Screen element shape "R73" mutation with method of growth function parameterization.

Pap, Klaudio ; Vujic Ziljak, Jana ; Ziljak, Ivana 等

1. INTRODUCTION

A screen is defined by conceptually laying a uniform rectangular grid of halftone cells over the device pixel array (Adobe Systems I., 1999). As the use of PostScript developed, there came a natural demand for the inclusion of halftones in the pages, first monochrome, around 1988, and then colour, around 1989/90, which brought a number of added difficulties to both rip and system designer (Brett, 2000). All kinds of methods have been used in the past to create this illusion of tone, including woodcuts, etchings, and engravings on copper and steel (Green, 1999). New halftone screening shapes have been created by us that alter their basic shape as their parameter alters. Due to this transformation of shape we have named them mutants. These shapes have a high dot gain in printing, so they are not to be recommended for high screen ruling. Therefore we recommend them for the area visible to the human eye. Such screen systems are applied in jumbo posters and in graphic work with exceptionally strong messages. Due to the fact that these designs are subject to pseudo-random generating where the initiator is known (congruent method seed), they are ideal for individualizing neutral surfaces in documents. The security is based on secrecy of parameters in the congruent generator algorithm and in parameters with which the screen shape is distorted.

It has been established during our research work on mutating screen element limitations with parameters that are found within the screen element mathematical definition that there is no general rule for free screening element altering. Mathematical modeling helps in setting the boundaries for permissible screen element shape shifting, although errors may occur here as well. The blow to the screening cell border can be set correctly only on basis of testing programs for carrying out graphic samples' screening.

2. SCREEN ELEMENT R73 AND ITS DEFINITION

The new complex stochastically modified screen mutant being the subject of this paper is given with mathematic equation for z growth function (1) .

z = 1 - Abs [Kory x y + Abs(x) - Sin([square root of [x.sup.A] + 4[y.sup.4]])] (1)

Screen element growth function z is the function with the help of which the screening cell is built in the screening process for a set gray level and screen ruling (Foley et al., 1997). The 'kory' correction parameter has been incorporated into the mathematical formula program sequence with the help of which experiments are made as to generating the initial form mutating sequence.

We are using 2D and 3D mathematical models developed by ourselves (Ziljak at al., 2003) for experimental display of results during the development of this complex growth function. Model 2D (Fig. 1) shows the appearance of the screen element for 16 discrete gray levels for one and the same growth function. If the halftone screen that we are developing rapidly changes its shape through the grayscale, we can increase the number of discrete gray levels in this 2D simulation model in the course of experimenting. Changing of the shape throughout the grayscale should not be mixed up with halftone screen altering due to our mutation parameter. These are completely different issues.

The 2D model is not sufficient for determining the allowed 'kory' parameter values. This is the reason for using the 3D model (Fig. 2) for screen element growth. With this model we can research much better the growth function boundary conditions. The allowed values for 'kory' parameter within the [0, 1] interval have been determined on basis of experimental research of shapes with the 2D model and boundary conditions control in the 3D model.

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3. PAREMETER OF MUTATION AND RESULT

The 'kory' parameter introduced here is included in the continuous function with values from 0 to 1 in the execution program. Figure 3 shows the mutant with the kory parameter that equals to =0.5, and figure 4 shows the mutant with the 'kory' parameter equalling to 0.

The mutation parameter has been designed in such a way that by its application there is altering of the screen element shape from symmetric shape (kory=0) to asymmetric shape (kory=1). Thus the 'kory' parameter is at the same time the shape deformation parameter for the screen shape so that the name mutant suits it even better.

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Figure 5 shows stochastic application of mutant R73 screen element on linear gradient from 0 to 88% grayscale. Parameter Kory, screen ruling and screen angle is stochasticly changed during screening phase.

4. CONCLUSION

There is no knowledge and experience on parameter screening. The original PostScript definition for pixel use allows pixel deformation, but the screen element itself does not change. Parameters screen element are a novelty in screening technology. The reason for studying them is the need for various different solutions in future stochastic screen element application used for special security design. A need for this type of application lies in the area of reproduction of graphics with a fixed number of prints, reproduction of postal stamps, securities and other documents printed digitally in a single copy; an integrated passport photograph, badge or pass. This results are very excited for us because we can produce many experimental mutants in the future for different security applications.

5. REFERENCES

Adobe Systems I., (1999). PostScript Language Reference, third edition, Adobe Systems Incorporated, pp. 482, ISBN 0-201-37922-8,

Brett, G. (2000), Digital Prepress Technologies, Pira International Ltd, pp. 122, ISBN 1-85802-261-4

Foley, K.; van Dam; Feiner & Hughes (1997). Computer Graphics Principles and Practice, pp. 569, Addison-Wesley, ISBN 0-321-21056-5

Green, P. (1999), Understanding Digital Color, GATF 1999, pp. 224, ISBN 1-85802-450-1

Ziljak, J.; Vancina V.; Agic, D.; Ziljak, I. & Pap K. S. (2003). New screening elements in multi-colour printing for scecial purposes, Advances in printing Science and Technolog, pp. 261, Acta Graphica Publishers, ISBN: 953-9676-8-0