multimedia compression

E.G.M. Petrakis Multimedia Compression 1

Multimedia Compression

Audio, image and video require vast amounts of data320x240x8bits grayscale image: 77Kb1100x900x24bits color image: 3MB640x480x24x30frames/sec: 27.6 MB/sec

Low network’s bandwidth doesn't allow for real time video transmission

Slow storage or processing devices don't allow for fast playing back

Compression reduces storage requirements


Classification of Techniques

Lossless: recover the original representation

Lossy: recover a representation similar to the original onehigh compression ratiosmore practical use

Hybrid: JPEG, MPEG, px64 combine several approaches


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Compression Standards


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Lossless Techniques


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Lossy Techniques


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


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JPEG Block Diagrams


JPEG Encoder

Three main blocks:Forward Discrete Cosine Transform (FDCT)QuantizerEntropy Encoder

Essentially the sequential JPEG encoderMain component of progressive, lossless

and hierarchical encoders For gray level and color images


Sequential JPEG

Pixels in [0,2p-1] are shifted in [-2p-1,2p-1-1] The image is divided in 8x8 blocksEach 8x8 block is DCT transformed

0for 1

0for 2

1)(

0for 1

0for 2

1)(

16

)12(cos

16

)12(cos),(

2

)(

2

)(),(

7

0

7

0

v

vvC

u

uuC

vyuxyxf

vCuCvuF

x y


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 encodedThis fact achieves compression


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 0Discards information which is not

visually significantQuantization coefficients Q(u,v) are

specified by quantization tablesA set of 4 tables are specified by JPEG


Quantization Tables

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 compressionquality = 25: poor quality, highest compression

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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

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DC Coefficients

Predictive coding of DC CoefficientsAdjacent blocks have similar DC intensitiesCoding differences yields high

compression


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 valuesize: number of bits to encode amplitude 0 0 0 0 0 0 476: (6,9)(476)


Huffman coding

Converts each sequence into binaryFirst DC following with ACsHuffman tables are specified in JPEGEach (runlength, size) is encoded

using Huffman codingEach (amplitude) is encoded using a

variable length integer code(1,4)(12) => (11111101101100)


Example of Huffman table

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JPEG Encoding of a 8x8 block


Compression Measures

Compression ratio (CR): increases with higher compressionCR = OriginalSize/CompressedSize

Root Mean Square Error (RMS): better quality with lower RMS

Xi: original pixel values

xi: restored pixel valuesn: total number of pixels

n

i ii xXn

RMS1

2)(1


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JPEG Decoder

The same steps in reverse orderThe binary sequences are converted to

symbol sequences using the Huffman tables

F’(u,v) = Fq(u,v)Q(u,v)Inverse DCT

7

0

7

0 16

)12(cos

16

)12(cos),()()(

4

1),(

u v

vyuxvuFvCuCyxF


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

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Progressive Spectral Selection

The DCT coefficients are grouped into several bandsLow-frequency bands are firstband1: DC coefficient only

band2: AC1,AC2 coefficients

band3: AC3, AC4, AC5, AC6 coefficients

band4: AC7, AC8 coefficients


Lossless JPEG

Simple predictive encoding

prediction schemes

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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


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 24. Interpolate by 2 in x, y5. Use the up-sampled image as predictor 6. Encode differences (predictive coding)7. Go to step 1 until the full resolution is

encoded


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JPEG for Color images

Encoding of 3 bands (RGB, HSV etc.) in two ways:Non-interleaved data ordering: encodes

each band separatelyInterleaved data ordering: different

bands are combined into Minimum Coded Units (MCUs)Display, print or transmit images in parallel

with decompression


Interleaved JPEG

Minimum Coded Unit (MCU): the smallest group of interleaved data blocks (8x8)

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Video Compression

Various video encoding standards: QuickTime, DVI, H.261, MPEG etcBasic idea: compute motion between

adjacent frames and transmit only differences

Motion is computed between blocks Effective encoding of camera and object

motion


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

http://mpeg.telecomitalialab.com/

http://mpeg.telecomitalialab.com/


MPEG Features

Random accessFast forward / reverse searchesReverse playbackAudio – visual synchronizationRobustness to errorsAuditabilityCost trade-off


MPEG -1, 2

At least 4 MPEG standards finished or under construction

MPEG-1: storage and retrieval of moving pictures and audio on storage media352x288 pixels/frame, 25 fps, at 1.5 MbpsReal-time encoding even on an old PC

