Multimedia Compression

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 doesn't allow for real time video transmission Slow storage devices don't allow for fast playing back Compression reduces storage requirements E.G.M. Petrakis Multimedia Compression 1

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 approaches E.G.M. Petrakis Multimedia Compression 2

Compression Standards Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 3

Lossless Techniques Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 4

Lossy Techniques Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 5

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 reproduction E.G.M. Petrakis Multimedia Compression 6

JPEG Block Diagrams Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 7

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 images E.G.M. Petrakis Multimedia Compression 8

Sequential JPEG Pixels in [0,2 p -1] are shifted in [-2 p-1,2 p-1-1] The image is divided in 8x8 blocks Each 8x8 block is DCT transformed F( u, v) C( v) = C( u) 2 C( v) 2 = 1 for u = 0 C( u) = 2 1for u > 0 1 for v = 0 2 1for v > 0 7 7 x= 0 y= 0 (2x + 1) uπ (2 y + 1) vπ f ( x, y)cos cos 16 16 E.G.M. Petrakis Multimedia Compression 9

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 compression E.G.M. Petrakis Multimedia Compression 10

Quantization Step All 64 DCT coefficients are quantized F q (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 JPEG E.G.M. Petrakis Multimedia Compression 11

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 compression E.G.M. Petrakis Multimedia Compression 12

AC Coefficients The 63 AC coefficients 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 bits Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 13

DC Coefficients Predictive coding of DC Coefficients Adjacent blocks have similar DC intensities Coding differences yields high compression E.G.M. Petrakis Multimedia Compression 14

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

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

Example of Huffman table Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 17

JPEG Encoding of a 8x8 block Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 18

Compression Measures Compression ratio (CR): increases with higher compression CR = OriginalSize/CompressedSize Root Mean Square Error (RMS): better quality with lower RMS RMS = 1 n X i : original pixel values x i : restored pixel values n: total number of pixels n i = 1 ( X x i i E.G.M. Petrakis Multimedia Compression 19 2 )

Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 20

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 F( x, y) 7 7 1 (2x + 1) uπ (2 y + 1) vπ C( u) C( v) F( u, v)cos cos 4 u= 0 v= 0 16 16 = E.G.M. Petrakis Multimedia Compression 21

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. 96 E.G.M. Petrakis Multimedia Compression 22

Progressive Spectral Selection The DCT coefficients are grouped into several bands Low-frequency bands are first band 1 : DC coefficient only band 2 : AC 1,AC 2 coefficients band 3 : AC 3, AC 4, AC 5, AC 6 coefficients band 4 : AC 7, AC 8 coefficients E.G.M. Petrakis Multimedia Compression 23

Lossless JPEG Simple predictive encoding Furht at.al. 96 prediction schemes E.G.M. Petrakis Multimedia Compression 24

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 image E.G.M. Petrakis Multimedia Compression 25

Encoding 1. Down-sample the image by 2 a 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 encoded E.G.M. Petrakis Multimedia Compression 26

Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 27

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 decompression E.G.M. Petrakis Multimedia Compression 28

Interleaved JPEG Minimum Coded Unit (MCU): the smallest group of interleaved data blocks (8x8) Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 29

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 motion E.G.M. Petrakis Multimedia Compression 30

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.com E.G.M. Petrakis Multimedia Compression 31

MPEG Features Random access Fast forward / reverse searches Reverse playback Audio visual synchronization Robustness to errors Auditability Cost trade-off E.G.M. Petrakis Multimedia Compression 32

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 Mbps E.G.M. Petrakis Multimedia Compression 33

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 ratios E.G.M. Petrakis Multimedia Compression 34

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 available E.G.M. Petrakis Multimedia Compression 35

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. 96 E.G.M. Petrakis Multimedia Compression 36

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 compression E.G.M. Petrakis Multimedia Compression 37

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 8 E.G.M. Petrakis Multimedia Compression 38

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

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 blocks E.G.M. Petrakis Multimedia Compression 40

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 frames E.G.M. Petrakis Multimedia Compression 41

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 blocks E.G.M. Petrakis Multimedia Compression 42

MPEG encoder JPEG encoding Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 43

MPEG Decoder Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 44

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 = 6 E.G.M. Petrakis Multimedia Compression 45

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) frame E.G.M. Petrakis Multimedia Compression 46

Cost functions The block has moved to the position that minimizes a cost function I. Mean Absolute Difference (MAD) MAD( dx, dy) = 1 mn n / 2 m / 2 i= n / 2 j= m / 2 F( i, j) G( i + dx, j + dy) 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

More Cost Functions II. Mean Squared Difference (MSD) MSD( dx, dy) = 1 mn n / 2 m / 2 i= n / 2 j= m / 2 F( i, j) G( i + dx, j + dy) 2 III. Cross-Correlation Difference (CCF) CCF( dx, dy) = i j F 2 i ( i, j j) F( i, 1/ 2 j) G( i i j + dx, j + dy) G 2 ( i + dx, j + dy) 1/ 2 E.G.M. Petrakis Multimedia Compression 48

More cost Functions IV. Pixel Difference Classification (PDC) PDC( dx, dy) = i j T ( dx, dy, 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 PDC E.G.M. Petrakis Multimedia Compression 49

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

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 slow E.G.M. Petrakis Multimedia Compression 51

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 half E.G.M. Petrakis Multimedia Compression 52

Three-Step Motion Vector Estimation (p=6) Furht at.al. 96 E.G.M. Petrakis Multimedia Compression 53

Three Step Search 1. Compute cost (MAD) at 9 locations Center + 8 locations at distance 3 from center 2. Pick min MAD location and recompute MAD at 9 locations at distance 2 from center 3. Pick the min MAD locations and do same at distance 1 from center The smallest MAD from all locations indicates the final estimate M 24 at (dx,dy)=(1,6) Requires 25 computations of MAD E.G.M. Petrakis Multimedia Compression 54

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 region E.G.M. Petrakis Multimedia Compression 55

Furht at.al. 96 if cost at M(0,0) < T then search ends! compute min cost at M 1,M 2,M 3,M 4 ; 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 (M 5,M 6 in the example); else compute cost at the neighborhood of min cost within p/2 (M 5 in the example) E.G.M. Petrakis Multimedia Compression 56

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 mins E.G.M. Petrakis Multimedia Compression 57

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 coding E.G.M. Petrakis Multimedia Compression 58

References B. Furht, S. W. Smoliar, H-J. Zang, Video and Image Processing in Multimedia Systems, Kluwer Academic Pub, 1996 E.G.M. Petrakis Multimedia Compression 59