Compression

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Compression

  1. 1. Multimedia Compression Audio, image and video require vast amounts of data  320x240x8bits grayscale image: 77Kb  1100x900x24bits color image: 3MB  640x480x24x30frames/sec: 27.6 MB/sec Low network’s bandwidth doesnt allow for real time video transmission Slow storage or processing devices dont allow for fast playing back Compression reduces storage requirementsE.G.M. Petrakis Multimedia Compression 1
  2. 2. Classification of TechniquesLossless: recover the original representationLossy: recover a representation similar to the original one high compression ratios more practical useHybrid: JPEG, MPEG, px64 combine several approachesE.G.M. Petrakis Multimedia Compression 2
  3. 3. Compression Standards Furht at.al. 96E.G.M. Petrakis Multimedia Compression 3
  4. 4. Lossless Techniques Furht at.al. 96E.G.M. Petrakis Multimedia Compression 4
  5. 5. Lossy Techniques Furht at.al. 96E.G.M. Petrakis Multimedia Compression 5
  6. 6. JPEG Modes of OperationSequential DCT: the image is encoded in one left-to-right, top-to-bottom scanProgressive DCT: the image is encoded in multiple scans (if the transmission time is long, a rough decoded image can be reproduced)Hierarchical: encoding at multiple resolutionsLossless : exact reproductionE.G.M. Petrakis Multimedia Compression 6
  7. 7. JPEG Block Diagrams Furht at.al. 96E.G.M. Petrakis Multimedia Compression 7
  8. 8. JPEG EncoderThree main blocks: Forward Discrete Cosine Transform (FDCT) Quantizer Entropy EncoderEssentially the sequential JPEG encoder Main component of progressive, lossless and hierarchical encoders For gray level and color imagesE.G.M. Petrakis Multimedia Compression 8
  9. 9. Sequential JPEG Pixels in [0,2p-1] are shifted in [-2p-1,2p-1-1] The image is divided in 8x8 blocks Each 8x8 block is DCT transformed C (u ) C ( v ) 7 7 ( 2 x + 1)uπ ( 2 y + 1)vπ F ( u, v ) = 2 ∑∑ f ( x, y ) cos 16 cos 16 2 x =0 y =0  1  for u = 0 C (u ) =  2  1 for u > 0   1  for v = 0 C (v ) =  2  1 for v > 0 E.G.M. Petrakis Multimedia Compression 9
  10. 10. DCT CoefficientsF(0,0) is the DC coefficient: average value over the 64 samplesThe remaining 63 coefficients are the AC coefficientsPixels in [-128,127]: DCTs in [-1024,1023] Most frequencies have 0 or near to 0 values and need not to be encoded This fact achieves compressionE.G.M. Petrakis Multimedia Compression 10
  11. 11. Quantization StepAll 64 DCT coefficients are quantized Fq(u,v) = Round[F(u,v)/Q(u,v)] Reduces the amplitude of coefficients which contribute little or nothing to 0 Discards information which is not visually significant Quantization coefficients Q(u,v) are specified by quantization tables A set of 4 tables are specified by JPEGE.G.M. Petrakis Multimedia Compression 11
  12. 12. Quantization Tables Furht at.al. 96 for (i=0; i < 64; i++) for (j=0; j < 64; j++) Q[i,j] = 1 + [ (1+i+j) quality];  quality = 1: best quality, lowest compression  quality = 25: poor quality, highest compressionE.G.M. Petrakis Multimedia Compression 12
  13. 13. AC Coefficients The 63 AC coefficients Furht at.al. 96 are ordered by a “zig-zag” sequence Places low frequencies before high frequencies Low frequencies are likely to be 0 Sequences of such 0 coefficients will be encoded by fewer bitsE.G.M. Petrakis Multimedia Compression 13
  14. 14. DC Coefficients Predictive coding of DC Coefficients Adjacent blocks have similar DC intensities Coding differences yields high compressionE.G.M. Petrakis Multimedia Compression 14
  15. 15. Entropy Encoding Encodes sequences of quantized DCT coefficients into binary sequences AC: (runlength, size) (amplitude) DC: (size, amplitude) runlength: number consecutive 0’s, up to 15  takes up to 4 bits for coding  (39,4)(12) = (15,0)(15,0)(7,4)(12) amplitude: first non-zero value size: number of bits to encode amplitude 0 0 0 0 0 0 476: (6,9)(476)E.G.M. Petrakis Multimedia Compression 15
