Post on 04-Jan-2016
PowerPoint
Basic Image Compression Concepts
PresenterGuan-Chen PanResearch AdvisorJian-Jiun Ding , Ph. D.Assistant professor
Digital Image and Signal Processing LabGraduate Institute of Communication EngineeringNational Taiwan University
11OutlinesIntroductionsBasic concept of image compressionProposed method for arbitrary-shapeimage segment compressionImprovement of the boundary region by morphologyJPEG2000Triangular and trapezoid regions and modified JPEG image compression
2IntroductionLossless or lossy(widely used)
3YCbCr Ythe luminance of the image which represents the brightnessCbthe chrominance of the image which represents the difference between the gray and blueCrthe chrominance of the image which represents the difference between the gray and red
4Chrominance SubsamplingThe name of the format is not always related to the subsampling ratio.
567Reduce the Correlation between PixelsTransform coding Coordinate rotationKarhunen-Loeve transformDiscrete cosine transformDiscrete wavelet transformPredictive coding8Coordinate rotation
HeightWeight9do the inverse transform to get the data and reduce the correlation
10Karhunen-Loeve transform(KLT)1112Discrete cosine transformThe DCT is an approximation of the KLT and more widely used in image and video compression.The DCT can concentrate more energy in the low frequency bands than the DFT.13Discrete wavelet transformWavelet transform is very similar to the conventional Fourier transform, but it is based on small waves, called wavelet, which is composed of time varying and limited duration waves.We use 2-D discrete wavelet transform in image compression.14
15Predictive CodingPredictive coding means that we transmit only the difference between the current pixel and the previous pixel.The difference may be close to zero.However, the predictive coding algorithm is more widely used in video.EX. Delta modulation (DM), Adaptive DM. DPCM ,Adaptive DPCM (ADPCM)16Quantization17Luminance quantization matrix
Chrominance quantization matrix
Removes the high frequencies1611101624405161121214192658605514131624405769561417222951878062182237566810910377243555648110411392496478871031211201017292959811210010399
18Entropy Coding AlgorithmsHuffman CodingDifference Coding (DC)Zero Run Length Coding (AC)Arithmetic CodingGolomb Coding
19Huffman CodingHuffman coding is the most popular technique for removing coding redundancy.Unique prefix propertyInstantaneous decoding propertyOptimalityJPEG(fixed, not optimal)20
21Difference Coding22Zero Run Length CodingEncode each value which is not 0, than add the number of consecutive zeroes in front of it EOB (End of Block) = (0,0)Only 4-bit value[57,45,0,0,0,0,23,0,-30,-16,0,,0][(0,57)(0,45)(4,23)(1,-30)(0,16)EOB]Eighteen zeroes, 3 (15,0) ; (2,3)where (15,0) is 16 consecutive zeroes
23
24Arithmetic Coding25
26SymbolProbabilitySub-intervalk0.05[0.00,0.05)l0.2[0.05,0.25)u0.1[0.25,0.35)w0.05[0.35,0.40)e0.3[0.40,0.70)r0.2[0.70,0.90)?0.1[0.90,1.00)
27SymbolProbabilitySub-intervalk0.05[0.00,0.05)l0.2[0.05,0.25)u0.1[0.20,0.35)w0.05[0.35,0.40)e0.3[0.40,0.70)r0.2[0.70,0.90)?0.1[0.90,1.00)0.071334 LSymbolProbabilitySub-intervalk0.05[0.05,0.06)l0.2[0.06,0.1)u0.1[0.1,0.12)w0.05[0.12,0.13)e0.3[0.13,0.19)r0.2[0.19,0.23)?0.1[0.23,0.25)For interval 0.05~0.250.071334 L28Golomb Coding293031Encoding of quotient partqoutput bits00110211031110411110511111061111110::N0Encoding of remainder partroffsetbinaryoutput bits00000000011000100122001001033001101144010010055010110161211001100713110111018141110111091511111111Decode 101111
q = 1, r = 9 a = 10*1+9 = 19
32Without codeword tableFlexibility and adaptationHuffmanNOGOODGolomb YESMIDDLEAdaptive GolombYESGOOD33Proposed Method for Arbitrary-Shape Image Segment Compression
