N-, Orthonormlty,N- N-,N- N- A A N- (trnspose) Deoder CSEP 59 - eture 7 - Autumn 7 9 CSEP 59 - eture 7 - Autumn 7 Why Coeffents Why Orthonomlty A,N-,N- N-, N-,N- + + N-, N-,N- N- N- N- he energy of the dt equls the energy of the oeffents ( A (A) (A) )(A) (A A) bss vetors oeffents CSEP 59 - eture 7 - Autumn 7 CSEP 59 - eture 7 - Autumn 7 Squred Error s Preserved wth Orthonorml rnsformtons In lossy odng we only send n ppromton of beuse t tkes fewer bts to trnsmt the ppromton. et + ε (A( - ' )) (A( - ( - ' ) (A A)( - ( ' ) ( ' ) ( - ' ) ( -') (A - A' ) (A - A' ) ' )) ' ) (( - ' ) A )(A(- ( - ' ) ( - ' ) Squred error n orgnl. ' )) CSEP 59 - eture 7 - Autumn 7 3 Compton Emple A A A A A A A A b b orthonorml b ompton CSEP 59 - eture 7 - Autumn 7 4 4

5 Dsrete Cosne rnsform Bss Vetors N 4 d N os N (j + )π N f f > row row D row row 3 CSEP 59 - eture 7 - Autumn 7 5 CSEP 59 - eture 7 - Autumn 7 6 Deomposton n erms of Bss Vetors Imge Blok rnsform Eh 88 blok s ndvdully oded DC oeffent AC oeffents CSEP 59 - eture 7 - Autumn 7 7 CSEP 59 - eture 7 - Autumn 7 8 -Dmensonl Blok rnsform Blok of pels X A rnsform DC Bss rnsform rows r rnsform olumns k kj k r m mj m m m kj mk k m k Summry C AXA CSEP 59 - eture 7 - Autumn 7 9 m kj mk CSEP 59 - eture 7 - Autumn 7 3 5

6 Importne of Coeffents he DC oeffent s the most mportnt. he AC oeffents beome less mportnt s they re frther from the DC oeffent. Emple Bt Alloton ompresson 65 bts for pels.86 bpp CSEP 59 - eture 7 - Autumn 7 3 Quntzton For nn blok we onstrut nn mtr Q suh tht Q ndtes how mny quntzton levels to use for oeffent. Enode wth the lbel Deode s to s +.5 Q ' s Q rger Q ndtes fewer levels. CSEP 59 - eture 7 - Autumn 7 3 Emple Quntzton Emple Quntzton ble 54., Q 4 54., Q 54., Q s ' s ' s ' Inrese the bt rte hlve the tble Derese the bt rte double the tble 99 CSEP 59 - eture 7 - Autumn 7 33 CSEP 59 - eture 7 - Autumn 7 34 Zg-Zg Codng DC lbel s oded seprtely. AC lbels re usully oded n zg-zg order usng spel entropy odng to tke dvntge of the orderng of the bt lloton (quntzton). CSEP 59 - eture 7 - Autumn 7 35 (987) et P [p ],,j < N be n mge wth p < 56. Center the pels round zero p - 8 Code 88 bloks of P usng DC Choose quntzton tble. he tble depends on the desred qulty nd s bult nto Quntze the oeffents ordng to the quntzton tble. he quntzton symbols n be postve or negtve. rnsmt the lbels (n oded wy) for eh blok. CSEP 59 - eture 7 - Autumn

7 Blok rnsmsson Emple Blok of bels DC oeffent DC oeffents don t hnge muh from blok to neghborng blok. Hene, ther lbels hnge even less. Predtve odng usng dfferenes s used to ode the DC lbel. AC oeffents Do zg-zg odng Codng order of AC lbels CSEP 59 - eture 7 - Autumn 7 37 CSEP 59 - eture 7 - Autumn 7 38 Codng bels Ctegores of lbels {} {-, } 3 {-3,-,,3} 4 {-7,-6,-5,-4,4,5 6 7} bel s ndted by two numbers C,B Emples lbel C,B 3, -4 4, 3 CSEP 59 - eture 7 - Autumn 7 39 Codng AC bel Sequene A symbol hs three prts (Z,C,B) Z for number of zeros preedng lbel < Z < 5 C for the tegory of the of the lbel B for C- bt number for the tul lbel End of Blok symbol (EOB) mens the rest of the blok s zeros. EOB (,,-) Emple: (,3,)(,5,7)(,3,3)(4,,)(,,)(,,)(,,-) CSEP 59 - eture 7 - Autumn 7 4 Codng AC bel Sequene Z,C hve pref ode B s C- bt number Z 3 C 3 (,3,) (,5,7) (,3,3) (4,,) (,,) (,,) (,,-) 46 bts representng 64 pels.7 bpp Prtl pref ode tble CSEP 59 - eture 7 - Autumn 7 4 Notes on rnsform Codng Vdeo Codng PEG uses DC H.63, H.64 uses DC Audo Codng P3 PEG - yer 3 uses DC Alterntve rnsforms pped trnsforms remove some of the blokng rtfts. Wvelet trnsforms do not need to use bloks t ll. CSEP 59 - eture 7 - Autumn 7 4 7