  16. 16. Huffman codingConverts each sequence into binaryFirst DC following with ACsHuffman tables are specified in JPEGEach (runlength, size) is encoded using Huffman codingEach (amplitude) is encoded using a variable length integer code(1,4)(12) => (11111101101100)E.G.M. Petrakis Multimedia Compression 16
  17. 17. Example of Huffman table Furht at.al. 96E.G.M. Petrakis Multimedia Compression 17
  18. 18. JPEG Encoding of a 8x8 block Furht at.al. 96E.G.M. Petrakis Multimedia Compression 18
  19. 19. Compression Measures Compression ratio (CR): increases with higher compression  CR = OriginalSize/CompressedSize Root Mean Square Error (RMS): better quality with lower RMS 1 ∑ n RMS = i =1 ( X i − xi ) 2 n Xi: original pixel values xi: restored pixel values  n: total number of pixelsE.G.M. Petrakis Multimedia Compression 19
  20. 20. Furht at.al. 96E.G.M. Petrakis Multimedia Compression 20
  21. 21. JPEG DecoderThe same steps in reverse order The binary sequences are converted to symbol sequences using the Huffman tables F’(u,v) = Fq(u,v)Q(u,v) Inverse DCT 1 7 7 ( 2 x + 1)uπ ( 2 y + 1)vπ  F ( x, y ) =  ∑∑ C (u )C ( v ) F (u, v ) cos cos  4  u =0 v = 0 16 16 E.G.M. Petrakis Multimedia Compression 21
  22. 22. Progressive JPEG When image encoding or transmission takes long there may be a need to produce an approximation of the original image which is improved gradually Furht at.al. 96E.G.M. Petrakis Multimedia Compression 22
  23. 23. Progressive Spectral SelectionThe DCT coefficients are grouped into several bands Low-frequency bands are first band1: DC coefficient only band2: AC1,AC2 coefficients band3: AC3, AC4, AC5, AC6 coefficients band4: AC7, AC8 coefficientsE.G.M. Petrakis Multimedia Compression 23
  24. 24. Lossless JPEGSimple predictive encoding Furht at.al. 96 prediction schemesE.G.M. Petrakis Multimedia Compression 24
  25. 25. Hierarchical JPEG Produces a set of images at multiple resolutions  Begins with small images and continues with larger images (down-sampling)  The reduced image is scaled-up to the next resolution and used as predictor for the higher resolution imageE.G.M. Petrakis Multimedia Compression 25
  26. 26. Encoding 1. Down-sample the image by 2a in each x, y 2. Encode the reduced size image (sequential, progressive ..) 3. Up-sample the reduced image by 2 4. Interpolate by 2 in x, y 5. Use the up-sampled image as predictor 6. Encode differences (predictive coding) 7. Go to step 1 until the full resolution is encodedE.G.M. Petrakis Multimedia Compression 26
  27. 27. Furht at.al. 96E.G.M. Petrakis Multimedia Compression 27
  28. 28. JPEG for Color imagesEncoding of 3 bands (RGB, HSV etc.) in two ways: Non-interleaved data ordering: encodes each band separately Interleaved data ordering: different bands are combined into Minimum Coded Units (MCUs) Display, print or transmit images in parallel with decompressionE.G.M. Petrakis Multimedia Compression 28
  29. 29. Interleaved JPEG Minimum Coded Unit (MCU): the smallest group of interleaved data blocks (8x8) Furht at.al. 96E.G.M. Petrakis Multimedia Compression 29
  30. 30. Video CompressionVarious video encoding standards: QuickTime, DVI, H.261, MPEG etc Basic idea: compute motion between adjacent frames and transmit only differences Motion is computed between blocks Effective encoding of camera and object motionE.G.M. Petrakis Multimedia Compression 30
  31. 31. MPEGThe Moving Picture Coding Experts Group (MPEG) is a working group for the development of standards for compression, decompression, processing, and coded representation of moving pictures and audioMPEG groups are open and have attracted large participationhttp://mpeg.telecomitalialab.comE.G.M. Petrakis Multimedia Compression 31
  32. 32. MPEG FeaturesRandom accessFast forward / reverse searchesReverse playbackAudio – visual synchronizationRobustness to errorsAuditabilityCost trade-offE.G.M. Petrakis Multimedia Compression 32
