Image compression

Image Compression Techniques

Presented by
PARTHA PRATIM
DEB
MTECH(CSE),1st YEAR

Outline
 Image Compression Fundamentals
◦ Why Compress
◦ How is compression possible?
◦ Redundancy
◦ The Flow of Image Compression
◦ General Image Storage System
Lossy compression:
 Reduce correlation between pixels
◦ Karhunen-Loeve Transform
◦ Discrete Cosine Transform
◦ Discrete Wavelet Transform
◦ Differential Pulse Code Modulation
◦ Differential Coding
 Lossless compression:
 Quantization and Source Coding
◦ Huffman Coding
◦ Arithmetic Coding
◦ Run Length Coding
◦ Lempel Ziv 77 Algorithm
◦ Lempel Ziv 78 Algorithm
 Overview of Image Compression Algorithms
◦ JPEG
◦ JPEG 2000
◦ Shape-Adaptive Image Compression

Outline
Image Compression Fundamentals
Reduce correlation between pixels
Quantization and Source Coding
Overview of Image Compression
Algorithms

The Flow of Image Compression
 What is the so-called image compression coding?
◦ To store the image into bit-stream as compact as possible and to display the
decoded image in the monitor as exact as possible
 Flow of compression
◦ The image file is converted into a series of binary data, which is called the bit-
stream
◦ The decoder receives the encoded bit-stream and decodes it to reconstruct the
image
◦ The total data quantity of the bit-stream is less than the total data quantity of the
original image

spatial redundancy
Elements that are duplicated within a structure, such as
pixels in a still image and bit patterns in a file. Exploiting
spatial redundancy is how compression is performed.

Intraframe coding
Compressing redundant areas within a single video frame.
Interframe coding
Interframe coding often provides substantial compression because in many motion sequences,
only a small percentage of the pixels are actually different from one frame to another.

Coding
 Java Syntax:
 private int[] capture() throws InterruptedException {
 dim = Toolkit.getDefaultToolkit().getScreenSize();
 Image tmp = robot.createScreenCapture(new
Rectangle(dim.width,dim.height)).getScaledInstance(800,600,BufferedImage.SCALE_SMOOTH);
 int pix[] = new int[IMG_WIDTH*IMG_HEIGHT];
 PixelGrabber pg = new PixelGrabber(tmp,0,0,IMG_WIDTH,IMG_HEIGHT,pix,0,IMG_WIDTH);
 pg.grabPixels();
 return pix;
 }

Outline
 ImageCompression Fundamentals
 Reduce correlation between pixels(lossy)
 Quantization and Source Coding

Reduce the Correlation between
Pixels
Lossy compression:
 Orthogonal Transform Coding
◦ KLT (Karhunen-Loeve Transform)
 Maximal Decorrelation Process
◦ DCT (Discrete Cosine Transform)
 JPEG is a DCT-based image compression standard, which is a lossy
coding method and may result in some loss of details and
unrecoverable distortion.
 Subband Coding
◦ DWT (Discrete Wavelet Transform)
 To divide the spectrum of an image into the lowpass and the highpass
components, DWT is a famous example.
 JPEG 2000 is a 2-dimension DWT based image compression standard.
 Predictive Coding
◦ DPCM
 To remove mutual redundancy between successive pixels and encode
only the new information

Outline
 ImageCompression Fundamentals
 Reduce correlation between pixels(lossy)
 Quantization and Source Coding(lossless)

Quantization and Source Coding
Lossless compression techniques:
 Quantization
◦ The objective of quantization is to reduce the precision and to achieve higher
compression ratio
◦ Lossy operation, which will result in loss of precision and unrecoverable
distortion
 Source Coding
◦ To achieve less average length of bits per pixel of the image.
◦ Assigns short descriptions to the more frequent outcomes and long
descriptions to the less frequent outcomes
◦ Entropy Coding Methods
 Huffman Coding
 Arithmetic Coding
 Run Length Coding
 Dictionary Codes
 Lempel-Ziv77
 Lempel-Ziv 78

Huffman Coding

Codeword
Codeword X Probability
length
01 00 1 0
2 01 1 0.25 0.3 0.45 0.55 1
10 01 00 1
2 10 2 0.25 0.25 0.3 0.45
11 10 01
3 11 3 0.2 0.25 0.25
000 11
3 000 4 0.15 0.2
001
3 001 5 0.15

