JPEG Compression Standard

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JPEG Compression Standard

Mitul Modi

ME II MSARoll No: 199

22-Mar-13 JPEG Compression Standard 1


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Outlines:

JPEG Compression Overview

YCbCr Color Mode

Discrete Cosine Transform

Block diagram of JPEG Compression

Steps For JPEG Compression

Matlab code for JPEG Compression using DCT

Examples


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JPEG Compression Overview

JPEG stands for Joint Photographic Experts Group

Used on 24-bit color files.

It is a lossy compression technique, But excellent quality image

with high compression rates.

22-Mar-13 JPEG Compression Standard

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YCbCr Color Mode:


YCbCrcolor mode stores color in terms of its luminance

(brightness) and blue and red chrominance (hue).

The human eye is less sensitive to chrominance than luminance.

YCbCr is not required for JPEG compression, but it gives abetter compression rate.


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Discrete Cosine Transform:

The DCT transforms the data from the spatial domain to thefrequency domain.

The spatial domain shows the amplitude of the color as you

move through space`The frequency domain shows how quickly the amplitude of thecolor is changing from one pixel to the next in an image file.The frequency domain is better representation for data becauseit makes it possible for you to separate out and throw away

information that isnt very important to human perception.The human eye is not very sensitive to high frequency changes

especially in photographic images, so the high frequency datacan, to some extent, be discarded.


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Block diagram of JPEG Compression


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Steps in JPEG Compression

1. (Optionally) If the color is represented in RGB mode,translate it to YCbCr.

2. Divide the file into 8 X 8 blocks.

3. Transform the pixel information from the spatial domainto the frequency domain with the Discrete CosineTransform.

4. Quantize the resulting values by dividing each coefficientby an integer value and rounding off to the nearest integer.

5. Look at the resulting coefficients in a zigzag order.

6. Do the Entropy Encoding Using Entropy Encoder likeHuffman Encoder and Run-Length Encoder.



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Step 1: Converting RGB to YCbCr.


Optional But gives better Compression rate.

For converting RGB to YCbCr. Take downsampling

The notation 4:1:1 means that for each block of four pixels,

you have 4 samples of luminance information (Y), and 1

each of the two chrominance components (U and V).

MCUminimum coded unit

U, V

Y

Y

Y

Y
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Step 2: Divide into 8 X 8 blocks

Note that with YCbCr color, you have 16 pixels ofinformation in each block for the Y component (thoughonly 8 in each direction for the U and V components).

If the file doesnt divide evenly into 8 X 8 blocks, extrapixels are added to the end and discarded after thecompression.

The values are shifted left by subtracting 128.



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Step 3: DCT (1D)

Transform the pixel information from the spatial domain to

the frequency domain with the Discrete Cosine Transform.

The DCT is an array of coefficients (for 1D sequence length

N)


where


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Step 3: DCT (2D)

For N X N pixel image

the DCT is an array of coefficients

where


N

vy

N

uxpCC

NDCT

N

y xy

N

xvuuv 2

)12(cos

2

)12(cos

2

1 10

1

0

where

otherwiseCC

vuforCC

vu

vu

1

0,2

1

NvNupuv 0,0,

NvNuDCTuv 0,0,


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Continue

For the 8 X 8 matrix of color data, youre getting an 8 X 8

matrix of coefficients for the frequency components.



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Continue

DCT is designed to work on pixel values ranging from -128 to

127, the original block is leveled off by subtracting 128 from

each entry. Finally D = TMT



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Step 4: Quantization

The DCT is lossless in that the reverse DCT will give you

back exactly your initial information (ignoring the rounding

error that results from using floating point numbers.)

The values from the DCT are initially floating-point.Common Quantization Matrix is given by


Q(i,j)=


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Continue..

Quantization involves dividing each coefficient by an integer

between 1 and 255 and rounding off.

The quantization table is chosen to reduce the precision of

each coefficient to no more than necessary.The quantization table is carried along with the compressed

file.



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Step 5: Arrange in zigzag order

This is done so that the coefficients are in order of increasingfrequency.

After quantization, most of the coefficients to equal zero.

JPEG takes advantage of this by encoding quantizedcoefficients in the zig-zag sequence.

The advantage lies in the

consolidation of relatively

large runs of zeros, whichcompress very well.



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An entropy encoder supplementary compresses thequantized values losslessly to provide a better overallcompression.

It uses a model to perfectly determine the probabilities foreach quantized value and produces an appropriate codebased on these probabilities so that the resultant outputcode stream is smaller than the input stream.

The most commonly used entropy encoders are the

Huffman encoder and the arithmetic encoder, although forapplications requiring fast execution, simple Run LengthEncoding (RLE) is very effective. This improves thecompression of run-length encoding.

Step 6: Entropy Encoder


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Matlab code :


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Examples :

DCT to rows only:


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Examples :

DCT to rows*Column :


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Reference:

Digital Image Processing by Rafael Gonzalez and Richard Woods

M.Mohamed Sathik , K.Senthamarai Kannan and Y.Jacob Vetha Raj,

Hybrid JPEG Compression Using Histogram Based Segmentation.

International Journal of Computer Science and Information Security, Vol.

8, No. 8, November 2010

Leger, A., T. Omachi, and T.K. Wallace, "JPEG Still Picture Compression

Algorithm," Optical Engineering, vol. 30, no. 7, July 1991, pp. 947-954.

Kiran Bindu, Anita Ganpati, Aman Kumar Sharma, A Comparative

Study Of Image Compression Algorithms.International Journal of

Research in Computer Science eISSN 2249-8265 Volume 2 Issue 5 (2012)

http://www.jpeg.org,

http://cnx.rice.edu,

http://www.datacompression.info

http://www.jpeg.org/http://cnx.rice.edu/http://www.datacompression.info/http://www.datacompression.info/http://cnx.rice.edu/http://www.jpeg.org/


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Lossy Compression Model

Documents

JPEG Compression Standard