An arbitrary-shape image segment f and its shape matrix.34Standard 8x8 DCT bases with the shape of f
35The 37 arbitrary-shape orthonormal DCT bases by Gram-Schmidt process
36Quantization
37Improvement of the Boundary Region by Morphology
38JPEG2000JPEG 2000 is a new standard and it can achieve better performance in image compression.AdvantagesEfficient lossy and lossless compressionSuperior image qualityAdditional features such as spatial scalability and region of interest.Complexity39JPEG 2000 encoder
JPEG 2000 decoder
Embedded Block Coding with Optimized Truncation(EBCOT) : Tier-1+Tier-240
41Irreversible component transform (ICT)
42Reversible component transform (RCT)Reversible and integer-to-integer
43
44Irreversible , Daubechies 9/7 filter
Analysis Filter CoefficientsSynthesis Filter CoefficientsnLowpass Filter Highpass Filter Lowpass Filter Highpass Filter 00.6029490182361.1150870524561.1150870524560.602949018236310.266864118442-0.0591271763110.591271763114-0.26686411844282-0.078223266528-0.057543526228-0.057543526228-0.07822326652893-0.01686411844280.091271763114-0.09127176311420.016864118442840.0267487574100.026748757410845
46Tier-1 Encoder
Each Fractional Bit-plane coding will generate the Context (CX) and the Decision (D), which are used for arithmetic coding.zero codingsign coding magnitude refinement codingrun length coding47Bit-plane ConversionConverts the quantized wavelet coefficients into several bit-planesFirst bit-plane is the sign planeThe other planes are the magnitude plane, from MSB to LSB
4817223348648096112222838526781961123338486275861001164852627083961101256467758396108118132808186961081171281429696100110118128140150112112116125132142150160
17 = 000100012160 = 10100000249Stripe and Scan Order
50Zero Coding
D : current encode data, binary : 0 or 1h :0~2v :0~2d :0~4
dvdhDhdvd51Sign Coding
vhDhv52Magnitude Refinement Coding[x,y] is initialized to 0, and it will become 1 after the first time of the magnitude refinement coding is met at [x,y]
53Run-Length CodingFor four zeros : (CX,D) is (0,0)Else is (0,1), and use 2 uniform(CX=18) to record the 1s position(0110)The first nonzero position is (01)2 (0,1), (18,0), (18,1) 54
D(0,1) CX(total 19)Arithmetic encoderCompressed data55Why Called Fractional
56Tier-2 EncoderRate/Distortion optimized truncation
57Triangular and Trapezoid Regions and Modified JPEG Image CompressionDivide an image into 3 parts: Lower frequency regionsTraditional image blocks and The arbitrarily-shaped image blocks
5811111111100111111111011111111001111111000011011110001001110000000011000000001100
1 sections1 sections1 sections1 sections2 sections2 sections1 sections1 sections
Zone 1Zone 2Zone 359-distance < threshold
60
Corner too close
Trapezoid inside the zone 61
N = K(m) + K(M-1-m)
N = 1062
63Reference:J.D Huang "Image Compression by Segmentation and Boundary Description, " 2008.G. Roberts, "Machine Perception of Three-Dimensional Solids," in Optical and Electro- Optical Information Processing, J. T. T. e. al., Ed. Cambridge, MA: MIT Press, 1965, pp. 159-197.J. Canny, "A Computational Approach to Edge Detection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, pp. 679-698, Nov. 1986.D. Comaniciu and P. Meer, "Mean Shift: A Robust Approach toward Feature Space Analysis, " IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, pp. 603-619, 2002.J.J Ding, P.Y Lin, S.C Pei, and Y.H Wang, "The Two-Dimensional Orthogonal DCT Expansion in Triangular and Trapezoid Regions and Modified JPEG Image Compression, ",VCIP2010J.J Ding, S.C Pei, W.Y Wei, H.H Chen, and T.H Lee, "Adaptive Golomb Code for Joint Geometrically Distributed Data and Its Application in Image Coding", APSIPA 2010W.Y Wei, "Image