在本篇論文中，我們將分別透過適度的門檻值調整，以及動態調整誤差擴散係數這兩種方法，來讓半色調影像達到銳化的效果且又能夠維持影像的品質。我們的作法主要參考影像所提供的梯度資訊，根據梯度的大小以及方向來對門檻值做適度的修改，並同樣視梯度資訊的變化來去動態修正誤差擴散比例。實驗中我們根據六張測試影像以及幾個比較對象，包含Floyd-Steinberg提出的方法、Eschbach和Knox共同提出的方法、Hwang提出的方法、Li提出的方法以及Feng提出的方法等六個方法，得知我們的方法確實可以擁有邊緣補強的效果，並兼顧到影像的品質。

This thesis presents a gradient--based adaptive error diffusion
method with edge enhancement effect while preserving the smoothness
effect. The proposed method not only can modulate the threshold in
halftoning dynamically but also can determine the weights of the
error diffusion filter adaptively to diffuse the quantization error
to neighboring pixels properly. Under six testing images,
experimental results demonstrate that our proposed new error
diffusion method has a good compromise between the edge enhancement
effect in the halftone image and the image quality effect in the
corresponding inverse halftone image when compared to the methods by
Floyd--Steinberg, Eschbach and Knox, Hwang et al., Li, and
Feng et al., but it has some execution-time degradation.

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