chapter 08 display

7/31/2019 Chapter 08 Display

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Image Printing and Display

Reproducing reality


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Display

Images are meant to be viewed Television screen

Computer monitor

Cell phone display

Newspaper

Glossy magazine

Overhead projector

Display device will be characterized by

pixel shape

spatial resolution

color depth


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Issues with Display

A typical computer monitor will use square pixelswith a spatial resolution of 72 pixels per inch and a

color depth of 32 bpp.

A black-and-white laser printer may use circular

pixels with a resolution of 1200 pixels per inch and acolor depth of 1 bpp.

Whenever a digital image is rendered for display, the

characteristics and limitations of the output device

must be considered in order to generate an image ofsufficient fidelity.


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Halftoning

The central problem when printing is color depth ofthe output device.

How to achieve the illusion of large color depth using

output devices of low color depth?

Color printers typically have 4 colors (CMYK) or 2 bpp.

Laser printers have 1 color (1 bpp)

Halftoning is the process of reducing the color depth

of a source image to the level of the output device

while maintaining the illusion that the output device

has the same color depth as the source.

The eye integrates

Generally buy color depth at the cost of resolution


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Analog Halftoning

In traditional, analog halftoning, a grayscale image is converted into a binary

image composed of a pattern of dots.

The dots are arranged in a grid and are themselves of various sizes. Figure 8.1

shows how black dots of various sizes printed on a white background can give the

visual illusion of all shades of gray when viewed from an appropriate distance.

The 8-bit grayscale gradient of (a) is halftoned to a 1-bit approximation. While

appearing to be a grayscale image, the image of part (b) is a 1 bpp halftone as

depicted by the highlighted inset. Halftoning in this example gives a 1-bit outputdevice the illusion of being an 8-bit device.


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Analog Halftoning

Traditional halftoning is a continuous domain oranalog process that is performed by projecting animage through an optical screen onto film. The surface of the optical screen is etched with lines in

such a way as to cause dots to appear on the film in

correspondence with the source intensity. Larger black dots appear in regions of dark intensity and

smaller black dots in regions of bright intensity.

The spatial resolution of halftone systems is given aslines per inch (LPI), which measures the density of the

etched lines on the optical screen. Newsprint, for example, is typically printed at 85 LPI while

glossy magazines are printed using 300 LPI halftonescreens.


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Digital Halftoning

Digital halftoning, also known as dithering, is any binaryprocess that reduces the color depth of a source whilemaintaining the sources spatial resolution.

A binary process is any process that outputs one of twocolors for every pixel.

Digital halftoning differs from traditional halftoning since thedigital halftoning process is discrete and the spatial resolutionof the source image and the output device are uniform.

Traditional halftoning takes place in the continuous domain andthe spatial resolution of the output device is flexible since dot

sizes are allowed to vary continuously. The output device normally has a color depth of 1 bpp;

hence the task is to convert a grayscale image into abinary image of the same dimensions.


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Dithering

The human visual system performs spatial integration (averaging) of colors

near the point of focus and hence the central idea of dithering is to ensurethat the local average of all output samples is identical to its corresponding

source sample.

Dithering increases the apparent color depth of an output device by carefully

intermingling colors from some limited palette in such a way that when local

regions are averaged they produce the desired colors. Figure 8.2 left: various shades of gray generated by interweaving only black and white,

Figure 8.2 right: various shade of green generated by interweaving only cyan and yellow.


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Thresholding

A dithering technique. Generate a black or white sample from an 8-

bit source sample.

A point processing technique

The dimensions of the destination are the same as the source

The result is dependent on the threshold

The output must be binary and hence each source sample is converted to

either black or white by comparison to a threshold value tau.

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Thresholding Thresholding rarely produces pleasing results and is solely dependent on proper

selection of the threshold value. The threshold is commonly set to the center of the source images dynamic range, which for an 8 -bit

image equates to 128.

While this threshold value is appropriate as a generic solution it does not produce good results in

many cases.

Figure 8.3 illustrates the effect of choosing an incorrect threshold. An overexposed source image is

thresholded with a cutoff of 128 to obtain the binary image of (b). Nearly all of the grayscale values in

the source exceed 128 and hence nearly all of the resulting binary output samples are converted towhite. Choosing a threshold of 196 produces much better results as can be seen in Figure 8.3(c).

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How to choose a good threshold?

