Ip Image Compression

8/3/2019 Ip Image Compression

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Module IV (13 hours)

Image restoration - image observation

models - inverse filtering - wiener filteringImage compression - pixel coding -

predictive coding - transform coding -

basic ideas


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Image observation models

Refer to anil k jain pge no 268 - 275

1. Image formation models2. Noise models

3. Detector and recorder models

4. Sampled image observation models


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Image compression

Concerned with minimizing the

number of bits required to rep animage


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The objective of a image coding method is torepresent images with as small data size aspossible.

Typicallyyou start with a bitmap image, i.e., atrivial image coding method where each pixel(image element) is represented individually withone or several bytes. This is often called anun-

coded image.Image coding is often called compression,

which means that you compare with the originalun-coded image.


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Two categories of image coding methods (for bitmapimages):

Lossless coding

Lossy coding

With loss-less coding no information is lost. You only tryto find the best (smallest) data representation for thatinformation.

Ex. GIF, PNG, BMP, TIFF.

With lossy coding, you will always loose some

information. However, the compression ratio is generallymuch better than for loss-less coding (smaller files).

Ex: JPG, JPG2000, (MPEG).


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Image data compression

techniques Pixel coding - each pixel is processed independently

PCM /quantization

Entropy coding

Huffman coding

Runlength coding

bit plane coding


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PCM

Incoming video signal is sampled , quantized and coded

by generally a fixed length binary code having B bits

B- average bit rate of original data

For monochrome 8 bits/pixelcolor-10 -12 bits/pixel


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Entropy coding

The basic principle ofentropy coding isthat pixel values that occur often should

be repressed with fewer bits that thosewho occur seldom.

Here we encode a block of M pixels havingMB bits with probabilities by log2 pi

Huffman coding is an optimal algoritm forcreating a data representation with

minimal size


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Run length coding

Run length coding is an

example of entropy

encoding.

Images with repeating

greyvalues along rows

(or columns) can be

compressed by storing

"runs" of identicalgreyvalues in the

format:

row # column #

run1 begin

column #

run1 end

column #

run2 begin

column #

run2 end


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Uncompressed, a character run of 15 A characters would normally require15 bytes to store:

AAAAAAAAAAAAAAA The same string after RLE encoding would requireonly two bytes:

15A The 15A code generated to represent the character string is called anRLEpacket. Here, the first byte, 15, is the run count and contains thenumber of repetitions. The second byte, A, is the run value and contains theactual repeated value in the run.

A new packet is generated each time the run character changes, or eachtime the number of characters in the run exceeds the maximum count.Assume that our 15-character string now contains four different characterruns:

AAAAAAbbbXXXXXt Using run-length encoding this could be compressed

into four 2-byte packets: 6A3b5X1t Thus, after run-length encoding, the 15-byte string would require

only eight bytes of data to represent the string, as opposed to the original 15bytes. In this case, run-length encoding yielded a compression ratio ofalmost 2 to 1.


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The run length coding is

0 3 5 9 9

1 1 7 9 9

3 4 4 6 6 8 8 10 10 12 14


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Bit plane coding

Consider 256 level iamge as a set of 8 one

bit palnes & each can be runlength coded

Here compression ratios of 1.5 to 2 can beachieved


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Predictive oding with

Quantization

Consider: high correlation between successive

samples

Predictive coding

Basic principle: Remove redundancy betweensuccessive pixels and only encode residual between

actual and predicted

Residue usually has much smaller dynamic range

Allow fewer quantization levels for the same MSE => getcompression

Compression efficiency depends on intersample

redundancy

UMCPE

NEE408G

Slides(create

dby

M.Wu&R.L

iu

200

2)


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u(n)

Predictor

Quantizer_

e(n) eQ(n)

EncoderEncoderuP(n) = f[u(n-1)]

uQ (n)

Predictor+

eQ(n)

uP(n) = f[uQ(n-1)]DecoderDecoder


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Problem with 1st try Input to predictor are different at encoder and decoder

decoder doesnt know u(n)!

Mismatch error could propagate to future reconstructed samples

Solution: Differential PCM (DPCM) Use quantized sequence uQ(n) for prediction at both encoder

and decoder

Simple predictor f[ x ] = x Prediction errore(n)

Quantized prediction erroreQ(n)

Distortion d(n) = e(n) eQ(n)


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Predictive Coding (contd)

uQ (n)

Predictor+

eQ(n)

uP(n)

= f[uQ(n-1)]

DecoderDecoder

EncoderEncoder

u(n)

Predictor

Quantizer_

e(n) eQ(n)

+

uP(n)=f[uQ(n-1)]

uQ(n)

UMCPE

NEE408G

Slides(create

dby

M.Wu&R.L

iu

200

2)

Note: Predictor contains one-step

buffer as input to the prediction


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Transform Coding theory Use transform to pack energy to only a few coeff.

How many bits to be allocated for each coeff.?

More bits for coeff. with high variance Wk2 to keep total MSE small

Also determined by perceptual importance

From Jains

Fig.11.15


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Zonal Coding and Threshold Coding

Zonal coding Only transmit a small predetermined zone of

transformed coeff.

Threshold coding

Transmit coeff. that are above certain thresholds

Compare Threshold coding is inherently adaptive

introduce smaller distortion for the same # of coded coeff.

Threshold coding needs overhead in specifying

index of coded coeff.


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Determining Block Size

W

hy block based? High transform computation

complexity for large block

O( m logm v m ) per block

in tranf. for (MN/m2

) blocks complexity in bit allocation

Block transform captures local

info. better than global transform

Rate & complexity vs. block size

Commonly used block size ~ 8x8

From Jains Fig.11.16

complexi


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oc agram o rans orm

Coding Encoder

Step-1 Divide an image into m x m blocks and perfromtransform

Step-2 Determine bit-allocation for coefficients

Step-3 Design quantizer and quantize coefficients (lossy!)

Step-4 Encode quantized coefficients Decoder


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How to Encode Quantized

Coeff. in Each Block Basic tools Entropy coding (Huffman, etc.) and run-length coding

Predictive coding ~ esp. for DC

Ordering

zig-zag scan for block-DCT to better achieve run-length

coding gain

Horizontal frequency

Vertical

frequency

DC

AC01AC07

AC70AC77

low-frequency coefficients,

then high frequency coefficients


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advantages

Transform coding achieves relatively

larger compression than predictive

methods

Here any distortions due to quantization

and channel errors gets distributed during

inverse transformation, over the entire

range

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