Compression", available in http://disp.ee.ntu.edu.tw/tutorial.phpK. R. Rao and P. Yip, Discrete Cosine Transform, Algorithms, Advantage, Applications, New York: Academic, 1990.S.S. Agaian, Hadamard Matrices and Their Applications, New York, Springer-Verlag, 1985.H. F. Harmuth, Transmission of information by orthogonal functions, Springer, New York, 1970.64R. Koenen, Editor, Overview of the MPEG-4 Standard, ISO/IEC JTC/SC29/WG21, MPEG-99-N2925, March 1999, Seoul, South Korea.T. Sikora, MPEG-4 very low bit rate video, IEEE International Symposium on Circuits and Systems, ISCAS 97, vol. 2, pp. 1440-1443, 1997.T. Sikora and B. Makai, Shape-adaptive DCT for generic coding of video, IEEE Trans. Circuits Syst. Video Technol., vol. 5, pp. 59-62, Feb. 1995.W.K. Ng and Z. Lin, A New Shape-Adaptive DCT for Coding of Arbitrarily Shaped Image Segments, ICASSP, vol. 4, pp. 2115-2118, 2000.S. C. Pei, J. J. Ding, P. Y. Lin and T. H. H. Lee, Two-dimensional orthogonal DCT expansion in triangular and trapezoid regions, Computer Vision, Graphics, and Image Processing, Sitou, Taiwan, Aug. 2009.D. A. Huffman, "A method for the construction of minimum-redundancy codes," Proceedings of the IRE, vol. 40, no. 9, pp. 1098-1101, 1952.S. W. Golomb, "Run length encodings," IEEE Trans. Inf. Theory, vol. 12, pp. 399-401, 1966.R. Gallager and D. V. Voorhis, "Optimal source codes for geometrically distributed integer alphabets," IEEE Trans. Information Theory, vol. 21, pp. 228230, March 1975.R. F. Rice, "Some practical universal noiseless coding techniquespart I," Tech. Rep. JPL-79-22, Jet Propulsion Laboratory, Pasadena, CA, March 1979. G. Seroussi and M. J. Weinberger, "On adaptive strategies for an extended family of Golomb-type codes," Proc. DCC97, pp. 131-140, 1997. C. J. Lian JPEG2000 , DSP/IC design lab, GIEE, ntu 65Image
R
G
B
YCbCr ColorTransform
ChrominanceDownsampling(4:2:2 or 4:2:0)
8 8 FDCT
Quantizer
QuantizationTable
Zigzag &Run Length Coding
DifferentialCoding
HuffmanEncoding
HuffmanEncoding
Bit-stream
Y
Cb
Cr
W
W
W
H
H
H
Y
W
H
Y
W
H
Cb
W/2
H
Cr
W/2
H
Cb
W/2
H/2
Cr
W/2
H/2
(a) 4 : 4 : 4
(b) 4 : 2 : 2
(c) 4 : 2 : 0
Y
W
H
Cb
W/4
H
Cr
W/4
H
(d) 4 : 1 : 1
Original sequence X=(x0,x1)
New Height y0New Width y1
181.9713.416
203.4060.887
161.5540.560
183.844-1.220
141.512-3.223
206.133-2.999
173.823-3.111
120.721-5.152
89.159-7.112
2
2
2
2
2
2
Columns
Rows
LL2
LH2
LH1
HH1
HL1
HL2
HH2
a2
a6
a1
a4
a3
a5
Symbol
Probability
0.4
0.3
0.1
0.1
0.06
0.04
1
0.4
0.4
0.3
0.3
0.2
0.1
0.1
0.1
0.1
0.4
0.3
0.3
0.6
0.4
2
3
4
Code
1
00
011
0100
01010
01011
7596
105989910173856660
100978994876455
849490817166
9386948170
86868172
989778
105104
00001100
11111111
01111111
00111111
00111110
00011110
00011100
00011000
01234567
0
1
2
3
4
5
6
7
12345678910
11121314151617181920
21222324252627282930
31323334353637
ForwardComponentTransform
Quantization
Forward2D DWT
RateControl
Tier-1Encoder
Tier-2Encoder
OriginalImage
CodedImage
Tier-2Decoder
Tier-1Decoder
Dequantization
Inverse2D DWT
InverseComponentTransform
ReconstructedImage
CodedImage
DWT in each tile
Image Component
Tiling
2
2
2
2
2
2
Columns
Rows
Bit-planeConversion
FractionalBit-planeCoding
ArithmeticCoding
Tier-1 Encoder
Context
Decision
QuantizedDWTcoefficients
N
Sign
MSB
LSB
M
codingorder
0
0
1
0
0
1
1
MSB
LSB
First 1 appear
Insignificant
Significant
The bit to be coded
Trapezoid and triangular regions
Traditional 8X8 image blocks
8X8 SADCT image blocks
Zone 1
Zone 2-1
Zone 2-2
Zone 3
2 zones
1 zone
1 zone
(M-1)th row
(M-2)th row
1st row
0th row
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m = M-1
m = M-2
m = 1
m = 0
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n = 0 1 2
Region A
Region B
Rotation by 180
Region A
Region B
Rectangular Region
(a)
(b)