Adaptive thresholding, also known as dynamicthresholding, is used to determine an appropriatethreshold for a particular image.

Adaptive thresholding is typically based on astatistical analysis of an images histogram, and

seeks to determine an optimal split between clustersof samples in the data distribution. The simplest adaptive thresholding technique is to use

either the average or median value of all source samples

as the threshold. Computing both the average and mean sample values

requires one pass through the image data and henceincurs a small amount of overhead.


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How to choose a good threshold?

A more sophisticated alternative is to use is an iterative technique

uncovered by Ridler and Calvard. This algorithm locates a threshold

that is midway between the means of the black and white samples in

the histogram. Listing 8.1 gives a pseudocode description of the

algorithm.


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Local Thresholding

Thresholding can also be done locally This is a regional process

Compute a threshold that is distinct for each individual sample. Thethreshold is the average of the samples in the region

Emphasizes local contrast but looses global contrast

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Patterning Substitute a pattern for each source pixel

Each pattern corresponds to a single intensity level (the average of thesamples in the pattern)

For an NxN pattern, there are N*N + 1 possible intensity levels

The destination is N times larger than the source in width AND height

Consider the following 3x3 font pattern


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Patterning

Generates a binary image from a grayscale or color source by increasing the

resolution of the output in order to compensate for the decreased colordepth.

Patterning works by using a group of pixels in the display device to represent a

single pixel from the source image.

The font patterns must be carefully chosen to avoid artificial patterns from forming

An NxN pattern can represent NxN+1 patterns. The font below is a clustered-dot pattern.

Each pattern in the sequence is obtained by changing one pixel

Each pattern is a subset of the previous in the sequence


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Patterning Example

33 113 234

64 121 219

92 133 245

1 4 8

2 4 8

3 5 9

Source image pixels scaled to thecorresponding font value

binary output image

G = (P P%26)/26


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Patterning

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Random Dithering Random dithering, as its name implies, chooses the threshold value

at random from a uniform distribution of values in the dynamic rangeof the source.

This technique does maintain both the global intensity value andlocal intensity values over reasonably small neighborhoods. Consider a grayscale image having an average grayscale intensity of 100.

On average, the randomly selected threshold will fall below the pixel value

approximately 100 out of every 255 samples, thus generating a whiteoutput, while about 155/255 percent of the thresholds will be above thepixel value and hence will likely generate a black output, thus maintainingthe proper average intensity value at any dimensional scale.

Digital random thresholding is similar to a high quality printmakingtechnique known as mezzotinting. An artist roughens the surface of a soft metal printing plate with

thousands of small randomly located depressions or dots. The density of the dots within a local region determines the tonality of the

print. When the plate is covered with ink and pressed against canvas orpaper, those regions with a high dot density produce areas of lessintensity than those areas with few or no dots. random!


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Dithering Matrices A dither matrix is a rectangular pattern of threshold values that seeks to produce

optimal output for a local region of the source. When dithering a WxH source image with a NxN dither matrix, the dithering matrix is

generally much smaller than the source and is therefore repetitively tiled to generate

threshold values for every source sample.

Dither matrices correspond to pattern fonts since the thresholds generally correspond

to the likelihood of a black pixel occurring in any one of the fonts.

Dither matrices are generally square and must be scaled to the color depth of the

source.


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Dither Matrices (Implementation)


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Dither Matrices (Implementation)


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Dither Matrix Example

33 45 88 123 200 210 222 255

45 51 93 113 173 221 233 240

12 61 87 120 188 200 235 254

3 43 73 152 193 199 221 223

0 23 55 135 199 200 210 201

0 10 21 110 183 173 198 177

0 3 2 32 18 98 100 123

0 0 0 1 12 33 73 110

255 0

0 0

0 128

192 64

Position the dither matrix at the upper-left and compute the outputs

using matrix entries as threshold values.


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33 45 88 123 200 210 222 255

45 51 93 113 173 221 233 240

12 61 87 120 188 200 235 254

3 43 73 152 193 199 221 223

0 23 55 135 199 200 210 201

0 10 21 110 183 173 198 177

0 3 2 32 18 98 100 123

0 0 0 1 12 33 73 110

255 0 255 0

0 0 0 255

0 128

192 64

Move the matrix and repeat.


