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Basic Image Compression Concepts Presenter ： Guan-Chen Pan Research Advisor ： Jian-Jiun Ding, Ph. D. Assistant professor Digital Image and Signal Processing Lab Basic Image Compression Concepts Presenter ： Guan-Chen Pan Research Advisor ： Jian-Jiun Ding, Ph. D. Assistant professor Digital Image and Signal Processing Lab Graduate Institute of Communication Engineering National Taiwan University 1

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Outlines Introductions Basic concept of image compression Proposed method for arbitrary-shape image segment compression Improvement of the boundary region by morphology JPEG2000 Triangular and trapezoid regions and modified JPEG image compression 2

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Introduction Lossless or lossy(widely used) 3

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YCbCr Y ： the luminance of the image which represents the brightness Cb ： the chrominance of the image which represents the difference between the gray and blue Cr ： the chrominance of the image which represents the difference between the gray and red 4

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Chrominance Subsampling The name of the format is not always related to the subsampling ratio. 5

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Reduce the Correlation between Pixels Transform coding 1.Coordinate rotation 2.Karhunen-Loeve transform 3.Discrete cosine transform 4.Discrete wavelet transform Predictive coding 8

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Coordinate rotation Height Weight 9

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do the inverse transform to get the data and reduce the correlation 10

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Karhunen-Loeve transform(KLT) 11

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Discrete cosine transform The 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. 13

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Discrete wavelet transform Wavelet 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

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Predictive Coding Predictive 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) 16

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Quantization 17

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Luminance quantization matrix Chrominance quantization matrix Removes the high frequencies 1611101624405161 12 141926586055 1413162440576956 1417222951878062 182237566810910377 243555648110411392 49647887103121120101 7292959811210010399 18

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Entropy Coding Algorithms 1. Huffman Coding ◦ Difference Coding (DC) ◦ Zero Run Length Coding (AC) 2. Arithmetic Coding 3. Golomb Coding 19

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Huffman Coding Huffman coding is the most popular technique for removing coding redundancy. ◦ Unique prefix property ◦ Instantaneous decoding property ◦ Optimality JPEG(fixed, not optimal) 20

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Difference Coding 22

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Zero Run Length Coding Encode 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

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Arithmetic Coding 25

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SymbolProbabilitySub-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) 27

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SymbolProbabilitySub-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 0.05~0.25 0.071334 ⇒ L 28

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Golomb Coding 29

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Encoding of quotient part qoutput bits0 110 2110 31110 411110 5111110 61111110: N 0 Encoding of remainder part roffsetbinaryoutput bits 000000000 110001001 220010010 330011011 440100100 550101101 61211001100 71311011101 81411101110 91511111111 Decode “101111” q = 1, r = 9 ⇒ a = 10*1+9 = 19 32

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Without codeword table Flexibility and adaptation HuffmanNOGOOD GolombYESMIDDLE Adaptive Golomb YESGOOD 33

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Proposed Method for Arbitrary- Shape Image Segment Compression An arbitrary-shape image segment f and its shape matrix. 34

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Standard 8x8 DCT bases with the shape of f 35

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The 37 arbitrary-shape orthonormal DCT bases by Gram-Schmidt process 36

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Quantization 37

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Improvement of the Boundary Region by Morphology 38

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JPEG2000 JPEG 2000 is a new standard and it can achieve better performance in image compression. Advantages ◦ Efficient lossy and lossless compression ◦ Superior image quality ◦ Additional features such as spatial scalability and region of interest. Complexity 39

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JPEG 2000 encoder JPEG 2000 decoder Embedded Block Coding with Optimized Truncation(EBCOT) : Tier-1+Tier-2 40

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Irreversible component transform (ICT) 42

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Reversible component transform (RCT) Reversible and integer-to-integer 43

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Irreversible, Daubechies 9/7 filter Analysis Filter CoefficientsSynthesis Filter Coefficients nLowpass FilterHighpass FilterLowpass FilterHighpass Filter 00.6029490182361.115087052456 0.6029490182363 ±1±1 0.266864118442-0.0591271763110.591271763114-0.2668641184428 ±2±2 -0.078223266528-0.057543526228 -0.0782232665289 ±3±3 -0.01686411844280.091271763114-0.09127176311420.0168641184428 ±4±4 0.026748757410 0.0267487574108 45

