1. 1
De-screen of Scanned Halftone Prints by Fractional-Pixel Averaging
Henry R. Kang
Color Imaging Consultant
Rolling Hills Estates, CA. 90274
ABSTRACT
A new approach, fractional-pixel averaging, was proposed for de-screening images that were scanned
from halftoned bilevel prints. The formulation of the fractional-pixel averaging was presented and illustrated
with examples. This method was tested by using IS&T-NIP16 Test Target under 3 different window sizes. In
addition, moving-average filters designed by the fractional-pixel-sum approach were also used for de-
screening under the same conditions for comparison with the fractional-pixel averaging method. The de-
screened RGB image was compared with the scanned RGB input. And the re-screened CMYK image was
compared with the re-halftoned input image. Results indicated that the fractional-pixel averaging and the
moving-average filters were very effective in removing moiré patterns generated by the scanning of halftoned
originals.
Keywords: De-screening, fractional-pixel averaging, moving-average filter, resolution conversion, and
moiré.
1. INTRODUCTION
A problem of image reproduction by copiers and scanners is to reproduce halftoned bilevel prints; the copier
resolution may interact with the screen frequency of a halftoned print to form moiré patterns. This problem is
particularly severe for pictorial images. The sources of pictorial inputs to copiers are come most often from
photographic and offset prints. Photographic prints consist of varying amounts of dyes on substrate; the
information therein is analog that gives a contone appearance to viewers. When a photographic print is used
as the input to a copier, the scanner converts analog information to digital by sampling at spatial domain (or
resolution) and quantizing at intensity domain (or depth). In this case, the digitalized image quality is solely
depended on the sampling and quantization processes; there is no interaction between the source image
content and the digitalization process. Offset printing, on the other hand, is bilevel; halftone process must be
used in order to simulate the gray sensation for pictorial images. Thus, offset prints are halftoned bilevel
images, having regular screen frequencies and angles with internal structures such as rosette. It is very likely
that halftone structures may interact with the sampling process of the scanner to cause a subsequent beating
problem when the digitized image is re-halftoned for printing. The beating between input screens and printer
screens creates moiré patterns. It is a detrimental problem for the image quality and must be addressed by
copier manufacturers.
There are at least two paths for reducing the screen-beating problem as shown in Fig. 1; the original
input is a halftoned bilevel image that is scanned by a copier or scanner to a 24-bit RGB (8-bit/color) image.
Path 1 preprocesses the RGB image by de-screening before it is halftoned by the copier for printing. A de-
screen module is inserted between the scanned 24-bit image and the color conversion. Path 2 processes the
image after it is halftoned by the internal software of the copier into 32-bit CMYK image. Path 2 relied on the
techniques of the inverse halftoning to remove the beating problem. Many methods have been developed for
inverting halftoned images to contone and are reviewed in the chapter “Inverse Halftoning” of the book
“Digital Color Halftoning”.1
In addition, two new approaches based on the fractional-pixel (or sub-pixel) sum
were shown to be effective for the inverse halftoning.2,3
As shown in Fig. 1, Path 2 is complex, redundant,
and costly. It involves the halftoning of the scanned and color-converted 32-bit CMYK image to 4-bit CMKY
2. 2
image, where vast information is lost. To remove the beating problem, an inverse-halftoning module is
employed to invert 4-bit bilevel CMYK image back to contone. And the resulting image must be rescreened
for printing, which is redundant by duplicating the halftone process. Moreover, it is known that the lost
information seldom be able to recover by the inverse-halftoning. Yet, a more serious problem is that the
periods of moiré patterns are much longer than the screen period; therefore, to remove moiré patterns
effectively requires a window size comparable to the moiré period that is usually too big to retain image
details. Path 1 is simple and has no redundancy in the image processing. The de-screen module removes the
beating problem while the image is still in the 24-bit RGB representation that keeps the loss of image content
to a minimum. The key of this approach is the de-screen process. It has been found that the sub-pixel-sum
with slight modifications can also be used for preprocessing images to remove or minimize the screen-beating
problem before re-halftoning for printing.2
This method of the sub-pixel averaging is presented and tested.
Fig. 1. Imaging paths of the de-screening process.
2. FORMULATION AND CHARACTERISTICS
The sub-pixel-sum via resolution conversion has shown to be a viable technique for inverse
halftoning.2
It can also be used for de-screening before the scanned image is halftoned. The method consists
of three steps. First, source and intermediate window sizes are selected such that the imaginary sub-pixels can
be created for the input and intermediate pixels. Second, each sub-pixel is assigned with a value based on the
value of the input pixel. A resolution conversion is performed to obtain the values of intermediate pixels,
which are computed by summing sub-pixels within a selected area (or window). The last step, a second
resolution conversion from the intermediate resolution back to the input resolution is performed for the output
pixels.