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25


33 45 88 123 200 210 222 255

45 51 93 113 173 221 233 240

12 61 87 120 188 200 235 254

3 43 73 152 193 199 221 223

0 23 55 135 199 200 210 201

0 10 21 110 183 173 198 177

0 3 2 32 18 98 100 123

0 0 0 1 12 33 73 110

255 0 255 0 255 255

0 0 0 255 0 255

0 128

192 64

Move the matrix and repeat.


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Dithering

3x3 Ordered Dither 4x4 Ordered Dither

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Error Diffusion

The error between the source and destination isused to adjust the threshold as the source image is

scanned

The error is then pushed into unprocessed nearby

samples in order to make sure that the correct

percentage of black/white pixels are generatedlocally.

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Floyd-Steinberg Diffusion

Various ways of diffusing the error

Floyd-Steinberg takes the error and distributes it

using the ratios given below

Remember that we are doing a raster scan. Samples

above and to the left have already been processed.

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Floyd-Steinberg Example

35 89 95 132

68 112 100 150

51 45 98 127

0 ? ? ?

? ? ? ?

? ? ? ?

35 104 95 132

79 114 100 150

51 45 98 127

35 89 95 132

68 112 100 150

51 45 98 127

15

11 2

35/16 = 2.1875


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0 0 ? ?

? ? ? ?

? ? ? ?

35 104 95 132

79 114 100 150

51 45 98 127

104/16 = 6.5

35 104 95 132

79 114 100 150

51 45 98 127

35 104 141 132

99 147 106 150

51 45 98 127

46

20 33 6


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0 0 255 ?

? ? ? ?

? ? ? ?

35 104 141 132

99 147 106 150

51 45 98 127

-114/16 = -7.12535 104 141 132

99 147 106 150

51 45 98 127

35 104 141 82

99 126 70 143

51 45 98 127

-50

-21 -36 -7


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127984551

15010011268

132958935

Input Image

255000

25502550

025500

Output Image

Note that this is not an in-place algorithm. Extra storage is required! (i.e. copy the

input image and then manipulate the copy)

The sum of all gray levels

in the input is 1102. The

sum of all values in the

output is 1020. The

average per-pixel error is

6.83


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Other diffusion techniques

Other techniques diffuse the error using different

weights or ratios.

The black square corresponds to the source sample

being processed

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Error Diffusion Examples

Floyd-Steinberg Jarvis-Judice-Ninke

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Error Diffusion Examples

Stucki Sierra

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What about color images?

How to reduce a 24 bpp image to a 1 bpp?

Extract the brightness band and halftone it.

How to reduce a 24 bpp image to N bpp?

Some devices have only 4 colors (CMYK color printers)

Some devices have only 216 or 256 total colors available Thin web clients and web-safe palette (216 colors)

Conversion to an indexed color model would limit to 256 colors

Can use error diffusion!


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Color Dithering

Given a color palette (i.e. the colors supported by theoutput device) perform a color dither.


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Stucki


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Stucki with 16 color paletteStucki with 8 color palette


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Stucki with web-safe paletteSource image


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Color Dithering GIF images contain at most 256 different colors

Uses an indexed color model of sorts The image has been dithered

What if a GIF image is being viewed on a system that supportsa color palette of 64 colors?

What if the viewers color palette is different that GIFs color

palette? The image is dithered twice and quickly deteriorates. GIF

images are highly compressed, but lack quality!

GIF

Dither

Display

Dither

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Color Dithering

Dithering assumes a pre-defined palette that corresponds

to the ability of the output to reproduce colors Consider GIF files

Must construct an arbitrary palette of 256 colors

Must then perform color dithering

What is the optimal palette?

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Median Cut

Median cut

A clustering algorithm

Used to identify clusters of data points

Used in the context of color palettes, identifies N clusters

of colors in some color space

Find the smallest box which contains all the colors in the image

Find the box having the longest length on any one side

Sort the colors in the box along the longest box axis.

Split the box into 2 at the median of the sorted list.

Repeat until the original color space has been divided into n boxes.Each box represents a color. The color is the average color of all

contained colors

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Median Cut

algorithm createPalette(Image IM, int PaletteSize)B = smallest bounding box of all colors in IM

PQ = new PriorityQueue()

PQ.add(B, B.maxDimension())

while(PQ.size() != PaletteSize) {

B = PQ.remove();

(B1,B2) = B.cut();

PQ.add(B1,B1.maxDimension())

PQ.add(B2,B2.maxDimension())

}

return PQ.toArray();

}

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