  33. 33. MPEG -1, 2At least 4 MPEG standards finished or under constructionMPEG-1: storage and retrieval of moving pictures and audio on storage media 352x288 pixels/frame, 25 fps, at 1.5 Mbps Real-time encoding even on an old PCMPEG-2: higher quality, same principles 720x576 pixels/frame, 2-80 MbpsE.G.M. Petrakis Multimedia Compression 33
  34. 34. MPEG-4Encodes video content as objectsBased on identifying, tracking and encoding object layers which are rendered on top of each otherEnables objects to be manipulated individually or collectively on an audiovisual scene (interactive video)Only a few implementationsHigher compression ratiosE.G.M. Petrakis Multimedia Compression 34
  35. 35. MPEG-7Standard for the description of multimedia content XML Schema for content description Does not standardize extraction of descriptions MPEG1, 2, and 4 make content available MPEG7 makes content semantics availableE.G.M. Petrakis Multimedia Compression 35
  36. 36. MPEG-1,2 Compression Compression of full motion video, interframe compression, stores differences between frames A stream contains I, P and B frames in a given pattern Equivalent blocks are compared and motion vectors are computed and stored as P and B frames Furht at.al. 96E.G.M. Petrakis Multimedia Compression 36
  37. 37. Frame Structures I frames: self contained, JPEG encoded  Random access frames in MPEG streams  Low compression P frames: predicted coding using with reference to previous I or P frame  Higher compression B frames: bidirectional or interpolated coding using past and future I or P frame  Highest compressionE.G.M. Petrakis Multimedia Compression 37
  38. 38. Example of MPEG Stream Furht at.al. 96 B frames 2 3 4 are bi-directionally coded using I frame 1 and P frame 5  P frame 5 must be decoded before B frames 2 3 4  I frame 9 must be decoded before B frames 6 7 8  Frame order for transmission: 1 5 2 3 4 9 6 7 8E.G.M. Petrakis Multimedia Compression 38
  39. 39. MPEG Coding SequencesThe MPEG application determines a sequence of I, P, B frames For fast random access code the whole video as I frames (MJPEG) High compression is achieved by using large number of B frames Good sequence: (IBBPBBPBB) (IBBPBBPBB)...E.G.M. Petrakis Multimedia Compression 39
  40. 40. Motion EstimationThe motion estimator finds the best matching block in P, B frames Block: 8x8 or16x16 pixels P frames use only forward prediction: a block in the current frame is predicted from past frame B frames use forward or backward or prediction by interpolation: average of forward, backward predicted blocksE.G.M. Petrakis Multimedia Compression 40
  41. 41. Motion Vectors block: 16x16pixles Furht at.al. 96 One or two motion vectors per block  One vector for forward predicted P or B frames or backward predicted B frames  Two vectors for interpolated B framesE.G.M. Petrakis Multimedia Compression 41
  42. 42. MPEG Encoding I frames are JPEG compressed P, B frames are encoded in terms of future or previous frames Motion vectors are estimated and differences between predicted and actual blocks are computed  These error terms are DCT encoded  Entropy encoding produces a compact binary code  Special cases: static and intracoded blocksE.G.M. Petrakis Multimedia Compression 42
  43. 43. MPEG encoder JPEG encoding Furht at.al. 96E.G.M. Petrakis Multimedia Compression 43
  44. 44. MPEG Decoder Furht at.al. 96E.G.M. Petrakis Multimedia Compression 44
  45. 45. Motion Estimation TechniquesNot specified by MPEGBlock matching techniquesEstimate the motion of an nxm block in present frame in relation to pixels in previous or future frames The block is compared with a previous or forward block within a search area of size (m+2p)x(n+2p) m = n = 16 p = 6E.G.M. Petrakis Multimedia Compression 45
  46. 46. Block Matching Furht at.al. 96 Search area in block matching techniques  Typical case: n=m=16, p=6  F: block in current frame  G: search area in previous (or future) frameE.G.M. Petrakis Multimedia Compression 46
