Image Compression Shabbir

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    IMAGE COMPRESSION

    TECHNIQUES

    BY: C.MD.SHABBIR

    (04098077)

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    INTRODUCTION

    WHAT IS AN IMAGE?

    WHAT IS IMAGE COMPRESSION?

    TYPES OF REDUNDANCIES

    WHY DO WE NEED IMAGE COMPRESSION?

    IMAGE COMPRESSION TECHNIQUES

    SUMMARY

    CONCLUSION

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    PIXELS

    This example shows an image with a portion

    greatly enlarged, in which the individual pixels

    are rendered as little squares and can easily be

    seen.

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    Memory requirements

    pixels Size (uncompressed)

    1.3 Mpixel 3.7 MB

    2.1 Mpixel 6 MB

    5 Mpixel 14.3 MB

    8 MPixel 22.8 MB

    The number of bytes to store an uncompressedimage can be really huge. So we need image

    compression techniques.

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    Overview Of Image Compression

    - Process of reducing or compressing size and imagedata files but still retaining important information.

    - compressed file is used to reconstruct image.

    - relationship between compressed and uncompressed

    file is denoted as the compression ratio

    Compression Ratio =Uncompressed file size

    Compressed file size=

    SIZEU

    SIZEC

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    COMPRESSION ALGORITHMS :

    The image compression algorithms can be

    divided into two branches : Lossless algorithms

    The information content is not modified .

    Lossy algorithmsThe information content is reduced and it is

    not recoverable .

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    Lossless Compression Method

    Lossless Compression Methods:

    1) Run length coding2) Huffman Coding

    3) Predictive Coding

    Lossless compression methods guarantees

    that the decompressed image is absolutely

    identical to the image before compression.

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    A simple example

    Suppose we have a message consisting of 5 symbols, e.g.

    []

    How can we code this message using 0/1 so the coded

    message will have minimum length (for transmission or

    saving!)

    5 symbols at least 3 bits

    For a simple encoding,

    length of code is 10*3=30 bits

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    A simple example cont.

    Intuition: Those symbols that are more frequent should have

    smaller codes, yet since their length is not the same, there

    must be a way of distinguishing each code

    For Huffman code,

    length of encoded message

    will be

    =3*2 +3*2+2*2+3+3=24bits

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    12

    Lossless compression

    techniques

    Run-length coding

    Huffman Coding Lossless Predictive Coding

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    Run-length coding

    replacing long sequences of the same valuewith a code indicating the value that isrepeated and the number of times it occurs in

    the sequence. Input sequence:

    0,0,-3,5,1,0,-2,0,0,0,0,2,-4,3,-2,0,0,0,1,0,0,-2

    Run-length sequence:(2,-3)(0,5)(0,1)(1,-2)(4,2)(0,-4)(0,3)(0,-2)(3,1)(2,-2)

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    15

    Lossless compression

    techniques Run-length coding

    Huffman Coding

    Lossless Predictive Coding

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    Huffman Coding

    When coding the symbols of an information

    source individually, Huffman coding yields

    the smallest possible number of code

    symbols per source symbol.

    The resulting code is optimal for a fixed value

    of n, subject to the constraint that the source

    symbols be coded one at a time.

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    Huffman Coding Steps

    (i) Arrange the symbol probabilities in a decreasing

    order and consider them as leaf nodes of a tree.

    (ii) While there is more than one node:

    Merge the two nodes with smallest probability toform a new node whose probability is the sum of

    the two merged nodes.

    Arbitrarily assign 1 and 0 to each pair of branchesmerging into a node.

    (iii) Read sequentially from the root node to the leaf

    node where the symbol is located.

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    Example

    1.0)()(

    4.0)(

    2.0)()(

    },,,,{

    54

    2

    31

    54321

    aPaP

    aP

    aPaP

    aaaaaA

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    Example

    Ax={ a , b , c , d , e }

    Px={0.25, 0.25, 0.2, 0.15, 0.15}

    d

    0.15

    e

    0.15

    b

    0.25

    c

    0.2

    a

    0.25

    0.3

    0 1

    0.45

    0 1

    0.55

    0

    1

    1.0

    0

    1

    00 10 11 010 011

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    20

    Lossless compression

    techniques Run-length coding

    Huffman Coding

    Lossless Predictive Coding

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    Lossless Predictive Coding

    Predicting the next pixel value based on the

    previous value

    Encoding the difference between the

    predicted value and the actual value

    Differential pulse code modulation (DPCM)

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    Lossless Predictive Coding

    Predictor

    Input

    imageSymbol

    encoder

    Compressed

    image

    Each successive pixel of the input image, denoted

    The output of the predictor is then rounded to thenearest integer, donated

    nf

    nf^

    A lossless predictive coding model: encoder

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    Lossless Predictive Coding

    Predictor

    Symbol

    decoder

    Compressed

    image

    A lossless predictive coding model: decoder

    Decompressedimage

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    Lossless Predictive Coding

    In most cases, however, the prediction is formed by alinear combination of m previous pixels. That is,

    where m is the order of the linear predictor, round is

    a function used to denote the rounding or nearest

    integer operation, and the for i=1,2,3m areprediction coefficients.

    ia

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    Lossy Compression

    In order to achieve higher rates of compression, we

    give up complete reconstruction and consider lossy

    compression techniques

    So we need a way to measure how good thecompression technique is

    How close to the original data the reconstructed

    data is

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    Lossy Compression Techniques

    Vector quantization

    Transformation coding

    Fractal coding

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    The basic idea in this technique is to develop a

    dictionary of fixed-size vectors, called code vectors.

    A vector is usually a block of pixel values. A given image

    is then partitioned into non-overlapping blocks (vectors)called image vectors.

    Then for each in the dictionary is determined and its

    index in the dictionary is used as the encoding of the

    original image vector.Thus, each image is represented by a sequence of

    indices that can be further entropy coded.

    Outline of Vector Quantization

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    S.R.Subramanya 28

    Outline of Vector Quantization of

    Images

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    Lossy Compression Techniques

    Vector quantization

    Transformation coding

    O tli f T f ti C di

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    In this coding scheme, transforms such as DFT (Discrete Fourier

    Transform) and DCT (Discrete Cosine Transform) are used tochange the pixels in the original image into frequency domain

    coefficients (called transform coefficients).

    These coefficients have several desirable properties. One is the

    energy compaction property that results in most of the energy of

    the original data being concentrated in only a few of the

    significant transform coefficients.

    Only those few significant coefficients are selected and theremaining are discarded.

    The selected coefficients are considered for further quantization

    and entropy encoding.

    Outline of Transformation Coding

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    Conclusion

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    References