Clustered-Dot Halftoning With Direct Binary Search

Goyal, Puneet; Gupta, Manisha; Staelin, Carl; Fischer, Mani; Shacham, Omri; Allebach, Jan P.

doi:10.1109/tip.2012.2218821

Cited by 30 publications

(13 citation statements)

References 16 publications

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“…Because cpp[0] > c (k) pp , we should consider only toggle operation until the solution converges before we consider swap operation to achieve faster convergence. The fact that swap operation converges much slower than toggle operation has also been observed in previous researches [16]. The second observation is that c (1) pp determines the range of cpẽ[m] and a swap with a pixel further away from the center of the filter results in a smaller range.…”

Section: Monotonically Non-decreasing Swap Dbs Algorithmmentioning

confidence: 59%

“…If convergence is established after the k-th swap, the opposite of either (16) or (17) must be satisfied so that no further swap is accepted. Therefore, one of the following two inequalities must be satisfied:…”

Section: Theoretical Analysismentioning

confidence: 99%

“…The execution time of the MNDS DBS algorithm can be further reduced by utilizing the fact that the number of swap at the edge of cpp[m] is small because the difference between cpẽ[m 1 ] and cpẽ[m 0 ] has to be larger in order to satisfy the swap criteria (16) or (17). Therefore, those pixel groups located at the edge of the filter can be skipped without significantly increasing the total squared perceived error.…”

Section: B Truncation Of Monotonically Non-decreasing Swap Conditionmentioning

confidence: 99%

“…The most commonly used algorithms for these three groups are screening or dithering [1] for point processes, error diffusion [2] for neighborhood processes, and direct binary search (DBS) [3]- [5] for iterative processes. Among these methods, the quality of the halftone image produced by DBS is the best and it has been extended to various printer models [7]- [9], different HVS models [10], color halftoning [11]- [13], screen design [14], [15], and clustered dots [16]. The reason that DBS can generate halftone images of the best quality is that it seeks to minimize the total squared perceived error while algorithms in point and neighborhood processes are mostly heuristic.…”

Section: Introductionmentioning

confidence: 99%

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Theoretical Bounds of Direct Binary Search Halftoning

Liao

2015

IEEE Trans. on Image Process.

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Direct binary search (DBS) produces the images of the best quality among half-toning algorithms. The reason is that it minimizes the total squared perceived error instead of using heuristic approaches. The search for the optimal solution involves two operations: (1) toggle and (2) swap. Both operations try to find the binary states for each pixel to minimize the total squared perceived error. This error energy minimization leads to a conjecture that the absolute value of the filtered error after DBS converges is bounded by half of the peak value of the autocorrelation filter. However, a proof of the bound's existence has not yet been found. In this paper, we present a proof that shows the bound existed as conjectured under the condition that at least one swap occurs after toggle converges. The theoretical analysis also indicates that a swap with a pixel further away from the center of the autocorrelation filter results in a tighter bound. Therefore, we propose a new DBS algorithm which considers toggle and swap separately, and the swap operations are considered in the order from the edge to the center of the filter. Experimental results show that the new algorithm is more efficient than the previous algorithm and can produce half-toned images of the same quality as the previous algorithm.

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Section: Monotonically Non-decreasing Swap Dbs Algorithmmentioning

confidence: 59%

Section: Theoretical Analysismentioning

confidence: 99%

Section: B Truncation Of Monotonically Non-decreasing Swap Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Theoretical Bounds of Direct Binary Search Halftoning

Liao

2015

IEEE Trans. on Image Process.

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“…More recently, a clustered-dot halftone technique based on direct binary search was proposed. 11 Although the proposed technique does allow control of halftone shape and texture parameters, such as homogeneity and clusteredness, the technique only allows indirect control of these attributes via the adjustment of filter sizes.…”

Section: Introductionmentioning

confidence: 99%

Parametrically controlled stochastically seeded clustered halftones: design strategies and applications

Bernal

Loce

Wang

et al. 2014

J. Electron. Imaging

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Abstract. We present a stochastically seeded, clustered halftoning method with parametric control of dot shapes as well as seed placement adaption to local image structure. While the literature on other randomly structured screens (blue noise, green noise, and stochastic halftoning) is quite extensive, there is very little discussion on optimization of dot shape for robustness or preferred tile appearance. The parametric control presented here can enable an imaging engineer to optimize robustness for a given printing system. The halftoning method that we introduce defines dot centers as seeds that are placed typically in a random, high spatial frequency configuration. Spot functions are defined about these randomly placed seeds, where the spot function allows control of dot cluster growth, touch points, cluster angle, and eccentricity. The spot function can also be applied to regular and irregular polygonal halftone tiling. The adaptability of the seed placement provided by the halftoning method allows for better edge rendition than conventional isotropic methods and enables the implementation of data-embedding techniques. The resulting monochromatic screens can be seamlessly integrated with novel successive filling techniques in order to provide dot-off-dot vector halftoning capabilities.

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Inverse Design of Unidirectional Transmission Nanostructures Based on Unsupervised Machine Learning

Liu

Deng

Liu

et al. 2022

Advanced Optical Materials

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Structural design is an important driving force for technological development in nanophotonics. To achieve better performance of nanophotonic devices, the freedom of structural design space needs to be expanded. Unsupervised learning algorithm in deep learning provides a great platform to expand design freedom of structures and avoid the “curse of dimensionality” effectively. It performs well on extracting important features from high‐dimensional data and excavating potential rules. In this work, an unsupervised convolutional neural network is built to inversely design nanostructures with unidirectional transmission. Near‐field information with high dimensions is recognized and extracted into a 2D feature space which maintains high physical continuity and maps to far‐field transmittance effectively. The feature space is further expanded to the whole space by optimistic Bayesian multisampling, from which nanostructures with transmittance over 95% forward while less than 40% backward are inversely designed. Moreover, the relation between near‐field information and far‐field transmittance is explored. A feasible design method of nanostructures is proposed based on unsupervised learning with design space expanded. This design mentality exhibits a way of extracting near‐field features to analyze far‐field spectra with deep learning algorithms, which is suitable for more abundant physical design and can be extended to other similar systems.

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Clustered-Dot Halftoning With Direct Binary Search

Cited by 30 publications

References 16 publications

Theoretical Bounds of Direct Binary Search Halftoning

Theoretical Bounds of Direct Binary Search Halftoning

Parametrically controlled stochastically seeded clustered halftones: design strategies and applications

Inverse Design of Unidirectional Transmission Nanostructures Based on Unsupervised Machine Learning

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