Image Compression 2

8/9/2019 Image Compression 2

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Image Compression

Lecture 9

Sankalp [email protected]


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Arithmetic Coding

The arithmetic codes do not generate block codes. There is no one to one correspondence between the

code word and the sequence of symbols.

A random number selected from an interval is used to

depict a symbol. The length of the symbol decides the interval length.

1

0 0

0.2

0.04

0.08

0.056

0.072

0.0624

0.0688

0.6752a4

a3

a2

a1

a4

a3 a3

a2


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Arithmetic Coding

The 3 decimal places are used to code thesequence.

3/5 0.6 decimal digits / source.

Bounds set by the noiseless coding theorem notmet due to message ending symbols getting

added.

Scaling and rounding.


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LZW Coding

Exploits interpixel redundancy and does not requirepriory knowledge of the probability.

It assigns fixed length codes to variable length symbol

sequences.

It is a dictionary based code. For an L bit data sourcewith 2L possible symbols the first 2L symbols are allotted

codes [0-2L

].

Beyond which a dictionary word is allotted to the symbolsequences.


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LZW Coding

Each entry in the dictionary is a code word for arecognized symbol sequence.

The decoder creates a dictionary as it parses the coded

sequence.

A problem with the practical implementation is dictionaryoverflow.

Usually the dictionary is flushed and reinitialized.

The compression ratio could be used as a threshold toreinitialize the dictionary.


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Example: LZW Coding

TOBEORNOTTOBEORTOBEORNOT#


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Bit-Plane Coding

The Bit planes of an image can be coded in order toexploit interpixel redundancy.

Using gray code instead of binary code is a way to

reduce the number of 0-1/1-0 transitions in adjacentpixels with adjacent pixel values.

The higher order bit planes tend to have less

randomness as compared to the lower bit planes.

Each of the bit planes could be compressed individuallyby binary compression methods.


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Constant Area Coding

Areas of constant white or black are identified andassigned code words.

The regions with mixed intensities are also identified andare appended with a prefix.

The most probable of the region is assigned a one bitcode 1 the other two categories are given two bit codes

10 and 11.


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White Block Skipping

Useful while compressing text.

Solid white blocks are 0 black and other blocks arecoded by 1 followed by a bit pattern.

There are slight variations in which the solid white linesare coded as 0 and mixed or black with 1 as a prefix.

2D sub-blocks could be created an treated in a similarfashion. Completely white sub-blocks are coded with 0.

Iteratively the sub-blocks get coded.


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One Dimensional run-length coding

The sequences of ones and zeros are encoded as runs[the lengths of the sequences] .

Used in Fax.

The common way to denote the runs

1) is to give the value of the first run at every line

2) assume the first run is white and the length could bebe zero.


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One Dimensional Run Length Coding

The variable length codes are usually used with the run lengthcodes to further compress the data.

Symbol aj is used to represent a black run length code of length j.

The probability of such a run could be calculated as [runs of size j] /

[all runs].

The entropy of the runs can be obtained from the probabilities.

The entropy of the run lengths is given by

10

10

LL

HHH

RL


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2D Run Length Coding

Relative Address Coding tracks the binary transitions.ec distance between consecutive transitions on the

same line [current line]cc- distance between transitions of same type on

consecutive lines [previous line]

ec

c cc

e c


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Contour Tracing and Coding

Direct Contour Tracing

Predictive Differential Quantizing

Front and back contour are coded as differences in the start

points on adjacent scan lines as well as the differences inlengths of the segment enclosed by the contour.

Start and end messages are needed to signal the starting andending [merge] points on the contours.

d1

d2


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Transform Coding

The spatial domain is converted to a transform domain

Followed by quantization in the transform domain.

Constructnxn

subimages

ForwardTransform

QuantizerSymbolEncoder

Symboldecoder

Inversetransform

Mergenxn

subimages

InputImage

NxN

Compressedimage

Compressed

image

Decompressed

image


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Transform Coding

The image is divided into smaller subimages.

The subimages are transformed into a transform domain.DFT and DCT are among the common transforms.

Each transformed subimage has the coefficients with theleast information is quantized away.

The quantized coefficients are then run length coded.

The local characteristics of the image can be used tovary the quantization adaptively.


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Transform Selection

Some useful properties that transformsmay have when used for compression are

1) separability

2) symmetry

3) energy compaction.

4) fast transforms

5) variance of the transform coefficents

6) decorrelation


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Transforms for Compression

Has a fast transform.

Can be implemented with circular convolution.

Separable Symmetric and Periodic.

Needs image sizes to be padded to powers of 2.

Needs complex arithmetic.

DFT

DCT

Fast.

Has very high energy compaction for correlated data.


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Fourier Transform Kernel

The matrix elements of the Fourier Transform


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Discrete Cosine Transform Kernel

Kernel elements of Discrete Cosine Transform


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Hadamard Transform Kernel


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Walsh Transform

The walsh transform is obtainable from the Hadamard transformby bit reversal permutation followed by gray code permutations.


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Basis Functions

Walsh basis functions DCT Basis Functions


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Bit Allocation

The process of transforming and truncating and encodingis called bit allocation.

Two kinds of quantizations are called Thresholding and Zonal encoding.

Thresholding is a coarse quantization of the coefficients on the basisof magnitude.

Zonal Coding finds the regions or coefficients with the maximumVariance or information and keeps them while discarding the low entropyzones.

The Zonal quantised coefiecients are coded in two possible ways1) same number of bits/coeff normalized by standard deviations and

uniformly quantized.


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Bit Allocation

2) fixed No. of bits distributed unequally- the coefficents are modeled asrayleigh, gaussian , laplacian and the bitsallocated depend on the standard deviation.

Threshold Coding uses a mask to quantize the coefficients with lowermagnitudes away. The coefficients that are retained are coded out ofsequence.

Different ways of thresholding are

1) to apply a global threshold2) to vary the threshold over the different positions of coefficients.3) N largest coefficients are retained .

Image Compression 2

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