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Tier-1 Encoder Each Fractional Bit-plane coding will generate the Context (CX) and the Decision (D), which are used for arithmetic coding. ◦ zero coding ◦ sign coding ◦ magnitude refinement coding ◦ run length coding 47

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Bit-plane Conversion Converts the quantized wavelet coefficients into several bit-planes First bit-plane is the sign plane The other planes are the magnitude plane, from MSB to LSB 48

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17223348648096112 22283852678196112 333848627586100116 485262708396110125 6467758396108118132 80818696108117128142 96 100110118128140150 112 116125132142150160 17 = 00010001 2 160 = 10100000 2 49

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Stripe and Scan Order 50

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Zero Coding D : current encode data, binary : 0 or 1 h :0~2v :0~2d :0~4 dvd hDh dvd 51

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Sign Coding v hDh v 52

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Magnitude Refinement Coding σ ′ [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] 53

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Run-Length Coding For four zeros : (CX,D) is (0,0) Else is (0,1), and use 2 uniform(CX=18) to record the 1’s position ◦ (0110) ◦ The first nonzero position is (01) 2 ⇒ (0,1), (18,0), (18,1) 54

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D (0,1) CX (total 19) Arithmetic encoder Compressed data 55

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Why Called Fractional ？ 56

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Tier-2 Encoder Rate/Distortion optimized truncation 57

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Triangular and Trapezoid Regions and Modified JPEG Image Compression Divide an image into 3 parts: 1.Lower frequency regions 2.Traditional image blocks and 3.The arbitrarily-shaped image blocks 58

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1111111110 0111111111 0111111110 0111111100 0011011110 0010011100 0000001100 0000001100 1 sections 2 sections 1 sections Zone 1 Zone 2 Zone 3 59

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α -distance < threshold 60

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Corner too close Trapezoid inside the zone 61

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N = K(m) + K(M-1-m) N = 10 62

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Reference: 1. J.D Huang "Image Compression by Segmentation and Boundary Description, " 2008. 2. 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. 3. J. Canny, "A Computational Approach to Edge Detection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, pp. 679-698, Nov. 1986. 4. 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. 5. 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, ",VCIP2010 6. J.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 2010 7. W.Y Wei, "Image Compression", available in http://disp.ee.ntu.edu.tw/tutorial.phphttp://disp.ee.ntu.edu.tw/tutorial.php 8. K. R. Rao and P. Yip, Discrete Cosine Transform, Algorithms, Advantage, Applications, New York: Academic, 1990. 9. S.S. Agaian, Hadamard Matrices and Their Applications, New York, Springer-Verlag, 1985. 10. H. F. Harmuth, Transmission of information by orthogonal functions, Springer, New York, 1970. 64

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11. R. Koenen, Editor, “Overview of the MPEG-4 Standard,” ISO/IEC JTC/SC29/WG21, MPEG-99-N2925, March 1999, Seoul, South Korea. 12. T. Sikora, “MPEG-4 very low bit rate video,” IEEE International Symposium on Circuits and Systems, ISCAS ’97, vol. 2, pp. 1440-1443, 1997. 13. 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. 14. 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. 15. 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. 16. D. A. Huffman, "A method for the construction of minimum-redundancy codes," Proceedings of the IRE, vol. 40, no. 9, pp. 1098-1101, 1952. 17. S. W. Golomb, "Run length encodings," IEEE Trans. Inf. Theory, vol. 12, pp. 399-401, 1966. 18. R. Gallager and D. V. Voorhis, "Optimal source codes for geometrically distributed integer alphabets," IEEE Trans. Information Theory, vol. 21, pp. 228–230, March 1975. 19. R. F. Rice, "Some practical universal noiseless coding techniques–part I," Tech. Rep. JPL- 79-22, Jet Propulsion Laboratory, Pasadena, CA, March 1979. 20. G. Seroussi and M. J. Weinberger, "On adaptive strategies for an extended family of Golomb-type codes," Proc. DCC’97, pp. 131-140, 1997. 21. C. J. Lian “JPEG2000 “, DSP/IC design lab, GIEE, ntu 65

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