Introduction to JPEG

m5141153 Akram Ben Ahmed

http://en.wikipedia.org/wiki/JPEG

Outline

• Introduction• Encoding• Decoding• Summary and Future work

Research Paper Reading 22010/7/12

Introduction

• JPEG (Joint Photographic Experts Group) is one of the most widely used lossy compression method.

• JPEG has many standards and can be encoded in many ways.

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Outline

• Introduction• Encoding• Decoding• Summary and Future work

Research Paper Reading 42010/7/12

Encoding: Color space transformation

• The image should be converted first from RGB to YCrCb.

• Y represents the brightness of the picture while Cr and Cb represent the red and bleu chrominance respectively.

• This picture shows a color image and the Y, Cb and Cr elements of it.

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Encoding: Color space transformation

• The conversion is done by multiplying the pixels values of the RGB image by Y, Cr and Cb factors as shown below.

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Encoding: Downsampling

• In this step, the resolution of the Chroma components (Cr and Cb) is reduced.

• This reduction came from the fact that human eyes detect the brightness change more than the color differences.

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Encoding: Downsampling

• The ratios at which the downsampling is ordinarily done for JPEG images are 4:4:4, 4:2:2 or 4:2:0 (most commonly) .

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Encoding

• The next process steps are done to each Y Cr Cb components separately.

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Encoding: Discrete cosine transform

• We divide first the image into 8x8 blocks.• If one block can’t be exactly represented in

8x8, the encoder must fill the remaining area of the incomplete blocks with some form of dummy data.

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Encoding: Discrete cosine transform

• Before computing the DCT of the 8×8 block, its values are shifted from a positive range (0-->255) to one centered around zero by subtracting the mid-point of the range (128 in our case) from the original block values.

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Encoding: Discrete cosine transform

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m= Original Block matrix g= Resulted shifted matrix

Encoding: Discrete cosine transform

• We perform now the 2D DCT given by:

– u is the horizontal spatial frequency, for the integers 0<u<8.– v is the vertical spatial frequency, for the integers 0<v<8.

– .

– gx,y is the pixel value at coordinates (x,y)– Gu,v is the DCT coefficient at coordinates (u,v)

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Encoding: Discrete cosine transform

• The resulted DCT matrix G is:

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Encoding: Quantization

• This step consists of dividing each component in the frequency domain by a constant for that component, and then rounding to the nearest integer.

• This makes the quantization the only lossy operation due to the rounding operation.

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Encoding: Quantization

• Assuming the following quantization matrix:

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Encoding: Quantization

• And that the quantization formula is:

• The resulted rounded matrix is:

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Encoding: Entropy coding

• Involves arranging the image components in a "zigzag" order employing run-length encoding (RLE) algorithm that groups similar frequencies together, inserting length coding zeros, and then using Huffman coding on what is left.

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Encoding: Entropy coding

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• The zigzag sequence for the above quantized matrix B is:

Encoding: Entropy coding

• In order to encode the above generated coefficient pattern, JPEG uses Huffman encoding.

• If we consider that an image can be divided into n 8x8 blocks {B1, B2, … Bn} and each block is represented by horizontal (x) and vertical (y)

coordinates, we distinguish 2 different types of encoding.

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Encoding: Entropy coding

• Baseline sequential encoding: Takes the components of one single block then go to next block of the image.

• Starting from i=1, the order of the zigzag encoding is Bi(0,0), B0(0,1), Bi(1,0), Bi(2,0), Bi(1,1), Bi(0,2), Bi(0,3), Bi(1,2). Then the next block (i+1) until Bn.

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Encoding: Entropy coding

• Progressive encoding: Takes one single component for all the different blocks, then move to the next component.

• The order of the zigzag encoding starts with Bi(0,0) for all the blocks {B1, B2, … Bn} then Bi(0,1) also for all the blocks.

• JPEG has a special Huffman code word for ending the sequence prematurely when the remaining coefficients are zero.

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Encoding: Entropy coding

• Using this special code word: "EOB", the sequence becomes:

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Encoding: Compression ratio and artifacts

• One of the problems that can be found with JPEG, is some differences between the original and the resulted compressed image.

• These differences are called artifacts and I should be fixed to assure a good compression quality.

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Outline

• Introduction• Encoding• Decoding• Summary and Future work

Research Paper Reading 252010/7/12

Decoding

• Decoding consists of doing all the encoding steps in reverse. Starting with DCT coefficient matrix of one single 8x8 block:

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Decoding

• Make entry-for-entry product with the same quantization Q matrix as in Encoding :

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Decoding

• Using the Inverse 2D-DCT expressed by:

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Decoding

• We round then the resulted values we can get the following matrix:

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Decoding

• As we did in the Encoding part, we should shift back the values by 128 to obtain :

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Decoding

• Since the previous steps are for one block, we should reassemble all the blocks together to form the complete image.

• One way to check the quality of the compression is to compare the original image with the decompressed one.

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Decoding

• Subtracting the uncompressed resulted image from the original one we can obtain the following error matrix:

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Decoding

• Finally we can calculate the average absolute error to evaluate the decompression quality:

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Outline

• Introduction• Encoding• Decoding• Other• Summary and Future work

Research Paper Reading 342010/7/12

Summary and Future work

• In this article, JPEG was presented as a well known compression technique widely used in different image processing domains thanks to its simplicity and high flexibility maintaining a good compression quality.

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Summary and Future work

• Unfortunately this article doesn’t explain the steps after the Huffman coding and the buffering operation after this process.

• As this part of the JPEG encoder is extremely important, I should investigate more about it as a future work.

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