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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
— 90minutes 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—"iFgmﬂ—"h—H n) nlIn1=ﬂ where cm _ (11.5} 1H
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 ‘zigzag’ 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 4111111111.
4341 1311314444
411411113311411114
111—11 1 11 11—11—13 1
—i 1 1 4—3—1 —3 3
1 3 13114 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 .... “kll)
Suﬁ"1} ' 71W“ I I 413211
3*J 1 I] I I
4] l n I I
lllll
IIIII
IIIII
IIIII
IIIII H (6) 219—239 Scan —I 3531 43111 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 Unliormlength 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: zerolength 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 (IraFf" ‘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 Welldefined Interchange format of encoded data Implementation in:
 Software only
 Software and hardware “MOTION JPEG” for video compression
 Sequence of JPEGencoded images ...
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