2.1 Sub-Pixel Creation
The creation of sub-pixels is governed by the source window size WS,x and WS,y in the number of
source pixels and intermediate window sizes WI,x and WI,y in the number of intermediate pixels, where
subscripts x and y represent the directions of the window. Source and intermediate window sizes, WS and WI,
can be freely chosen to meet the need of the de-screen requirements. However, for the purpose of smoothing
textures, it will be more effective if the number of intermediate pixels is smaller than that of input pixels, WI <
WS. A source window of size WS,x by WS,y is selected as a sliding window for the area selection, starting at the
beginning of the source image and moving from left-to-right and top-to-bottom one whole tile at a time to
generate the intermediate pixels contained in the WI,x by WI,y window. The source and intermediate windows
reside the same location and have the same physical size but different resolution. The ratio of the intermediate
window size, WI, to the source window size, WS, is the conversion ratio, Я, for two-dimensional image plane
Я = (WI,x/WS,x) (WI,y/WS,y).
Next, a whole pixel is divided into many sub-pixels for the source and the corresponding intermediate
Screened
bilevel
original
Copier or
Scanner
Scanned
RGB image
(8-bit/color)
Inverse
halftoning
Color
conversion
to CMYK
Rescreening
De-screened
RGB image
CMYK color
printer
Halftoning
by copier
Color
conversion
to CMYK
Path 1
Path 2
Halftoning
by copier
3. 3
pixels. The number of sub-pixels for each source and intermediate pixel is computed by using Equations (1)
and (2).
DS,x = WI,x / GCD(WS,x, WI,x) , and DS,y = WI,y / GCD(WS,y, WI,y) , (1)
DI,x = WS,x / GCD(WS,x, WI,x) , and DI,y = WS,y / GCD(WS,y, WI,y) (2)
where DS and DI are the source and intermediate pixel dimensions in the number of sub-pixels, respectively,
the subscript x or y again indicates the direction. GCD is the greatest common denominator between the
source window size in the number of the source pixels and the intermediate window size in the number of
intermediate pixels. The source and intermediate pixel sizes, AS and AI, in the number of the sub-pixel are
given in Eqn. (3).
AS = DS,x DS,y , and AI = DI,x DI,y . (3)
Moreover, the source and intermediate areas need not be a square; Equations (1) to (3) apply to rectangular
shapes when x y.
2.2 Sub-Pixel Summation
Upon determining the numbers of sub-pixels for the source and intermediate pixels, respectively, the
source resolution is converted to the intermediate resolution. Equation (4) computes the pseudo-gray value of
an intermediate pixel by summing source sub-pixels that are intercepted with the intermediate pixel.
WS,y WS,x
pI(i, j) = Xmn . pS(m, n) , (4)
m=1 n=1
and Xmn = WS(m, n) WI(i, j)
where pI is the pseudo-gray value of the intermediate pixel obtained from the resolution conversion where
indices i and j indicate the intermediate pixel location with i the row number and j the column number and pS
is the source pixel value within the selected window and indices m and n indicate the source pixel location
with m the row number and n the column number. The two-dimensional image plane is ordered from top-to-
bottom and left-to-right. This pixel ordering is used for all image planes in this paper. Xmn is the intersection
area (in the number of sub-pixels) between source pixels and the intermediate pixel of interest. Equation (4)
gives the intermediate pixel a value by summing up the number of source sub-pixels within the boundary of
the intermediate pixel.
2.3 Gray-Level Generation
The third step is to convert intermediate pixels back to the initial resolution by using Eqn. (5) to
generate the destination pixels, pD. Equation (5) is the inverse of Eqn. (4) normalized by dividing the sizes of
source and intermediate pixels. This normalization is in fact an average.
WI,y WI,x
pD(m, n) = (AS AI)1
{ Xij . pI(i,j)}, (5)
i=1 j=1
and Xij = WI(i, j) WS(m, n).
Now, suppose there is a diagonal line in a 33 input window, where pS(1,1) = 236, pS(2,2) = 252, pS(3,3) =
221 and the rest of pixels are zero. The intermediate pixels calculated from Eqn. (4) are pI(1,1) = 1196, pI(1,2)
= 252, pI(2,1) = 252, and pI(2,2) = 1136. The destination pixels computed from Eq. (5) are pD(1,1) = 133,
pD(1,2) = 80, pD(1,3) = 28, pD(2,1) = 80, pD(2,2) = 79, pD(2,3) = 77, pD(3,1) = 28, pD(3,2) = 77, and po(3,3) =
126. This example is depicted graphically in Fig. 2.
4. 4
Source Intermediate Destination
Fig. 2. The graphic illustration of the inverse halftoning.
