FIT 2011 Gradient

8/3/2019 FIT 2011 Gradient

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Gradient Adjusted Predictor with

Pseudo-distance Technique forLossless Compression

of Color-mapped Imagesby Basar KOC & Ziya ARNAVUT

SUNY Fredonia


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What are digital colors?

Human beings perceive colors by the nature of the lightreflected from an object!

Achromatic Color: means literally without color

Only intensities (amount of light)

Gray levels as seen on black/white TV-monitor Ranges from black to white

Chromatic Color: All colors other than neutral colors(white, black, and the pure grays), are chromatic.

The word color in ordinary language is often used torefer exclusively to chromatic colors, e.g., color vs.black-and-white television.

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RGB Color Theory

RGB stands for Red, Green, BlueRGB color is in use in many devices,

Televisions, computer screens, digital cameras.

When the visible color spectrum wavelength (400-700nm) is broken into thirds,

RGB colors are the predominant colors.

Three types of cone cells exist in human eye.

Each cell is more sensitive to either short ( S ), medium( M ), or long( L ) wavelength light.

These curves are often also referred as the tri-stimulus

functions.

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RGB Color Space

A single pixel consists of three components each inrange of [0,255].

Each pixel is a triplet

128 251 60 =

Pixel vector

in memory

Final pixel in

the image

Caution! Sometimes pixelsare not stored as vectors.Instead, first is stored thecomplete red component,then the complete green,then blue.

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Example RGB

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Size consideration in an RGB image

The lowest resolution for a monitor

Displaying a Windows desktop is 640 x 480 pixels.

In a bitmap of this resolution, then, there would be 3

bytes per pixel, For a total of 640 x 480 x 3, or about 900 kilobytes.

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Bit-Depth = Color-Depth

Number of Colors = 2^(Bit-depth)Bit-depth is the number of bits.

It is also called Color resolution.

Bit depthBit depth Color resolutionColor resolution CalculationCalculation1-bit 2 colors 2^1 = 2

2-bits 4 colors 2^2 = 4



8-bits 256 colors 2^8 = 256

16-bits 65,536 colors 2^16 = 65536

24-bits 16,777,215 colors 2^24 = 16.7 million

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Color Palettes

Images look best If theyre stored with as RGB images with 16,777,216

colors.

However, file seizes may be very large.

For practical purposes,

we would like to reduce the number of colors from16,777,216 to 256 colors.

Such files are referred to as using palette-color. The colors in a palette-color file are derived from a

potential palette of 16,777,216 colors, but no more than256 of them can be used in any one image.

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Graphics Interchange Format (GIF)

The GIF is one of the most commonly used graphic fileformats, especially on the Internet.

an indexed color image format.

The color of the image is indexed in a palette. (a color-table)

The GIF is only capable of supporting a maximum of256 colors.

Uses lossless compression algorithm.

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Structure of a BMP

Color-Palette Image

Information 56 bytes

Size

Dimensions Width, height

Bit per pixel 8, 4, 2, 1

Color Table 3 x 256 bytes at most

The color-mapped table of an image

Index R G B

0 28 0 1

1 19 2 5

2 34 1 1

3 39 2 3

4 44 0 2

.. .. .. ..

254 193 211 223

255 206 212 222

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Euclidean Distance Metric

Let E[a,b] be the Euclidean distance between two colorindices a and b.

(0 a, b 255)

where,

E[a,b]: Distance between index a and index b. eR: Difference between R values of a and b indices.

eG: Difference between G values of a and b indices.

eB: Difference between B values of a and b indices.

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Euclidean and Pseudo Distance

matrices

Pseudo-distance matrix

Distance matrixcreated from the color palette

converted

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Index R G B

0 28 0 1

1 19 2 5

2 34 1 1

3 39 2 3

4 44 0 2

.. .. .. ..

254 193 211 223255 206 212 222

Color-map table


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Encoding

Reference pixel x and its neighbors Ranking with pseudo-distance matrix

X is the index value to be predicted. a, b, c are neighboringindices.

Using (a, x) we determine ranking value, or error e.

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Pseudo-distance matrix


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Decoding

In error matrix E,

the index number of the first pixel at the top-left corner,call it a, is copied to I. Later we apply the following:

Receive the error signal e of the next pixel from the encodedimage.

In row a of the pseudo-distance matrix search the error signalvalue e. Emit the corresponding column valuexas the originalindex value of the image.

Letxbe a and repeat the process until we reach to the end offile.

Clearly, in decoding process, we obtain original indexvalues without any loss.

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a1 x1 x2e11 e12 e13 e14 e15 ..

e21

e22

e23

e24

..

..

ei1

..

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.. x12

.. x13

..

.. .. .. .. .. ..

a1 .. e12 .. .. ..

.. .. .. .. ..

a2

.. .. .. e13

..

. .. .. .. .. ..

Copy e11 to I(1,1)

Let a1 e11Determine x12 by searching e12 in row a1.

I(1,2) x12

Let a2 x12Determine x13 by searching e13 in row a2.

I(1,3) x13We repeat the process similarly.

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Decoding (cont.)

E: Encoded image P: Pseudo-distance matrix I: Image


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Why do we use the pseudo-distance

transformation?

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0%

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3Sunset Serrano Sea_dusk Yahoo

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3Sunset Serrano Sea_dusk Yahoo

Before transformation After transformation


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Distribution of Music.bmp (n = 8) before and after transformation

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Distribution of Serrano.bmp (n = 256) before and after transformation

Why do we use the pseudo-distance

transformation?


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Binary Arithmetic Coder

We observed that after the pseudo-distance metric isapplied to indices of various color-mapped images, onsome images percentage of 0s varies from 72-90.

Hence, we applied context-adaptive binary arithmeticcoder which includes run length coding and contextmodeling.

This yields better compression gain than Huffman coder,which was originally proposed by Kuroki et al.

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Images #Colors Size GIF Huffman SAC Proposed

Benjerry 48 28,326 1.239 1.789 1.218 1.207

Books 7 29,338 3.046 3.901 3.447 3.248

Clegg 256 719,158 3.623 3.161 2.808 2.784

Cwheel 256 481,078 1.492 1.915 0.984 0.941

Descent 122 64,542 2.928 3.153 2.765 2.676

Fractal 256 389,190 6.923 5.72 5.335 5.267

Frymire 256 1,238,678 1.485 2.089 1.373 1.392Gate 84 61,302 2.939 2.987 2.471 2.367

Ghouse 256 481,078 3.713 3.802 3.219 2.962Music 8 6,302 2.482 2.885 2.305 2.373

Netscape 32 61,382 2.113 2.297 1.922 1.936Party8 12 75,606 0.854 2.273 0.778 0.802

Pc 6 1,721,858 1.694 2.605 1.723 1.603

Sea_dusk 46 157,538 0.323 1.025 0.052 0.054

Serrano 256 502,886 1.629 2.07 1.389 1.289

Sunset 204 308,070 2.601 2.197 1.59 1.547Winaw 10 148,894 0.997 2.47 0.98 0.959

Yahoo 229 28,110 1.983 2.498 1.818 1.747

Average 361,296 2.337 2.713 2.01 1.953

W. Avg. 2.328 2.695 1.974 1.904

Normalized 1.223 1.415 1.037 1.000

Experimental Results

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Thank you!

Questions?

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Documents

FIT 2011 Gradient