data compression 2011 - jan sloot

Animation 1

Data extraction compression and recovery tutorial

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(right click/ open hyperlink)

Data compression

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Original Image --- 24 bits per pixel JPEG --- 0.5 bits per pixel

http://www.data-compression.com/image.shtml

De Broncode(1998)

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video films with a compression factor > 106

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‘De broncode’ (claims)

• “alleen essentiële onderdelen van beeld en geluid opslaan”

• “bijv. tekst niet letter voor letter opslaan, maar door middel van één getal dat de volgorde van alle letters

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in dat boek in zich draagt”• “de opslagcapaciteit kan met deze code 1 miljoen keer

worden vergroot”• “op een chipkaartje (16 kbyte) kunnen 16 films staan”• “alle speelfilms ooit gemaakt passen op één CD”

meer info op EN- en NL-wikipedia (Jan Sloot)

introductory bookDavid Salomon "A guide to data compression

methods“Springer-Verlag New York, 2002 [EL e91 s13]

See also:- Waser, Introduction to part VI Data

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- Waser, Introduction to part VI Datatransmission and interfaces

- Report Broadband applications on limited ...- http://www.data-compression.com/

Links to scanned book sections etc., and also this powerpoint,via Blackboard (Course Materials & Course Information)

general remarks (1)• compressing data = removing redundancy

data without redundancy (most files!) cannot be compressed

• ASCII-coded text is redundant (always 8 bits per character)

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per character)� variable-size codes

(short codes for common data)• digital images

� assign short codes to dominant colors� consider correlation of neighboring pixels

general remarks (2)

• redundancies depend on data type (text, image, sound)each data type has its own compression algorithm

• adaptive (example: adaptive Huffman)

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• adaptive (example: adaptive Huffman)non-adaptive (example: facsimile compression)

• lossy compression (loss of data: movie/sound)lossless compression (for text, computer data)

• (non)symmetric compression (“real-time” divX)

subject overview

• statistical methods Huffman coding• dictionary compression (LZW)• image compression (JPEG)

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• image compression (JPEG)• wavelet transform (SPIHT)• video compression (MPEG)• audio compression (MP3)

statistical methods (digrams)

digrams � ta, he, ca (common)xa, hz, qu (rare)

trigrams � and

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trigrams � and

assign variable-size codesto the many digrams (and trigrams)

statistical methods (entropy 1)

alphabet of symbols a1 - an, probabilities P1 - Pn

self-information of ai : -log2Pi → unit: “bits”-log20 = ∞ -log20.5 = 1 -log21 = 0

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entropy is “the average self-information”

entropy of entire alphabet: �=

−n

iii PP

12log

statistical methods (entropy 2)alphabet with 5 symbols

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23 = 8, so without compression we need10 (symbols) * 3 bits = 30 bits

statistical methods (variable-size codes)1. assign short codes to frequent symbols2. obey the prefix property

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ACBAcode 1 1 01 001 1 � 1 010 01 1

A B D A � A C B A

code 2 1 000 01 1

A C B A

statistical methods (Huffman 1)

produce the best (= shortest) code

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Huffman for Dutch text

http://nl.wikipedia.org/wiki/Huffmancodering

Letter frequencies in Dutch texts

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Letter percent Letter percent Letter percent Letter percent Letter percent Letter percent Letter percent

E 18,91% N 10,03% A 7,49% T 6,79% I 6,50% R 6,41% O 6,06%

D 5,93% S 3,73% L 3,57% G 3,40% V 2,85% H 2,38% K 2,25%

M 2,21% U 1,99% B 1,58% P 1,57% W 1,52% J 1,46% Z 1,39%

C 1,24% F 0,81% X 0,04% Y 0,03% Q 0,01%

�=

−n

iii PP

12log (entropy) is 4.1

Huffman tree and letter codes

Optimal

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Optimalcodesfor theDutch

language( capitals

&small letters)

statistical methods (fax)

fax machine

• scans document line by line

RLE = Run-Length Encoding

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RLE = Run-Length Encodingrun length = “combination of black/white pixels”

• most common run lengths assigned to the shortest codes (2, or 3, or 4 black pixels)

• modified Huffman algorithm, non-adaptive• compression 4-10

subject overview


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dictionary compression (1)

- example -

English text, with average word size 5 characters

output file = indexes and/or raw words

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output file = indexes and/or raw words

• index = flag bit 1, 19-bit index (219 = 524288)

• raw word = flag bit 0, 7-bit field (=size), 5 bytes

under conditions � 48 bits compressed to 20 bits

dictionary compression (2)this exampleprobability of a word found in dictionary: P� size of input file (N words) = 40N bits

size of output file = N[20P + 48(1-P)] bits

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size of output file = N[20P + 48(1-P)] bitscompression if P > 0.29 (matching rate > 29%)--------------more sophisticated:adaptive dictionary-based method

(building a dictionary from scratch)

ZIP code

applies 'deflate', a combination of• L777 dictionary method• Huffman

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• Huffman

subject overview


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image compression (1)

- book contains about 106 characters 1 Mbyteimage (512 x 512 x (8+8+8))/8 = 0.7 Mbyte

- lossy compression accepted(= removing “irrelevance”)

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(= removing “irrelevance”)

