De-screen of Scanned Halftone Prints by Fractional-Pixel Averaging

Henry R. KangColor 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

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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 CreationThe 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

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Screened bilevel original

Copier or Scanner

Scanned RGB image (8-bit/color)

Inverse halftoning

Color conversion to CMYK

Rescreening

De-screenedRGB image

CMYK color printer

Halftoning by copier

Color conversion to CMYK

Path 1

Path 2Halftoning by copier

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 SummationUpon 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 GenerationThe 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.

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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.

Inputtexture

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 23 79 79 79 77 79 80 58 138 161 49 155 177 38 175 195 34 183 202

4

133

0 221

252

236

0

0

00

0

11963 to 2conversion

252

1136252

80 28

80 79 77

28 77 126

2 to 3conversion

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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.

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 TechniqueSeveral 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

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Screened bilevel original

ScannerScanned RGB

image (8-bit/color)

Halftoning

Color conversion to CMYK

DescreenRGB image

CMYK color printer

Halftoning

Color print

Comparison of computer displays

Color conversion to CMYK

CMYK color printer

Color print

Comparison

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 ResultsVisual 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.

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

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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).

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