Image Printing and Display
Reproducing reality
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
Issues with Display



A typical computer monitor will use square pixels with 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 a color
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 of sufficient
fidelity.
Halftoning

The central problem when printing is color depth of the
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
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 output device the illusion of being
an 8-bit device.
Analog Halftoning

Traditional halftoning is a continuous domain or analog
process that is performed by projecting an image 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 as lines 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 halftone screens.
Digital Halftoning


Digital halftoning, also known as dithering, is any binary
process that reduces the color depth of a source while
maintaining the sources spatial resolution.
A binary process is any process that outputs one of two
colors for every pixel.



Digital halftoning differs from traditional halftoning since the digital
halftoning process is discrete and the spatial resolution of the source
image and the output device are uniform.
Traditional halftoning takes place in the continuous domain and the
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 a binary image of
the same dimensions.
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 ensure that 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.
Thresholding
A dithering technique. Generate a black or white sample from an 8-bit
source sample.





9
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.
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 image’s 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 to white.
Choosing a threshold of 196 produces much better results as can be seen in Figure 8.3(c).
10
How to choose a good threshold?


Adaptive thresholding, also known as dynamic
thresholding, is used to determine an appropriate
threshold for a particular image.
Adaptive thresholding is typically based on a statistical
analysis of an image’s histogram, and seeks to determine
an optimal split between clusters of 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 hence incurs a small
amount of overhead.
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.
Local Thresholding

Thresholding can also be done locally


This is a regional process
Compute a threshold that is distinct for each individual sample. The threshold is
the average of the samples in the region

13
Emphasizes local contrast but looses global contrast
Patterning

Substitute a pattern for each source pixel




Each pattern corresponds to a single intensity level (the average of the samples
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
14
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 color depth.

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
Patterning Example
G = (P – P%26)/26
113 234
1
4
8
64 121 219
2
3
4
5
8
9
33
92 133 245
Source image
pixels scaled to the
corresponding font value
binary output image
16
Patterning
17
Random Dithering


Random dithering, as its name implies, chooses the threshold value at
random from a uniform distribution of values in the dynamic range of the
source.
This technique does maintain both the global intensity value and local
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 white output,
while about 155/255 percent of the thresholds will be above the pixel value and
hence will likely generate a black output, thus maintaining the proper average
intensity value at any dimensional scale.
Digital random thresholding is similar to a high quality printmaking
technique 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 or paper, those
regions with a high dot density produce areas of less intensity than those areas
with few or no dots. random!
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.
Dither Matrices (Implementation)
Dither Matrices (Implementation)
Dither Matrix Example
033
128
45
88
123
200
210
222
255
255
0
45
192
51
64
93
113
173
221
233
240
0
0
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
Position the dither matrix at the upper-left and compute the outputs using
matrix entries as threshold values.
23
Dither Matrix Example
33
45
0
88
128 200
123
210
222
255
255
0
255
0
45
51
93
192
113
64
173
221
233
240
0
0
0
255
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
Move the matrix and repeat.
24
Dither Matrix Example
33
45
88
123
0
200
128
210
222
255
255
0
255
0
255
255
45
51
93
113 192
173
221
64
233
240
0
0
0
255
0
255
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
Move the matrix and repeat.
25
Dithering
3x3 Ordered Dither
26
4x4 Ordered Dither
Error Diffusion

The ‘error’ between the source and destination is used 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 generated locally.
27
Floyd-Steinberg Diffusion


Various ways of diffusing the error
Floyd-Steinberg takes the error and distributes it using
the ratios given below

28
Remember that we are doing a raster scan. Samples above and
to the left have already been processed.
Floyd-Steinberg Example
35
89
95
132
0
?
?
?
68
112
100
150
?
?
?
?
51
45
98
127
?
?
?
?
35
89
95
132
68
112
100
150
51
45
98
127
29
35/16 = 2.1875
11
15
35
104
95
132
2
79
114
100
150
51
45
98
127
Floyd-Steinberg Example
35
104
95
132
0
0
?
?
79
114
100
150
?
?
?
?
51
45
98
127
?
?
?
?
35
104
95
132
79
114
100
150
51
45
98
127
30
104/16 = 6.5
20
33
46
35
104
141
132
6
99
147
106
150
51
45
98
127
Floyd-Steinberg Example
35
104
141
132
0
0
255
?
99
147
106
150
?
?
?
?
51
45
98
127
?
?
?
?
35
104
141
132
99
147
106
150
51
45
98
127
31
-50
35
104
141
82
-7
99
126
70
143
51
45
98
127
-114/16 = -7.125
-21
-36
Floyd-Steinberg Example
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
Input Image
Output Image
35
89
95
132
0
0
255
0
68
112
100
150
0
255
0
255
51
45
98
127
0
0
0
255
Note that this is not an in-place algorithm. Extra storage is required! (i.e. copy the input image and
then manipulate the copy)
32
Other diffusion techniques


Other techniques diffuse the error using different weights
or ratios.
The black square corresponds to the source sample being
processed
33
Error Diffusion Examples
Floyd-Steinberg
34
Jarvis-Judice-Ninke
Error Diffusion Examples
Stucki
35
Sierra
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!
Color Dithering

Given a color palette (i.e. the colors supported by the
output device) perform a color dither.
37
Stucki
Stucki with 8 color palette
Stucki with 16 color palette
Source image
Stucki with web-safe palette
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 supports a
color palette of 64 colors?
What if the viewers color palette is different that GIF’s color
palette?
The image is “dithered” twice and quickly deteriorates. GIF images
are highly compressed, but lack quality!
GIF
Dither
41
Display
Dither
Color Dithering


Dithering assumes a pre-defined palette that corresponds to
the ability of the output to reproduce colors
Consider GIF files



42
Must construct an arbitrary palette of 256 colors
Must then perform color dithering
What is the ‘optimal’ palette?
Median Cut
Median cut




•
•
43
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
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();
}
44