Chapter 08 Display
Transcript of 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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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 0 255 0
0 0 0 255
0 128
192 64
Move the matrix and repeat.
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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 0 255 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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Floyd-Steinberg Example
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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Floyd-Steinberg Example
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
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Floyd-Steinberg Example
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();
}