- redundancy & irrelevance properties dependon type of image(bi-level, grayscale, color, continuous tone,discrete tone, cartoon-like)

lossy image compression

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Original Image --- 24 bits per pixel JPEG --- 0.5 bits per pixel


• large number of elementary ‘symbols’224 = 16.78 106 (3 colors, each 28 intensities)(text: 256 ASCII characters, � 256 bytes)

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(text: 256 ASCII characters, � 256 bytes)• correlation between near-neighbour pixels

(= spatial redundancy)• methods exist for automatically deleting

irrelevant image information


“How to represent pixel properties?”RGB YCbCr

red green blue luminance Y B-Y R-Y

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• eye is more sensitive to brightness changesthan to color changes

• compression should focus on removing irrelevant color changes� represent pixels in YCbCr color space

image compression (image transforms)

1 transform (correlated) pixels to representation which is decorrelated e.g.discrete cosine transform- compression if new values are smaller than

original ones

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original ones- transformation to representation withdecorrelated pixels results in fully compressedimage

2 lossy compression by quantizing the transformed values

image compression (JPEG)

main steps• transform from RGB to YCbCr• color components are organized in groups of 8x8 pixels• discrete cosine transform (DCT) for pixel groups

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• discrete cosine transform (DCT) for pixel groups• quantization of frequency components (= loss of information)• encoding of freq. components using RLE and Huffman coding• add headers, values of JPEG parameters, output the results

image compression (DCT 1)

DCT (discrete cosine transform)

for pixels pxy:, the 2-dimensional DCT is

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for pixels pxy:, the 2-dimensional DCT is

( ) ( )��

= =��

��

� +��

��

� +=7

0

7

041

16

12cos

16

12cos

x yxyjiij

jyixpCCG

ππ

0for 1and ,0for 2

1 >=== f CfC ff


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calculating aone-dimensionaldiscrete cosine transform (DTC)

imagecompression

(DCT 3)

the 64 basis

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the 64 basis imagesof thetwo-dimensional discrete cosine transform (DCT)


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subject overview


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toepassing wavelets in jpeg2000-standaard

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Uit: Natuurwetenschap & Techniek, juli/aug 2006

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toepassing wavelets

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subject overview


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capacity of "tv-cable" at home

"2008"analog:35 tv channels35 radio channels

"1997"analog35 tv channels35 radio channels

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35 radio channels

digital100 tv channels

incl. HD channels60 audio channelstelephoneinternet

35 radio channels"kabel is vol"

tv cable (2)

see also Waser,pages 709-713 about encoding:

1 source encoding

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1 source encoding (data compression) +

2 channel encoding (error correction) +

3 line encoding and modulation(adapting to physical channel)

the need for 'line encoding'(here: 2-D magnetic patterned-media recording)

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video compression (1)

book contains ~106 characters 1 Mbyteimage (512 x 512 x (8+8+8))/8 = 0.7 Mbytevideo / studio camera ‘raw’ 35 Mbyte/s after compressionvideo / studio quality 720 x 576 1.25 Mbyte/s

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video / studio quality 720 x 576 1.25 Mbyte/svideo / HDTV 1920 x 1080 2.5 Mbyte/s

spacial redundancy (pixels in one frame)temporal redundancy (neighbor frames)

video compression(motion compensation)

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1 encode 1th frame � intra frame I

2a consider differences between I and next

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2a consider differences between I and nextframe(s),using past frame (I or P) � interframe P,or encode independently � I

2b encoding, based on a past frame (I or P)and a future frame (I or P) � B


I intra

P predictive

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P predictive

B bidirectional

Animation 2

Data compression error video art....

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(right click/ open hyperlink)

subject overview


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Sampling andquantization ofa signal (red)for 4-bit

audio compression

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for 4-bitpulse-codemodulation(PCM )

CD: 44100 Hz sampling rate (each channel)16-bit PCM (65536 levels) � 1411.2 kbit/s

audio compression (3)• lossless compression of 16-bit PCM audio is

possible to factor 2.6 (using LA, WMA, ..)

• MP3 represents PCM audio, discarding portions that are less important for human ear and brain

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with respect to CD bit rate:• mp3 compression factor 4.3 to 43• for best encoder

“good” 128 kbit/s 11 “excellent” 192 kbit/s 7.4

audio compression (mp3 encoding)

• filtering, 32 bands

• Modified Discrete Cosine Transform (MDCT)

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• Modified Discrete Cosine Transform (MDCT)36 or 12 tap

• quantizing, using a psychoacoustic model �(frequency & temporal masking)

final conclusions ondata compression

• achievable compression factors depend on redundancy and irrelevance

• compression method must match the type of

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• compression method must match the type of raw data (text, image, video, ...)

• “assuming that current compression factors will essentially improve in future does not appear realistic”

some compression factors

• statistical methods Huffman coding fax 4-10• dictionary compression ‘english dictionary’ < 2.4• image compression JPEG 10-20, ‘monkey’ 48

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• image compression JPEG 10-20, ‘monkey’ 48• wavelet transform (SPIHT)• video compression DV 5, MPEG-2 dvd 3hr 40

iPod video player (if from 18 MB/s to 0.11 MB/s) 160 audio compression WMA (lossless) 2.5

MP3 (lossy) 4-40

and finally...

compression costs processing power !

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compression costs processing power !

consider this in your 'case studies' and'design projects'

laatste slide

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data compression 2011 - jan sloot

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