Compression

Compression

•Word document: 1 page is about 2 to 4kB

•Raster Image of 1 page at 600 dpi is about 35MB

•Compression Ratio, CR = , where is the number of bits

•Compression techniques take advantage of:

• Sparse coverage

• Repetitive scan lines

• Large smooth gray areas

• ASCII code, always 8 bits per character

• Long words frequently used

comp

orig

i

N

ii ppsH 2

1

log)(

Entropy

•Entropy is a quantitative term used for amount of information in a string

0.0 0.2 0.4 0.6 0.8 1.0

1.00

0.80

0.60

0.40

0.20

0.00

H(1)+H(0)

H(1)

H(0)

)(log)()(1

2

N

iii lplpsH

For N clusters, where li is the length of the ith cluster

)(/max sHlCR

Binary Image Compression Techniques

•Packing: 8 pixels per byte

•Run Length Encoding: Assume 100 dpi, 850 bits per line

• encode only the white bits as they are long runs

• Top part of a page could be 0(200)111110(3)111110(3) ….

•Huffman Coding: use short length codes for frequent messages

Message Probability

A 0.30

B 0.25

C 0.20

D 0.10

E 0.15

A .30 .30 .45 .55

B .25 .25 .30 .45

C .20 .25 .25

E .15 .20

D .10

A 00

.30

00 .30

1 .45

0

.55

B 01.25

01.25

00.30

1.45

C 11.20

10.25

01.25

E 100.15

11.20

D 10110

Encode Decode

Huffman Encoding0

(2,7) (13,2) 0

(2,7) (13,2) 0

(2,7) (13,2) 0

(2,2) (7,2) (13,2) 0

(2,2) (7,2) (13,2) 0

(2,7) (13,2) 0

(2,2)(7,2)(13,2) 0

(2,2)(7,2)(13,2) 0

0

Bit map: 160 bits

50 numbers in range 0-15

Use 4 bits per number: 200 bits

2 bits per symbol: 100 bits

HC: 1.84 x 50 = 92 bits

84.116.0316.0320.0248.01)( ii

iaverage sPlL

Predictive Coding

•Most pixels in adjacent scan lines s1 and s2 are the same

•S2’ is the predicted version 212 ' sss '212 sss

2112 ssss

x4 x3 x2

x1 x0 x

2 dimensional predictionX4 X3 X2 X1 X0

p(0)

p(1)

Xp

0 0 0 0 0 0.99 0.01 0

0 0 0 0 1 0.40 0.60 1

0 0 0 1 0 0.60 0.40 0

0 0 0 1 1 0.25 0.75 1•Probabilities gathered from document collections

•Tradeoff between context size and table size; Context size of 12 pixels common which uses a 4096 entries table

Group III Fax

•White runs and black runs alternate

•All lines begin with a white run (possibly length zero)

•There are 1728 pixels in a scan line

•Makeup codes encode a multiple of 64 bits

•Terminating codes encode the remainder (0 to 63)

•EOL for each line

•CCITT lookup tables

•Example,

• White run of 500 pixels would be encoded as

• 500 = 7x 64 + 52

• Makeup code for 7x 64 is 0110 0100

• Terminating code for 52 is 0101 0101

• Complete code is 0110 0100 0101 0101

Group IV READ

1 1 1 1 0 0 0 0 1 1 1 0 0 0 0

1 1 0 0 0 0 1 1 1 1 1 1 0 0 0

Reference

Coding

a0

b1

a2a1

b2

•a0 is the reference changing pixel; a1 is the next changing pixel after a0; and a2 is the next changing pixel after a1.

•b1 is the first changing pixel on the reference line after a0 and is of opposite color to a0; b2 is the next changing pixel after b1.

•To start, a0 is located at an imaginary white pixel point immediately to the left of the coding line.

•Follow READ algorithm chart

Group IV

READ

Grayscale Compression- JPEG

16

)12(cos

16

)12(cos),(

4

)()(),(

vkujkjf

vCuCvuF

16

)12(cos

16

)12(cos),()()(

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1),(

7

0

7

0

vjuivuFvCuCjif

u v

7

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2

)(),(

j

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0

vkkjf

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k

Information Retrieval (Typed text documents)•IR goal is to represent a collection of documents were a single document is the smallest unit of information

•Typify document content and present information upon request

Requests DocumentsSimilarity Measure

1. OCR translates images of text to computer readable form and IR extracts the text upon request

2. Inverted Index: Transpose the document-term relationship to a term-document relationship

3. Remove Stopwords: the, and, to, a, in, that, through, but, etc.

4. Word Stemming: Remove prefixes and suffixes and normalize

Term Docid: Frequency

character 1:1 3;1

computer 1:1 2:1 3:1

devices 1:2 3:1

extract 2:1 3:1

form 1:1 3:1

information 2:2 3:2

IR 2:1 3:1

OCR 1:1 3:1

optical 1:1 3:1

printed 1:1 3;1

readable 1:1 2:1 3:1

recognition 1:1 3:1

request 3:1

retrieval 2:1 3:2

sequentially 3:1

system 2:2 3:2

text 1:1 2:1 3:2

translate 1:1 3:1

Query 1: recognition or retrievalResponse: 1 2 3

Query 2:sequentially and readableResponse: 3

Query 3: not translateResponse: 2

Query:character and recognition or retrieval

Vector Space Model

•Each document is denoted by a vector of concepts (index terms)

•If the term is present in the document 1 is placed in the vector

•Vector of document 1 from table: (1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1)

•Weighting: Favor terms with high frequency in a few documents

Term i Document j

dfi tij wij

character 1 2 1 0.17609

Computer

1 3 1 0.00000

Retrieval 3 2 2 0.35218

N = total documents

Dfi = no. of docs containing term i

Tij = frequency of term i in doc j

iijij df

Ntfw log

Document similarity measure

between Dj (wi,w2j,…wmj) and Qr (q1r,q2r,..qmr)

m

k

m

kkj

m

kkrkj

rj

krqw

qwQD

1 1

22

1),cos(

Relevance FeedbackN = no. of documents in collection

R = number of documents relevant to query q

N = no. of documents containing t

R = no. of relevant documents containing t

F = proportion of relevant documents to non-relevant documents in which term occurs

F’ = without relevance feedback

k = constant, adjusted with collection size

c = collection size

fi = no. of documents in which term i occurs

tij = frequency term i in document j

Maxtfj = maximum term frequency in document j

)()(

log

rRnNrnrRr

F

c

fc

tf

tkk i

j

ij

log

log

maxlog

log)1(

Precision and Recall

•Coverage: extent to which system includes relevant documents

•Time lag: average time it takes to produce an answer to a search request

•Presentation: quality of the output

•Effort: energies put forth by user to obtain information sought

•Recall: proportion of relevant material received from a query

•Precision: proportion of retrieved documents actually relevant

ca

a

ba

a

Recall=

Precision=

Relevant Not relevant

Retrieved a b

Not retrieved

C d