In the following, we quantitatively compare the performance between the proposed algorithm and Calibre pxOPC software with respect to image fidelity, computational efficiency, and mask complexity. We first use the metric of EPE and the pattern error to compare the image fidelity performance between these two methods. The pattern error is defined as the area of the difference region between the print image and the target pattern. We use Calibre to detect and collect all sites on the print images with an absolute EPE value ($|EPE|$) larger than 3 nm. Then, we normalize the site number to 2000 and plot the histograms in Fig. 10 to show the distributions of $|EPE|$ values. Figures 10(a) and 10(b) are the histograms for the 90- and 45-nm metal layers, respectively. Table 1 summarizes the distributions of $|EPE|$ values for these 2000 detected sites with different methods. The initial mask patterns without optimization lead to many large $|EPE|$ values falling in the range of [20, 35 nm), while the Calibre pxOPC and the proposed algorithm can effectively suppress the $|EPE|$ values by concentrating most of them into the range of [0, 20 nm). The third row of Table 2 provides the average $|EPE|$ values, which is defined as the sum of all $|EPE|$ values divided by the detected site count. The fourth row of Table 2 provides the pattern errors. For the 90-nm metal layer, compared to the initial mask pattern, Calibre pxOPC and the proposed algorithm may reduce the average $|EPE|$ by 84% and 81%, while reducing the pattern error by 93% and 92%, respectively. The average $|EPE|$ and pattern error of the proposed algorithm are 16% and 21% higher than Calibre pxOPC. For the 45-nm metal layer, compared to the initial mask pattern, Calibre pxOPC and the proposed algorithm may reduce the average $|EPE|$ by 62% and 58%, while reducing the pattern error by 83% and 81%, respectively. The average $|EPE|$ and pattern error of the proposed algorithm are 12% and 10% higher than Calibre pxOPC. According to the above analysis, both of the Calibre pxOPC and proposed algorithm can effectively reduce the $|EPE|$ in contrast to the initial mask pattern. In addition, the image fidelity of Calibre pxOPC is better than that of the proposed algorithm. The computational efficiency of different methods is compared in the following. All of the computations are carried out on an Intel(R) Xeon(R) x5650 CPU, 2.67 GHz, 32.00 GB of RAM. The nonparametric regression process of the proposed algorithm is implemented in C language, and the postprocessing is implemented by the Calibre software. The test layouts are saved as OASIS files. In order to fairly compare the runtimes, we removed the hierarchies in the OASIS files, and ran both of the Calibre software and C codes using one CPU core. The runtimes of Calibre pxOPC and the proposed algorithm are summarized in the fifth row of Table 2. For the simulations of 90-nm metal layer, the Calibre pxOPC and the proposed algorithm took 1910 and 991 s, respectively. In particular, the nonparametric regression process based on the C language took 219 s. In the postprocessing method, Steps 1 and 2 together took 20 s, and Step 3 took 752 s. For the simulations of 45-nm metal layer, the Calibre pxOPC and the proposed algorithm took 881 and 341 s, respectively. The nonparametric regression process based on C language took 99 s. In the postprocessing method, Steps 1 and 2 together took 7 s, and Step 3 took 235 s. Compared to the Calibre pxOPC, the proposed algorithm reduced the runtime by 48% and 61% for the 90- and 45-nm metal layers, respectively. It is also noted that the times to build up the OPC training datasets are 10.0 and 11.6 h for the 90- and 45-nm metal layers, respectively. However, whenever the training datasets are built up, they can be repeatedly applied for different layers with similar geometric characteristics.