Figure 2 shows a unique nature of this fractional-pixel averaging that input textures are partial retained. Also,
the intensity is conserved; the source gray-level is 236 + 252 + 221 = 709, whereas the destination level is
133 + 80 + 28 + 80 + 79 + 77 + 28 + 77 + 126 = 708. The small deviation of one gray-level is due to the
computational round-off errors. This method modifies source image by broadening its texture and selectively
dispersing high values to their neighbors based on the input pixel pattern. It reduces to the low-pass filtering
via area averaging if the intermediate window size is 1×1. For higher intermediate sizes, this method is
similar to the weighed averaging. More examples are given in Fig. 3.
Input
texture
3 to 1 3 to 2 3 to 4 3 to 5 3 to 7 3 to 8
Я = 0.111 Я = 0.444 Я = 1.78 Я = 2.78 Я = 5.44 Я = 7.11
236 252 221 79 79 79 161 158 154 202 197 193 209 205 200 219 214 210 221 217 212
79 79 79 80 79 77 41 40 39 32 32 31 23 22 22 20 19 19
79 79 79 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
79 79 79 80 79 77 41 40 39 32 32 31 23 22 22 20 19 19
236 252 221 79 79 79 80 79 77 161 158 154 177 173 169 195 191 187 202 197 193
79 79 79 80 79 77 41 40 39 32 32 31 23 22 22 20 19 19
236 79 79 79 28 80 133 7 60 172 5 51 184 2 40 198 2 35 202
252 79 79 79 77 79 80 58 119 60 49 136 51 38 160 40 34 168 35
221 79 79 79 126 77 28 163 58 7 174 49 5 187 38 2 192 34 2
236 79 79 79 80 80 80 41 161 41 32 177 32 23 195 23 20 202 20
252 79 79 79 79 79 79 40 158 40 32 174 32 22 191 22 19 197 19
221 79 79 79 77 77 77 39 154 39 31 169 31 22 187 22 19 193 19
79 79 79 52 54 56 32 13 34 27 9 28 20 5 22 17 4 19
236 252 79 79 79 77 79 81 135 79 141 151 70 158 171 55 179 178 49 187
221 79 79 79 102 103 105 64 143 66 53 156 55 40 175 41 35 181 36
79 79 79 28 54 80 7 33 41 5 28 32 2 21 23 2 18 20
252 236 79 79 79 77 79 80 58 138 161 49 155 177 38 175 195 34 183 202
221 79 79 79 126 103 80 164 65 41 174 54 32 188 40 23 192 36 20
79 79 79 28 54 80 7 33 41 5 28 32 2 21 23 2 18 20
252 236 79 79 79 53 79 105 32 158 164 27 173 178 20 191 194 18 197 199
221 79 79 79 77 103 130 39 162 71 31 176 57 22 191 42 19 196 37
Fig. 3. The graphic illustration of the inverse halftoning by using 3×3 window.
133
0 221
252
236
0
0
00
0
11963 to 2
conversion
252
1136252
80 28
80 79 77
28 77 126
2 to 3
conversion
5. 5
3. RESULTS AND DISCUSSION
In this study, the IS&T NIP16 Test Target printed by Quickmaster DI 46-4, a waterless offset print
kindly provided by Heidelberg,4
was used as the original input to a Microtek ScanMaker 5 scanner. The
resolution of NIP16 test target is 1270 dpi and the scanner resolution is 600 dpi. The scanned RGB image was
cropped into two parts: the ISO N7 image and the color patches above N7. Both test images contained
extensive moiré patterns due to the beating between offset screens and scanner resolution; they still were used
for the de-screening. The image path and comparisons were shown in Fig. 4. The scanned RGB test images
and de-screened RGB images by the sub-pixel averaging were displayed in a computer monitor for
comparisons. They were then color transformed to CMYK and halftoned at the printer resolution of 600 dpi
with a set of four halftone screens for printing by a Tektronix Phaser 740 printer. The color prints were also
compared (Fig. 4).
Fig. 4. Imaging paths of the de-screening process.
The moving-average filters designed by the sub-pixel-sum approach were also used to preprocess
scanned images for testing the ability of these filters in removing beating.3
Selected filters from Reference 3
were used.
