LECTURE I:

GRAPHICS & IMAGE DATA

REPRESENTATION

DR. OUIEM BCHIR

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DIGITAL IMAGE

REPRESENTATION

An image is a spatial representation of an object, a2D or 3D

scene, etc.

Abstractly, an image is a continuous function

defining a rectangular region of a plane

An image can be thought of as a function with resulting values

of the light intensity at each point over a planar region.

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DIGITAL IMAGE

REPRESENTATION

For computer representation, the function (e.g. intensity) must

be sampled at discrete intervals.

Sampling quantizes the intensity values into discrete intervals.

Points at which an image is sampled are called picture

elements or pixels.

Resolution: specifies the distance between points - accuracy

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DIGITAL IMAGE

REPRESENTATION

A digital image is represented by a matrix of numeric values

each representing a quantized intensity value.

I(r,c) - intensity value at position corresponding to row r and

column c of the matrix.

Intensity value can be represented by

1-bit: black & white images

8-bits: grayscale images

24-bits: color images (RGB)

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1-BIT IMAGES

Each image is stored as a single bit (0 or 1), so also

referred to as binary image.

Such an image is also called a 1- bit monochrome

image since it contains no color.

Monochrome 1-bit Lena image

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8-BIT GRAY-LEVEL

IMAGES

Each pixel has a gray- value between 0 and 255. Each pixel is

represented by a single byte: e.g. dark pixels might have a

value of 10, and a bright one might be 230.

Bitmap: The two- dimensional array of pixel values that

represent the graphics/image data.

Image resolution: The number of pixels in a digital image

(higher resolution better quality).

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8-BIT GRAY-LEVEL

IMAGE

Each image is usually stored as a byte (value between 0&255)

A 640x480 grayscale image requires a 300 KB of storage (640 x

480 = 307,200 bytes)

When an image is printed, the basic strategy of dithering is

used, which trades intensity resolution for spatial resolution to

provide ability to print multi-level images on 2-level (1-bit)

printers.

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DITHERING

Dithering is used to calculate patterns of dots such that values

from 0 to 255 correspond to patterns that are more and more

filled at darker pixel values, for printing on a 1-bit printer.

Main strategy: replace a pixel value by a larger pattern, say

2x2 or 4x4, such that the number of printed dots approximates

the varying-sized disks of ink used in analog, in halftone

printing (e.g. for newspaper photos).

Half-tone printing is an analog process that uses smaller or

larger filled circles of black ink to represent shading, for

newspaper printing.

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DITHERING

Example: If we use a 2x2 dither matrix

Re-map image values in 0..255 into the new range 0..4 by

(integer) dividing by 256/5.

If pixel value = 0

print nothing in a 2x2 area of printer output.

If pixel value = 4

print all four dots

Rule: If intensity > dither matrix entry

print an on dot at that entry location: replace each pixel by a

nxn matrix of dots.

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DITHERING

Note: Image size may be much larger for a dithered image

(replacing each pixel by a 2x2 array of dots, makes an image 4

times as large).

Can get around this problem.

Ordered dither: turn on the printer output bit for a pixel if the

intensity level is greater than the particular matrix element just

at that pixel position

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AN ALGORITHM FOR

ORDERED DITHER

Using n x n dither matrix

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EXAMPLE

4x4 dithering matrix

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IMAGE DATA TYPES

The most common data types for graphics and image file

formats: 24-bit color and 8-bit color.

Some formats are restricted to particular hardware/operating

system platforms, while others are “cross-platform” formats.

Even if some formats are not cross-platform, there are

conversion applications that will recognize and translate

formats from one system to another.

Most image formats incorporate some variation of

compression technique due to the large storage size of image

files. Compression techniques can be classified into either

lossless or lossy.

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24-BIT COLOR IMAGES

In a color 24- bit image, each pixel is represented by three

bytes, usually representing R, G, B.

This format supports 256 x 256 x 256 possible combined

colors, or a total of 16,777,216 possible colors.

Such flexibility does result in a storage penalty:

A 640 x 480 24-bit color image would require 921.6 KB of

storage without any compression.

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EXAMPLE

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8-BIT COLOR IMAGES

Many systems can make use of 8 bits of color information (the

so-called “256 colors”) in producing a screen image.

Such image files use the concept of a lookup table to store

color information.

Basically, the image stores not color, but instead just a set of

bytes, each of which is actually an index into a table with 3-

byte values that specify the color for a pixel with that lookup

table index.

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COLOR QUANTIZATION

With 8 bits per pixel and color lookup table we can display at

most 256 distinct colors at a time.

To do that we need to choose an appropriate set of

representative colors and map the image into these colors

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COLOR

QUANTIZATION

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QUANTIZATION PHASES

Sample the original image for color statistics

Select color map based on those statistics

Map the colors to their representative in the

color map

Redraw the image, quantizing each pixel

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COLOR LOOK-UP TABLES

(LUTS)

The idea used in 8-bit color images is to store only the index,

or code value, for each pixel. Then, e.g., if a pixel stores the

value 25, the meaning is to go to row 25 in a color look-up

table (LUT).

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HOW TO DEVISE A

COLOR LUT?

The most straightforward way to make 8-bit look up color out of 24-bit

color would be to divide the RGB cube into equal slices in each dimension.

The centers of each of the resulting cubes would serve as the entries in the color LUT.

Simply scaling the RGB ranges 0..255 into the appropriate ranges would generate the 8-bit codes.

Since humans are more sensitive to R and G than the B, we could

Shrink the R range and G range 0..255 into the 3 bit range 0..7.

Shrink the B range down to 2 bit range 0..3.

To shrink R and G, we could simply divide the R and G value by (256/8)=32 and then truncate.

Each pixel in the image gets replaced by its 8-bit index, and the color LUT serves to generate 24-bit color.

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3-3-2

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3-3-2

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MEDIAN-CUT ALGORITHM

A simple alternative solution that does a better job for the color

reduction problem.

Sort the R byte values and find their median.

Values smaller than the median are labeled with a “0” bit.

Values larger than the median are labeled with a “1” bit.

This type of scheme will concentrate bits where they most need to

differentiate between high populations of close

colors.

We can easily visualize finding the median by using a histogram

showing counts at position 0..255.

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MEDIAN-CUT ALGORITHM

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24 BIT

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