Arithmetic Coding (1/3)
 Arithmetic Coding: a direct extension of Shannon-Fano-Elias coding
calculate the probability mass function p(x n) and the cumulative distribution
function F(xn) for the source sequence xn
◦ Lossless compression technique
◦ Treate multiple symbols as a single data unit
Arithmetic Coding Algorithm
Input symbol is l
Previouslow is the lower bound for the old interval
Previoushigh is the upper bound for the old interval
Range is Previoushigh - Previouslow
Let Previouslow= 0, Previoushigh = 1, Range = Previoushigh – Previouslow =1
WHILE (input symbol != EOF)
get input symbol l
Range = Previoushigh - Previouslow
New Previouslow = Previouslow + Range* intervallow of l
New Previoushigh = Previouslow + Range* intervalhigh of l
END

Symbol Probability Sub-interval Input String : l l u u r e ?
k 0.05 [0.00,0.05)
l l u u re ?
l 0.2 [0.05,0.25)
u 0.1 [0.20,0.35) 0.0713348389
w 0.05 [0.35,0.40)
=2-4+2-7+2-10+2-15+2-16
e 0.3 [0.40,0.70)
r 0.2 [0.70,0.90) Codeword : 0001001001000011
? 0.2 [0.90,1.00)

1 0.25 0.10 0.074 0.0714 0.07136 0.071336 0.0713360
1.00

0.90
? ? ? ? ? ? ? ?
r r r r r r r r
0.70

e e e e e e e e
0.40

0.35
w w w w w w w w
0.25
u u u u u u u u

0.05 l l l l l l l l
0
k k k k k k k k
0 0.05 0.06 0.070 0.0710 0.07128 0.07132 0.0713336

Symbol Probability Huffman codeword
Input String : l l u u r e ?
k 0.05 10101
Huffman Coding 18 bits
l 0.2 01
Codeword :
u 0.1 100
01,01,100,100,00,11,1101
w 0.05 10100
e 0.3 11
Arithmetic Coding 16 bits
r 0.2 00
Codeword : 0001001001000011
? 0.2 1011

Arithmetic coding yields better compression because it encodes a message as
a whole new symbol instead of separable symbols
Most of the computations in arithmetic coding use floating-point arithmetic.
However, most hardware can only support finite precision
While a new symbol is coded, the precision required to present the range grows
There is a potential for overflow and underflow
If the fractional values are not scaled appropriately, the error of encoding occurs

Zero-Run-Length Coding-JPEG
 (1/2)
The notation (L,F)
◦ L zeros in front of the nonzero value F
 EOB (End of Block)
◦ A special coded value means that the rest elements are all zeros
◦ If the last element of the vector is not zero, then the EOB marker will not be added
 An Example:
1.57, 45, 0, 0, 0, 0, 23, 0, -30, -16, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, ..., 0
2. (0,57) ; (0,45) ; (4,23) ; (1,-30) ; (0,-16) ; (2,1) ; EOB
3. (0,57) ; (0,45) ; (4,23) ; (1,-30) ; (0,-16) ; (2,1) ; (0,0)
4. (0,6,111001);(0,6,101101);(4,5,10111);(1,5,00001);(0,4,0111);(2,1,1);(0,0)
5.1111000 1111001 , 111000 101101 , 1111111110011000 10111 ,
11111110110 00001 , 1011 0111 , 11100 1 , 1010

Dictionary Codes
 Dictionary based data compression algorithms are based on
the idea of substituting a repeated pattern with a
shorter token
 Dictionary codes are compression codes that dynamically
construct their own coding and decoding tables “on the fly”
by looking at the data stream itself
 It is not necessary for us to know the symbol probabilities
beforehand. These codes take advantage of the fact that,
quite often, certain strings of symbols are “frequently
repeated” and these strings can be assigned code words that
represent the “entire string of symbols”
 Two series
◦ Lempel-Ziv 77: LZ77, LZSS, LZBW
◦ Lempel-Ziv 78: LZ78, LZW, LZMW

Joint Photographic Experts Group (JPEG)
The JPEG Encoder

The JPEG Decoder

Reference

Digital
image processing, by Rafael
C.Gonzalez and Richard E.Woods
page no:421-423,440-456,459-486.

THANK
U
FOR UR PATIENCE

Image compression

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