Introduction to Multimedia Computing - Çankaya Üniversitesiceng460.cankaya.edu.tr/uploads/files/Introduction to Multimedia... · Introduction to Multimedia Computing . Topics 2

Digital Image Representation

Image Compression

11/5/2010 CENG 460 By: Roya Choupani 1

Introduction to Multimedia

Computing

Topics


Image Representation (Review)

Need for compression

Compression types (Review)

Lossless compression

Lossy compression

Image Compression Basics (Review)

Redundancy/redundancy types

Lossy image compression methods

JPEG

Cosine Transform and Quantization

Entropy Encoding

Image Representation


An image is a 2D matrix of pixels

Each pixel consists of RGB components

Sample dimension:

1024 rows

2048 columns

3 bytes per pixel

Image size = 1024 * 2048 * 3 = 6 Mbytes

Compressed size of this image is about 600KBytes (about 10%

of its uncompressed size)

Data Redundancy


Definition: If some parts of data are stored repeatedly, or can

be derived from other parts, the data is said to be redundant

e.g. If the pixels of a region in an image have the same color,

we do not need to store the color value for all of them.

Redundancy Types


Visual Redundancy

Spatial Redundancy

Temporal Redundancy

Stochastic Redundancy

Visual Redundancy


Our visual system is more sensitive to brightness than color.

Therefore less color information can be stored for each pixel.

Spatial Redundancy


Pixels that are near to each other with similar colors have

spatial redundancy. This property can be used to reduce the

stored data size.

Stochastic Redundancy


If a pixel color is used more than other colors, we can use

less bits for it.

Stochastic redundancy is present in all media data types

Lossy Image Compression


Motivation: Compression rates of the lossless algorithms are about 30%.

This rate is not enough for large images

Solution: Using lossy image compression.

In lossy compression, decompressed image and the original image are different

but generally the difference is not noticeable

Lossy JPEG


Jpeg is a standard for image compression

Jpeg has lossless and lossy versions

Lossy Jpeg standard uses:

Visual redundancy

Spatial redundancy

Stochastic redundancy

To compress an image

Visual Redundancy


Human visual system is less sensitive to color than brightness.

JPEG standard stores less color information than brightness

To separate color information from brightness, RGB data is

converted into YCbCr

Color space transformation


2

RGB values of the pixels are converted to YCbCr

Dividing Image into Blocks


3

The image is divided into blocks of 16x16 pixels called macro-

blocks

Color transformation from RGB to YCbCr is done for each

macro-block

Y component is divided into four 8x8 blocks

Cb and Cr components are down-sampled

Down Sampling (1)


4

Cb and Cr components are down-sampled as shown below.

Down Sampling (2)


Effect of Removing Visual Redundancy


Each macro-block consists of three components (Y, Cb, Cr)

Each component has 4 blocks

Each macro-block contains 3x4=12 blocks

After down-sampling (4:1:1), a macro-block has 4 (Y) + 1 (Cb)

+ 1 (Cr) = 6 blocks

This is equal to 50% compression

Spatial Redundancy


If neighboring pixels are close in color, the signal has low

frequency

If neighboring pixels are very different, the image contains

high frequency

Discrete Cosine Transform is used to separate low frequency

from high frequency data

Discrete cosine transform


8

Cosine transform is applied to each block after down-

sampling.

where

Example DCT Transform (1)


208 244 108 173 71 112 181 245

231 246 234 193 12 97 192 87

32 40 202 189 25 195 70 149

233 248 245 100 210 203 173 57

161 244 167 167 177 48 167 192

25 124 9 44 81 125 41 65

71 204 217 180 242 114 30 129

139 36 238 8 9 165 127 178

1116 102 45 -99 -95 -25 40 -26

135 59 80 -21 -10 109 -71 -86

-18 -31 99 -58 3 53 64 -31

-20 10 44 22 90 -104 -189 -46

142 2 136 35 1 5 -16 81

60 0 -112 43 29 -102 8 4

-211 -169 24 22 0 15 97 -80

37 -65 -47 -135 94 -16 0 -26

Example DCT Transform (2)


149 149 147 147 148 146 146 146

150 146 149 148 147 148 150 150

148 150 148 145 145 146 146 145

146 147 148 145 147 148 149 149

146 146 150 148 146 148 148 149

146 146 146 149 149 149 150 149

149 148 149 150 147 147 145 145

146 147 149 146 148 145 147 147

1180 1 1 -2 -1 1 1 1

1 1 3 1 0 0 0 0

0 4 -1 1 2 0 -1 1

2 -2 -2 1 2 1 0 -2

-2 -1 0 -1 -1 -2 0 2

-2 4 -1 1 0 -2 -1 -1

-2 0 0 1 -1 -2 -2 0

-2 5 -1 -1 -1 0 1 -1

Quantization


1

DCT coefficients are rounded to some integer number.

Quantization is done using a quantization table.

B is the quantized value, G is the coefficient and Q is

quantization table value.

Quantization Example


2

Zig-zag coding


The quantized coefficients are listed after a zig-zag tracing.

The list has many zeros in it

Effect of Removing Spatial Redundancy


The quantized coefficients at the right bottom corner

correspond to high frequency content

After zig-zag scanning, high frequency coefficients are at the

end of the list.

The zeros at the end of the list are not stored.

Removing Stochastic Redundancy


Some of the quantized coefficients are repeated more than

others.

These coefficients can be sent using less bits

This is called removing stochastic redundancy

Code Blocks


Code blocks: After zig-zag scanning, code blocks are

created by the number of zeros and the non-zero value

coming after them.

<number of zeros, nonzero value>

e.g. 304000500000006

(0,3), (1,4), (3,5), (7,6)

Entropy coding


7

The code blocks after zig-zag scaning are coded using a

stochastic or entropy coding method to store less number of

bits.

In entropy coding less number of bits are assigned to the

codes that are repeated more. (variable length codes)

The Huffman method is used for variable length coding.

Image Quality


JPEG image quality depends on

Down sampling type (4:4:4, 4:2:2, 4:1:1)

Quantization matrix (If values of the quantization matrix is

large, more zeros are resulted, and more data is lost. )

Higher compression rate causes lower quality of the image

Sample Coded Data



JPEG Coding Algorithm


1

The encoding process steps of JPEG:

The color of the pixels in the image is converted from RGB to

YCbCr

The resolution of the Cb and Cr data is reduced, usually by a factor

of 2. (Down-sampling)

The image is split into blocks of 8×8 pixels, and each block of Y, Cb,

and Cr undergoes a discrete cosine transform (DCT).

The DCT coefficients are quantized and zig-zag scanned.

The resulting data for all 8×8 blocks is further compressed with a

loss-less stochastic algorithm.

Assignment


2

Read and summarize the JPEG algorithm from the paper given at

the assignment part of the course web page.

Questions?


3

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Introduction to Multimedia Computing - Çankaya Üniversitesiceng460.cankaya.edu.tr/uploads/files/Introduction to Multimedia... · Introduction to Multimedia Computing . Topics 2