误差扩散是图像半色调和蓝噪声采样中的常用方法，传统误差扩散算法仅适用于二维空间中单通道信号的处理，在本项目中，将对误差扩散在新领域中的发展和应用进行深入研究，提出一系列采样和图像处理的新方法。 本项目中首先将提出一种多类误差扩散算法，同时对多通道输入信号进行采样，并保证每个通道、以及各通道叠加后的采样点分布都具有蓝噪声性质。在此基础上还将研究它在彩色图像半色调、向量化等方面的新应用。其次，针对具有明显方向性特征的采样空间，还将提出一种新颖的各向异性误差扩散采样算法，通过采样密度函数及各向异性方向来描述空间中的特征，对误差扩散参数进行调节，生成具有各向异性且能保持特征的采样点分布。最后还将研究三维体数据上的误差扩散采样，根据体数据的特点对误差扩散的关键步骤进行拓展，从而产生三维蓝噪声采样结果。 本项目研究内容是本领域中的前沿问题，可以预期取得具有学术价值的研究成果，同时也具有广泛的应用前景。

Error-diffusion is a frequently used method in image halftoning and blue-noise sampling. Traditional error-diffusion methods can only process single-channel signals in 2D image. In this project, a series of novel methods for sampling and image processing will be proposed, which will expand the use of error-diffusion methods into new areas and applications. First, we will present a multi-class error-diffusion algorithm, which can perform sampling on multi-channel input signals simultaneously, and ensure the blue-noise property in each individual channel and their superposition. Then, we will further research on its applications in color image halftoning and vectorization. Secondly, for sampling-spaces with distinct directional features, we will propose a novel anisotropic error-diffusion sampling method, which can generate anisotropic and feature-preserving sampling points by adjusting the error-diffusion parameters according to the sampling density function and its variation vectors. Finaly, an error-diffusion sampling method for 3D volume data will also be proposed. For this purpose, some key approaches and parameters of the standard error-diffusion will be modified according to the features of volume data to produce 3D blue-noise sample point sets. This project concerns the frontier of the areas of sampling and image processing, and both academic achievements and practical applications can be expected.