MPEG-2: higher quality, same principles720x576 pixels/frame, 2-80 Mbps


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 implementationsHigher compression ratios


MPEG-7

Standard for the description of multimedia content XML Schema for content descriptionDoes not standardize extraction of

descriptionsMPEG1, 2, and 4 make content

availableMPEG7 makes content semantics

available


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

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Frame Structures

I frames: self contained, JPEG encoded Random access frames in MPEG streamsLow compression

P frames: predicted coding using with reference to previous I or P frameHigher compression

B frames: bidirectional or interpolated coding using past and future I or P frameHighest compression


Example of MPEG Stream

B frames 2 3 4 are bi-directionally coded using I frame 1 and P frame 5P frame 5 must be decoded before B frames 2 3 4I frame 9 must be decoded before B frames 6 7 8Frame order for transmission: 1 5 2 3 4 9 6 7 8

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MPEG Coding Sequences

The MPEG application determines a sequence of I, P, B framesFor fast random access code the

whole video as I frames (MJPEG)High compression is achieved by

using large number of B framesGood sequence: (IBBPBBPBB)

(IBBPBBPBB)...


Motion Estimation

The motion estimator finds the best matching block in P, B framesBlock: 8x8 or16x16 pixelsP 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


Motion Vectors

One or two motion vectors per blockOne vector for forward predicted P or B frames

or backward predicted B framesTwo vectors for interpolated B frames

block: 16x16pixles

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MPEG Encoding

I frames are JPEG compressedP, B frames are encoded in terms of future

or previous framesMotion vectors are estimated and

differences between predicted and actual blocks are computed These error terms are DCT encoded Entropy encoding produces a compact binary

codeSpecial cases: static and intracoded blocks


MPEG encoder

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JPEG encoding


MPEG Decoder Furht at.al. 96


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 framesThe block is compared with a previous

or forward block within a search area of size (m+2p)x(n+2p)

m = n = 16p = 6


Block Matching

Search area in block matching techniquesTypical case: n=m=16, p=6F: block in current frameG: search area in previous (or future) frame

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Cost functions

The block has moved to the position that minimizes a cost function

I. Mean Absolute Difference (MAD)

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)

2/

2/

2/

2/

),(),(1

),(n

ni

m

mj

dyjdxiGjiFmn

dydxMAD


More Cost Functions

II. Mean Squared Difference (MSD)

III. Cross-Correlation Difference (CCF)

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2/

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2),(),(

1),(

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m

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2/1

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),(),(

),(

i ji j

i j

dyjdxiGjiF

dyjdxiGjiF

dydxCCF


More cost Functions

IV. Pixel Difference Classification (PDC)

t: predefined threshold each pixel is classified as a matching

pixel (T=1) or a mismatching pixel (T=0) the matching block maximizes PDC

otherwise

tdyjdxiGjiFifjidydxT

jidydxTdydxPDCi j

0

),(),(1),,,(

),,,(),(


Block Matching Techniques

Exhaustive: very slow but accurateApproximation: faster but less

accurateThree-step search2-D logarithmic searchConjugate direction searchParallel hierarchical 1-D search (not

discussed) Pixel difference classification (not discussed here)


Exhaustive Search

Evaluates the cost function at every location in the search areaRequires (2p+1)2 computations of the

cost functionFor p=6 requires169 computations per

block!!Very simple to implement but very

slow


Three-Step Search

Computes the cost function at the center and 8 surrounding locations in the search areaThe location with the minimum cost

becomes the center location for the next step

The search range is reduced by half


Three-Step Motion Vector Estimation (p=6)

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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

• M24 at (dx,dy)=(1,6)

• Requires 25 computations of MAD


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


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)

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Conjugate Direction Search

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

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Other Compression Techniques

Digital Video Interactive (DVI)similar to MPEG-2

Fractal Image CompressionFind regions resembling fractalsImage representation at various

resolutionsSub-band image and video coding

Split signal into smaller frequency bandsWavelet-based coding


References

B. Furht, S. W. Smoliar, H-J. Zang, “Video and Image Processing in Multimedia Systems”, Kluwer Academic Pub, 1996

multimedia compression

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petrakismultimedia compression

jpegmultimedia compression

highest compression

j quality quality

amplitude of coefficients

multimedia compressionaudio

dct coefficientsf0

rough decoded image