  47. 47. Cost functions The block has moved to the position that minimizes a cost function I. Mean Absolute Difference (MAD) 1 n/2 m/2 MAD ( dx, dy ) = ∑/ 2 j=∑/ 2F (i, j ) − G (i + dx, j + dy ) mn i = − n − m  F(i,j) : a block in current frame  G(i,j) : the same block in previous or future frame  (dx,dy) : vector for the search location  dx=(-p,p), dy=(-p,p)E.G.M. Petrakis Multimedia Compression 47
  48. 48. More Cost Functions II. Mean Squared Difference (MSD) 1 n/2 m/2 ∑/ 2 j =∑/ 2F (i, j ) − G(i + dx, j + dy ) 2 MSD (dx, dy ) = mn i = − n − m III. Cross-Correlation Difference (CCF) ∑∑ F (i, j )G(i + dx, j + dy ) CCF (dx, dy ) = i j 1/ 2 1/ 2      ∑∑ F 2 (i, j )   ∑∑ G 2 (i + dx, j + dy )       i j   i j E.G.M. Petrakis Multimedia Compression 48
  49. 49. More cost Functions IV. Pixel Difference Classification (PDC) PDC ( dx, dy ) = ∑∑ T ( dx, dy , i, j ) i j 1 if F (i, j ) − G (i + dx, j + dy ) ≤ t T ( dx, dy , i, j ) =  0 otherwise  t: predefined threshold  each pixel is classified as a matching pixel (T=1) or a mismatching pixel (T=0)  the matching block maximizes PDCE.G.M. Petrakis Multimedia Compression 49
  50. 50. Block Matching TechniquesExhaustive: very slow but accurateApproximation: faster but less accurate Three-step search 2-D logarithmic search Conjugate direction search Parallel hierarchical 1-D search (not discussed) Pixel difference classification (not discussed here)E.G.M. Petrakis Multimedia Compression 50
  51. 51. Exhaustive SearchEvaluates the cost function at every location in the search area Requires (2p+1)2 computations of the cost function For p=6 requires169 computations per block!!Very simple to implement but very slowE.G.M. Petrakis Multimedia Compression 51
  52. 52. Three-Step SearchComputes the cost function at the center and 8 surrounding locations in the search area The location with the minimum cost becomes the center location for the next step The search range is reduced by halfE.G.M. Petrakis Multimedia Compression 52
  53. 53. Three-Step Motion Vector Estimation (p=6) Furht at.al. 96E.G.M. Petrakis Multimedia Compression 53
  54. 54. Three–Step Search1. Compute cost (MAD) at 9 locations • Center + 8 locations at distance 3 from center1. Pick min MAD location and recompute MAD at 9 locations at distance 2 from center2. Pick the min MAD locations and do same at distance 1 from center • The smallest MAD from all locations indicates the final estimate • M24 at (dx,dy)=(1,6) • Requires 25 computations of MADE.G.M. Petrakis Multimedia Compression 54
  55. 55. 2-D Logarithic SearchCombines cost function and predefined threshold TCheck cost at M(0,0), 2 horizontal and 2 vertical locations and take the minimumIf cost at any location is less than T then search is completeIf no then, search again along the direction of minimum cost - within a smaller regionE.G.M. Petrakis Multimedia Compression 55
  56. 56. Furht at.al. 96 if cost at M(0,0) < T then search ends! compute min cost at M1,M2,M3,M4; take their min; if min cost < M(0,0)  if (cost less than T) then search ends!  else compute cost at direction of minimum cost (M5,M6 in the example); else compute cost at the neighborhood of min cost within p/2 (M5 in the example)E.G.M. Petrakis Multimedia Compression 56
  57. 57. Conjugate Direction Search Furht at.al. 96 Repeat  find min MAD along dx=0,-1,1 (y fixed): M(1,0) in example  find min MAD along dy=0,-1,1 starting from previous min (x fixed): M(2,2)  search similarly along the direction connecting the above minsE.G.M. Petrakis Multimedia Compression 57
  58. 58. Other Compression TechniquesDigital Video Interactive (DVI) similar to MPEG-2Fractal Image Compression Find regions resembling fractals Image representation at various resolutionsSub-band image and video coding Split signal into smaller frequency bandsWavelet-based codingE.G.M. Petrakis Multimedia Compression 58
  59. 59. References B. Furht, S. W. Smoliar, H-J. Zang, “Video and Image Processing in Multimedia Systems”, Kluwer Academic Pub, 1996E.G.M. Petrakis Multimedia Compression 59

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