# NICE: Superpixel Segmentation Using Non-Iterative Clustering with Efficiency
## 4 Experiments and Analysis
### Quantitative Evaluation by Metrics  
To objectively evaluate the performance of segmentation results, three evaluation metrics in [22] are taken into account, namely boundary recall (BR), under-segmentation error (UE) and achievable segmentation accuracy (ASA). All of them are commonly used in superpixel segmentation methods with emphasis on edge and region consistency, as well as the performance of subsequent visual tasks, respectively. More formally, let \(\Omega=\{\Omega_{k}\}_{k=1}^{K}\) and \(G=\{G_{m}\}_{m=1}^{M}\) be the calculated superpixels and the ground truth of the same image \(\{l_{i}\}_{i=1}^{N}\), respectively. These metrics will be described in detail subsequently. As mentioned above, there is little difference between SNIC and ANIC, as well as ENIC and NICE, thus the raw data of metrics in Tables 1-3 are more precise than figures (the curves are too close to distinguish visibly). The difference of values caused by AIR is marked in which blue and red indicate amelioration and deterioration, respectively. In the following tables and Figure 8, \(\sigma\) is set to 0.03 that merely verifies the effectiveness of EIR, and it would be covered in more detail in the next subsection. Boundary recall (BR) is a standard boundary-detection and segmentation evaluation criterion. It can be described mathematically as the ratio of ground truth boundaries covered by superpixel boundaries [1]  
\[\text{BR}=\frac{\sum_{i\in G_{b}}\Pi\Big{(}\min_{j\in\Omega_{b}}\lVert P(I_{i} )-P\big{(}I_{j}\big{)}\rVert_{2}<r\Big{)}}{G_{b}}, \tag{6}\]  
where \(\Omega_{b}\) and \(G_{b}\) represent boundary pixels in \(\Omega\) and \(G\), respectively. The indicator function \(\Pi()\) returns the logic value whether the expression is true. In addition, the coverage radius \(r\) is set to 2 pixels in this paper. Therefore, the higher the value of BR, the better boundary adherence the algorithm performs. In Table 1, performance difference with and without AIR are ignorable, while ENIC and NICE benefits from EIR and outperform SNIC and ANIC, respectively. The reason is that \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{8}{c}{**User-Expected Number of Superpixels**} \\ \cline{2-11}  & **50** & **100** & **150** & **200** & **250** & **300** & **350** & **400** & **450** & **500** \\ \hline SNIC & 0.6740 & 0.7921 & 0.8428 & 0.8668 & 0.8985 & 0.9059 & 0.9195 & 0.9311 & 0.9387 & 0.9493 \\ ANIC & 0.6740 & 0.7922 & 0.8428 & 0.8669 & 0.8985 & 0.9060 & 0.9195 & 0.9311 & 0.9386 & 0.9493 \\ ENIC & 0.6757 & 0.7957 & 0.8457 & 0.8694 & 0.9010 & 0.9085 & 0.9213 & 0.9334 & 0.9405 & 0.9506 \\ NICE & 0.6757 & 0.7957 & 0.8457 & 0.8694 & 0.9010 & 0.9084 & 0.9212 & 0.9334 & 0.9405 & 0.9506 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of SNIC and the proposed three algorithms in terms of boundary recall (BR). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{8}{c}{**User-Expected Number of Superpixels**} \\ \cline{2-11}  & **50** & **100** & **150** & **200** & **250** & **300** & **350** & **400** & **450** & **500** \\ \hline SNIC & 0.1753 & 0.1100 & 0.0898 & 0.0809 & 0.0706 & 0.0680 & 0.0645 & 0.0603 & 0.0578 & 0.0545 \\ ANIC & 0.1751 & 0.1100 & 0.0897 & 0.0809 & 0.0706 & 0.0680 & 0.0645 & 0.0603 & 0.0578 &EIR introduces color context information to pixels that are adjacent to a common frontier inspector. Therefore, as depicted in Figure 3c, three pixels into a line with similar colors may be assigned an identical label. It efficiently alleviates the risk of shape constraint in complex boundaries. In addition, rather than AIR, EIR still plays a positive role in the non-iterative clustering framework, which also can be verified by the following two metrics.