jpeg стандарт Лекц-15 · jpeg down-samples-дээж the “color channels” by...
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JPEG стандарт
Лекц-15
МУИС ХШУИС МКУТийн багш П.Гантуяа
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What is JPEG?
JPEG: Joint Photographic Expert Group —
an international standard in 1992.
Works for both color and grayscale images.
Targets at natural images.
Applications include satellite, medical
imaging, general photography ...
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Color Space Conversion
JPEG first converts RGB to YUV or YCrCb.
Y is the luminance component (brightness).
Y = 0.299 R + 0.587 G + 0.144 B
U and V are color components
U = B – Y
V = R - Y
Y U V
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Color Subsampling
JPEG down-samples-дээж the “color channels” by
half-хагас and partitions-хуваах,тусгаарлах
images into-руу 8x8 small blocks.
Y1 Y2
Y3 Y4
U V
Intensity-эрч Component-бүрэлдэхүүн Color components
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DCT (Discrete Cosine Transform)
DCT converts each image 8x8 block into another
8x8 block.
The energy in DCT domain is concentrated into
very few coefficients.
DCT
Image
block
DCT
coefficients
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0
2
4
6
8
0
2
4
6
8
-10
0
10
20
col
row
DC
T C
oeff
icie
nts
0
24
6
8
0
2
4
6
80
2
4
6
8
10
colrow
Gra
yscale
Level
Image block DCT Coefficients
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Definition of DCT
A linear transfrom F(u,v) = x=07
y=0 7 h(u,v,x,y) f(x,y)
where h(u,v,x,y) is the linear weighting-нэмэгдэл function.
DCT:
The inverse transform IDCT recovers the original data from DCT
coefficients.
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For DCT, h(u,v,x,y) can be decomposed-задрах
into g(u,x) * g(v,y)
F(u,v) = x=07
y=0 7 h(u,v,x,y) f(x,y)
= y=07
g(v,y) [x=0 7 g(u,x) f(x,y)]
Horizontal 1D DCT Vertical 1D DCT
followed
by
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Given u and v, h can be viewed as an image of x and y.
u
v
DCT coefficients are projection of image block into these patterns.
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Quantization
Recall that quantization can be used to collapse-
нурах the input into smaller number of values.-
эрхэм
For DCT coefficients,- we quantize different
coefficients in different details:
DC coefficient should have the most quantization
levels.
Quantization for AC coefficients can be coarser and
coarser as the frequency increases.
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Y quantization table
17 18 24 99 99 99 99 99
18 21 26 66 99 99 99 99
24 26 56 99 99 99 99 99
47 66 99 99 99 99 99 99
99 99 99 99 99 99 99 99
99 99 99 99 99 99 99 99
99 99 99 99 99 99 99 99
U, V quantization table
Fq(u,v) = round(F(u,v)/Q(u,v)) Quantization:
Fr(u,v) = Fq(u,v) * Q(u,v) De-quantization:
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quantization
dequantization
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The Quality Factor
For most-ихэнх current-урсгал JPEG encoders,
we can choose a quality-чанар factor-хүчин зүйл
from 1 to 100.
The method-арга of controlling the compression-
шахах quality is by scaling- the quantization table.
For example,-жишээ
Fq(u,v) = round(F(u,v)* (quality) / Q(u,v))
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DC Coefficients Encoding
D(m,n) D(m,n+1) D(m,n+2) D(m,n+3)
We compute the difference of each two successive quantized
coefficients
D(m,n) – 0 => d(m,n)
D(m,n+1) – D(m,n) => d(m,n+1)
D(m,n+2) – D(m,n+1) => d(m,n+2)
D(m,n+3) – D(m,n+2) => d(m,n+3)
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DC Coefficients Encoding
Then, we encode each DC difference value by
(size, coefficient)
1 -1, 1
2 -3, -2, 2, 3
3 -7 …-4, 4, …,7
4
…
11 -2047,…,-1024,1024,…,2047
The Size Table
7 will be coded as (3, 7)
• The first number 3 is Huffman -
coded.
• The second 7 is encoded as
1’s complement 111.
(-7 will be 000)
Can we encode the dc difference value directly?
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AC Coefficients Encoding
AC coefficients are not differentially encoded.
Instead, we first do run-length coding.
Zig-zag scanning
(0,11), (0,-12), (1, -12),
(0, 10), (0,16), (0, 0)
The run length code:
Indicates all are 0
from here
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AC Coefficients Encoding (cont)
For AC coefficients, we now have a bunch-баглаа
of symbols-тэмдэг like
The “value”-үнэ цэнэ has large number of
possible-боломжтой values in [-1023, 1023].
Direct Huffman coding is infeasible.-
Instead, we generate-гаргах symbols like
(zero-run length, value)
( zero-run length, size, value)
Huffman coded 1’s complement
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JPEG File Format
Start of image Frame End of image
Tables Header Scan Scan Scan …
Tables Header Segment Restart Segment ….
Block Block Block
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JPEG Extensions
The basic mode of JPEG supports-дэмжлэг
sequential –дараалсан coding (the order-дэс
дараа is from top-оройгоос to bottom –төгсгөл
and left to right-зүүнээс баруун).
JPEG extensions support progressive-аажим,
дэвшилтэт modes-төрөлүүд*(JPEG өрөгтгөлийг
дэмждэг дэвшилтэт төрөлүүд)
Spectrum selection.-спектер сонголт
Successive approximation.-дараалсан утга
Hierarchical mode.-шаталсан төлөв
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JPEG 2000
JPEG 2000 is a new standard-стандарт based on
wavelet- transform.-өөрчлөн хувиргах
JPEG2000 does not partition-хуваах, хуваагдал,
тусгаарлах an image into-руу small blocks.
Wavelet decomposes-зардал the whole-бүхэл
image into different-ялгаатай “bands” and then-
тэгээд дараа нь encodes-кодолсон the
coefficients in different-ялгаатай bands smartly.
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50 100 150 200 250 300 350 400 450 500
50
100
150
200
250
300
350
400
450
500
The wavelet decomposition of Lena image using Haar Wavelet.
HL
LH
HH
LL