论文标题
通过加权Sigma-Delta调制增强数字半强
Enhanced Digital Halftoning via Weighted Sigma-Delta Modulation
论文作者
论文摘要
在本文中，我们从1位Sigma-Delta量化的角度研究了数字硬质量的误差扩散技术。我们介绍了一种生成二维信号的Sigma-Delta方案，作为其一维对应物的加权组合，并表明文献中提出的各种误差扩散方案可以通过本框架中的Sigma-Delta方案表示。在二维带限制信号的模型下，这是由人类视觉感知的数学模型激励的，我们得出了这种加权Sigma-Delta方案的定量误差界限。我们将这些界限视为对误差扩散的良好经验性能的数学理解的一步，即使它们是在超级规范中表达的，众所周知，这并未完全捕获图像的视觉相似性。 由现有的误差扩散算法和一阶Sigma-Delta方案之间的对应关系，我们研究了二阶Sigma-Delta方案的类似加权组合的性能，并表明它们在二维带限制信号的保证误差衰减方面表现出卓越的性能。在对现实世界图像的广泛数值模拟中，我们证明，通过一些修改以增强稳定性，这种卓越的性能也转化为数字半强化的问题。 更具体地说，我们发现某些二阶加权Sigma-Delta方案表现出竞争性能，可根据特征相似性指数（FSIM）（FSIM）的数字性能，这是图像质量评估的最先进措施。
In this paper, we study error diffusion techniques for digital halftoning from the perspective of 1-bit Sigma-Delta quantization. We introduce a method to generate Sigma-Delta schemes for two-dimensional signals as a weighted combination of its one-dimensional counterparts and show that various error diffusion schemes proposed in the literature can be represented in this framework via Sigma-Delta schemes of first order. Under the model of two-dimensional bandlimited signals, which is motivated by a mathematical model of human visual perception, we derive quantitative error bounds for such weighted Sigma-Delta schemes. We see these bounds as a step towards a mathematical understanding of the good empirical performance of error diffusion, even though they are formulated in the supremum norm, which is known to not fully capture the visual similarity of images. Motivated by the correspondence between existing error diffusion algorithms and first-order Sigma-Delta schemes, we study the performance of the analogous weighted combinations of second-order Sigma-Delta schemes and show that they exhibit a superior performance in terms of guaranteed error decay for two-dimensional bandlimited signals. In extensive numerical simulations for real world images, we demonstrate that with some modifications to enhance stability this superior performance also translates to the problem of digital halftoning. More concretely, we find that certain second-order weighted Sigma-Delta schemes exhibit competitive performance for digital halftoning of real world images in terms of the Feature Similarity Index (FSIM), a state-of-the-art measure for image quality assessment.
