基于图像分割和加权最小二乘法的数字半色调技术

Digital Halftoning Technique Based on Image Segmentation and Weighted Least Squares Method

应用K—menas聚类法进行灰度图像分割，计算各个分割区域像素的均值和方差，通过分析各区域像素均值和方差发现随机误差项具有异方差性，应用加权最小平方法构建新的能量函数，采用各个分割区域像素方差倒数作为权重因子，进行半色调图像的转换。所构造的半色调算法与基于模型的最小平方法（LSMB）相比，随着聚类分区的增加，图像平滑且边缘清晰度增加，尤其是在图像细节部位。与LSMB算法比较，该算法的均方误差值（MSEv）有所降低，而权重信噪比（WSNR）和峰值信噪比（PsNR）则有一定提高，模拟实验结果验证了算法的有效性。该算法四次迭代计算以后，收敛误差降到0．20以下，具有较快的收敛速度。

A weighted least-squares-based halftoning model from human visual system （HVS） model and an efficient iterative strategy using gray image statistical information are proposed. The gray image is partitioned using K-means image segmentation method, whose performance depends on the selection of distance metrics. The statistics of the mean and variance of the gray-scale pixel of each clustering are calculated. It is found that random error has the charcteristics of heteroscedasticity. The new energy function is constructed using the weighted least squares method, which the reciprocal variance of pixel of the segmented regions are referred to as the weighting operator. The analysis and simulation results show that the proposed algorithm produces better gray-scale halftone image quality when increase the number of clustering with a certain range. A performance measure for halftone images is used to evaluate our algorithm. The proposed algorithm achieves consistently better values of mean square error value （MSEv） and peak signal to noise ratio （PSNR） for two, three and four partitions than the least-squares model-based （LSMB） algorithm. The proposed algorithm can further reduce the number of iterations, Mter four iterations of the proposed algorithm, the convergence error drops to 0.20.