part2_jpeg - 2. Image Compression _+ Motivation — Size of...

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Unformatted text preview: 2. Image Compression _+ Motivation — Size of an image = 921,600 bytes — One second of a Vldeo stream 9 921,600 bytes * 30 frames/sec = 22] Mbit/see -— 90-minutes of video _ o 221 Mbits/sec * 5400 seconds = 149 a ham Fundamental Methods + The following signal processing techniques are used to reduce the size of an image — Subsampling — Transform Coding — Entropy Coding + Popular Standards: JPEG Subsampling 4 Recall YUV and Y’CbCr schemes which has one brightness component and two color components + Humans are more sensitive on the changes in brightness than the changes in colors + Thus, sampling the color components less- frequently than the brightness comp ht \ can save the number of pixels ‘ Example of Subsampling 4:' 2:1 heriznntal dummpling, 'nn verti- cal dnwsampling I K 4 Y samples for every 2 Ch and 2 Cr 55 samples _ . .1 (f v Subsampling (cont) : reduction in both vertical and horizontal directions Differen'f’ resolutions for luminanee'end chraihin'afi'a’é oOSsible: - Luminance Yzhigh resolution - Chrominance U, V: lower resolution Examples: _ - 4:2:2: double resolution for luminance Coding of four pixels: JPEG - image Preparation Example 4:2:2 YUV, 4:1 :1 YUV, and YUV9 Coding " - tuminance (Y): - brightness - sampling frequency 13.5 MHz - Chrominance (U, V): 0 color differences - sampling frequency 6.75 MHz "is System Components 0 Major components of oompruclon m: i'r'ltlnpy |*!‘H mimg (ac) loam CL. Lin, TILE). Discrete Cosine Transform (DCT) +DCT is the discrete analog of the consine transform 9 Transformation from spatial to frequency domain § Redistribute redundancy to enable more efficient entropy encoding , r” / .-‘ + Most current video compression st ds l” x are DCT—based k . Assumptions: - Data in the transformed domain is easier to compress - Related processing is feasible " Example: Fourier Transformation —————-—-————-—p - - frequency time domain domain 41$, ‘_________ bi» Inverse Fourier Transformation FFT: Fast Fourier Transformation DCT: Discrete Cosine Transformation General F arm of DC T 0 Mil term 0! DOT for NxN matrix N—l "—1 2 l k I ' at.» - Em.ww[ E E *IWflmfl—"iF-gmfl—"h—H n) nl-In1=fl where cm _ (11.5} 1-H kl,krnl,l, :- 11...,“ DCT Example 0 Example for 313 image block with range [0.253]: T T sacral) = %C{kl)c(k2)[n z “n z 'elnl.nz)eue( I H 1 = nan1 + 1m1 nun2 + nit: T)“‘["T‘)] 98m: - Subtract 128 from each element to center the signal " around 0 I Perform DCT on original image swung) to yield S(k1,k2) I Apply quantization matrix, T(k1.k2), on result of DCT to yield 3(k1ak2)=NlNT(5(k1 sk2VT(k1 #2)), where NINT is nearest integer function Use of quantization tables for the DCT—coefiieients: - Map.interval of real numbers to one integer number JPEG - Baseline Mode: Entropy COding . . 63 AC coefficients: - Ordering in ‘zig-zag’ form I A001 A007 DC/’%R//7- A070,,” ‘ ‘ KACT; - reason: coefficients in lower right corner are likely to be zero - Huffman coding of all coefficients: - Transformation into a code a where amount of bits depends on frequency of respective value %‘ - Subsequent runlength coding of zeros DCT Example 0 Example for 313 image block with range [0.253]: T T sacral) = %C{kl)c(k2)[n z “n z 'elnl.nz)eue( I H 1 = nan1 + 1m1 nun2 + nit: T)“‘["T‘)] 98m: - Subtract 128 from each element to center the signal " around 0 I Perform DCT on original image swung) to yield S(k1,k2) I Apply quantization matrix, T(k1.k2), on result of DCT to yield 3(k1ak2)=NlNT(5(k1 sk2VT(k1 #2)), where NINT is nearest integer function (1) Original Frame I“WI-"'1’" 111111 11131311113131 mmmmmmm raummmmm 0“ 11111113111151.11- mmmnnnnumm I'HIIIIIHIIJIIIII mmmmmmm mmmmmmm (3) Mar DOT Sufi-*1}: 313 51 411111-1111.- 4341 1311314444 41141111331141-1114 -111—11 1 11 11—11—13 1 —i 1 1 4—3—1 —3 3 1 3 1-31-14 11 3 4 :1 4—1—11 1 4 1 1 14—1-: 3 1 DC T Example ( cont. ) (2) Subtract "128" ""rW' 531—3415113343": 55154145553514! 5144' 43 54514533! 454'! 5145513133! 545' 51 455435145 5151 51 515541441 5151 51 545541145 5151 53 515541141 (4) Quantization Matrix 1111.11; . 15111111514 411 51 51 1111141515 55 ill 55 1413151444 51' 55 55 14111115 51 5? BI 51 1511315555 11191031? 14.355554511114113 51 “54155111111113”! 115155551111I1I3” DC T Example (cont. ) (5) After Dlvlnlon by Mutilation matrix .... “kl-l) Sufi-"1} ' 71W“ I I 413-211 -3*J 1 I] I I 4-] l n I I lllll IIIII IIIII IIIII IIIII H (6) 219—239 Scan —I- 35-3-1 4-311-1 400 1'1r'9r' cannon“ a 10000 ooau0fi°°°°°°fl ‘fifiunflfi Oi i H uficman Encoding (cont) 0 Symbols with higher probabilities are assigned shorter codewords. Symbol Code Probability 32,32 31 0 p1: 5f3 "-" 1%; I 32 100 [32: 3’32 " ' 53 110 [33: W32 ' 34: 1110 p4: 1332 - . 55 101 p5=1i&=%z ss 1 111 p3: 1332 ' I Unliorm-length code: I Huffman code: I Optimal (entropy): 5. Entropy Coding: Assumption: - Long sequences of identical symbols Example: ...ABCEEEEEEDACB... compression y: DACB... symbol number of occurrences special flag Special variant: zero-length encoding - onlv repetition of zeroes count J PEG 0Became an ISO international standard in 1992 + Use most of the techniques introduced earlier § Both. of the sequential and progressive presentations are supported I / ' I ...__.-..._\~ I u $0“ a '15 1:; fi‘ ' a i m. I; (E J (Ira-Ff" ‘1 K N. as“ ~. wee w" ' a): .9352” g Wié'mwmfim.‘ 2 x JPEG v15 '25 5:4 it“: Very general compression scheme 'Independence of: - Image resolution - Image and pixel aspect ratio - Color representation - Image complexity and statistical characteristics Well-defined Interchange format of encoded data Implementation in: - Software only - Software and hardware “MOTION JPEG” for video compression - Sequence of JPEG-encoded images ...
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This note was uploaded on 11/30/2011 for the course CIS 6930 taught by Professor Staff during the Fall '08 term at University of Florida.

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part2_jpeg - 2. Image Compression _+ Motivation — Size of...

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