3.1 Halftone Technique
Several sets of halftone screens were used to re-screen the inputs. The outputs were visually
compared to select a set of screens that gave the worst image quality. The idea was that if the worst screens
can be overcome by the de-screen method; there will be fewer problems with other screens. The worst set of
screens was Dot-136 that has four clustered-dot screens, one for each primary color of cyan, magenta, yellow,
and black. Each screen has eight centers, forming an octa-dot pattern for the purpose of increasing the
apparent screen frequency. Cyan screen has 136 levels with a screen angle of 31, giving a screen frequency
of 145.5 lpi at 600 dpi. Magenta screen is the mirror image of the cyan screen, having the same size and
frequency as cyan screen but a different screen angle of 59. Yellow screen has 128 levels and a screen angle
of 45, giving a screen frequency of 150.0 lpi at 600 dpi. Black screen has 144 levels and an angle of 0 with
a screen frequency of 141.4 lpi at 600 dpi.
3.2 Results
Visual comparisons of the scanned input, called RGB-original, with de-screened image, called RGB-
de-screen, were made by displaying RGB images on a computer monitor for comparison by one observer.
Adobe Photoshop software was used to open and size images.
Screened
bilevel
original
Scanner
Scanned RGB
image
(8-bit/color)
Halftoning
Color
conversion
to CMYK
Descreen
RGB
image
CMYK color
printer
Halftoning
Color print
Comparison of
computer displays
Color conversion
to CMYK
CMYK color
printer
Color print
Comparison
6. 6
The scanned test targets were converted to CMYK and halftoned by Dot-136, labeled as CMYK-
original. Similarly, the same scanned image was de-screened by the sub-pixel averaging method, converted to
CMYK, and halftoned by Dot-136, labeled as CMKY-re-screen image. Both CMYK images were printed by
a Tektronix Phaser 740 printer and were visual compared.
Three conversion ratios, 3-to-1 (Я = 0.11), 5-to-2 (Я = 0.16), and 7-to-2 (Я = 0.082), were tested. For
all conversion ratios, the RGB-de-screen images were better than the RGB-original. They were smoother,
more saturated, better in contrast, and yet retaining shadow details. For CMYK printers, the CMYK-original
image showed severe color shift and moiré patterns, whereas the CMYK-de-screen images did not show the
color shift and moiré. They looked much better than the CMYK-original. With closer observations of
CMYK-re-screen images, there were slight differences with respect to window size (or conversion ratio); 7-
to-2 conversion gave very good image quality, 5-to-2 conversion showed slight moiré patterns on sweeps and
skin, and 3-to-1 conversion showed screen patterns but not objectionable. These differences implied that the
quality of de-screening is affected by the window size. If the window size is small, it may not blend enough
pixels to remove the beating and moiré patterns.
For the testing of using the moving-average filters, filters from 3-to-1, 5-to-2, and 7-to-2 conversions
via sub-pixel sum approach were used. Again, the RGB-de-screen images were better than the RGB-original.
They were smoother, more saturated, and better in contrast. By using 3-to-1 filter, RGB-de-screen images
retained some dot structures. CMYK-de-screen images showed color shifts and moiré patterns, but they still
looked better than the CMYK-original. By using 5-to-2 filter, the image qualities of CMYK-de-screen images
were much improved than those of 3-to-1 filter; the color shift and moiré seen on 3-to-1 outputs were largely
removed. By using 7-to-2 filter, the qualities of CMYK-de-screen images were very good, showing no color
shift and moiré. In general, the sub-pixel averaging seemed more effective than the moving-average filters,
giving a slightly better image quality. If the window size is big enough, such as 7-to-2 conversion, both
methods are effective for removing moiré patterns from copying a halftoned bilevel input.
4. CONCLUSION
This study showed that the sub-pixel averaging and the moving average filters developed by the sub-pixel-
sum are viable techniques for removing beating and moiré patterns from the scanned halftone prints, provided
the window size is large enough.
ACKNOWLEDGEMENT
Many thanks to IS&T, Heidelberg, and Dr. Yee S. Ng of NexPress Solution, LLC, for providing IS&T NIP16
Test Targets.
REFERENCES
1. H. R. Kang, Color Digital Halftoning,Chap. 19, “Inverse Halftoning”, pp. 357-395, SPIE and IEEE press
(1999).
2. H. R. Kang, “Inverse halftoning using sub-pixel sum”, to be published.
3. H. R. Kang, “Digital filter design using sub-pixel sum”, to be published.
4. ISO/JIS-SCID, “Graphic technology – Prepress digital data exchange – Standard color image data
(SCID),” JIS X 9201-1995 (1995).
