Accurate color reproduction is important in many applications of 3D printing, from design prototypes to 3D color copies or portraits. Although full color is available via other technologies, multi-jet printers have greater potential for graphical 3D printing, in terms of reproducing complex appearance properties. However, to date these printers cannot produce full color, and doing so poses substantial technical challenges, from the shear amount of data to the translucency of the available color materials. In this article, we propose an error diffusion halftoning approach to achieve full color with multi-jet printers, which operates on multiple isosurfaces or layers within the object. We propose a novel traversal algorithm for voxel surfaces, which allows the transfer of existing error diffusion algorithms from 2D printing. The resulting prints faithfully reproduce colors, color gradients and fine-scale details.
2D Halftoning. Generations of researchers in the field of 2D halftoning focused on finding methodologies to optimally arrange printed dots for maximizing print quality (by preserving tone and structure and shifting quantization errors to the highest spatial frequencies possible - see Section ) subject to technical limitations of printing systems (e.g. the ability to accurately deposit isolated dots) @cite_8 .
@cite_8
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3D halftoning is a new technique that allows the approximation of digital volumetric objects of varying material density e.g. porous media for example, by an ensemble of binary material volume elements called vels. In theory, 3D halftoning is basically an extension of the well known 2D halftoning process, as widely used in binary printing applications. In practice, however, the development of 3D halftoning algorithms is strongly related to hardware specific boundary conditions, such as particular characteristics of additive volumetric object manufacturing procedures. This paper addresses theoretical as well as practical aspects of 3D halftoning that allow the rendition of digital volumetric objects of varying density using the stereolithographic additive fabrication technique. An ultimate application of 3D halftoning is the reproduction of volumetric objects in medicine that consist of a mixture of bone, cartilage and soft-tissues, for example. Introduction AM Digital Halftoning FM Digital Halftoning AM-FM Hybrids AM Halftoning Dot Shape Screen Angles and Moire Screen Frequency Supercells Zero-Angle Dither Arrays Stochastic Halftone Analysis Point Processes Spatial Statistics Spectral Statistics Color Halftoning Halftone Visibility Campbell's CSF Model Nasanen (Exponential) Model Mixed Gaussian Models Alpha Stable HVS Models Blue-Noise Dithering Spatial and Spectral Characteristics Error Diffusion Blue-Noise Dither Arrays Simulated Annealing Void and Cluster BIPPSMA Dither Pattern Ordering Direct Binary Search Halftoning by DBS Efficient Implementation of DBS Effect of HVS model Hexagonal Grid Halftoning Spectral Aliasing Modified Blue-Noise Model Hexagonal Sampling Grids Printers: Distortions and Models Printer Distortion Dot Models Corrective Measures Green-Noise Dithering Spatial and Spectral Characteristics EDODF Green-Noise Masks BIPPCCA Optimal Green-Noise Masks Color Printing Generalized Error Diffusion Multichannel Green-Noise Masks Stochastic Moire Spatial Analysis of Periodic Moire Spatial Analysis of Aperiodic Moire Spectral Analysis of Aperiodic Moire Minimizing Stochastic Moire Stochastic Moire and Green-Noise Multitone Dithering Spectral Statistics of Multitones Multitone Blue-Noise Model Blue-Noise Multitoning Optimization Lenticular Halftoning Model Based Error Diffusion Iterative Tone Correction Conclusions Bibliography List of Figures Index We introduce a method for automated conversion of scanned color comic books and graphical novels into a new high-fidelity rescalable digital representation. Since crisp black line artwork and lettering are the most important structural and stylistic elements in this important genre of color illustrations, our digitization process is geared towards faithful reconstruction of these elements. This is a challenging task, because commercial presses perform halftoning (screening) to approximate continuous tones and colors with overlapping grids of dots. Although a large number of inverse haftoning (descreening) methods exist, they typically blur the intricate black artwork. Our approach is specifically designed to descreen color comics, which typically reproduce color using screened CMY inks, but print the black artwork using non-screened solid black ink. After separating the scanned image into three screening grids, one for each of the CMY process inks, we use non-linear optimization to fit a parametric model describing each grid, and simultaneously recover the non-screened black ink layer, which is then vectorized. The result of this process is a high quality, compact, and rescalable digital representation of the original artwork. A novel digital halftoning technique, by which the halftoning is achieved by a pixelwise comparison of the gray-scale image to an array (halftone screen), the blue-noise mask, is presented. This mask is designed so that the halftone image has blue-noise (high-frequency) characteristics in the frequency domain. The algorithm for the construction of the blue-noise mask and an algorithm for the construction of binary patterns with the same first-order but different second-order statistics are presented. Two psychovisual tests in which human subjects rated halftone patterns and images according to various criteria are also described.