# NICE: Superpixel Segmentation Using Non-Iterative Clustering with Efficiency
## 4 Experiments and Analysis
### More Discussions on the Performance  
The proposed NICE framework with two strategies allows conventional SNIC to be more efficient, therefore, some key factors that influence the performance are analyzed together. Figure 8 demonstrates  
Figure 8: Comparison of runtime in milliseconds. (**a**) Time required for superpixels of increasing number in BSDS500; (**b**) time required for size-fixed superpixels of increasing size in multiple resolution image sets; (**c**) time required for number-fixed superpixels of increasing size in multiple resolution image sets. Green boxes show the local details of curves in (**b,c**). the comparison of execution time (ET) on four algorithms. The performance on the BSDS500 dataset with respect to different expected superpixel numbers is shown in Figure 8a. In addition, a number of supplementary natural images ranging from \(720\times 576\) to \(1920\times 1080\) with multiple characteristics, are packed into 6 sets to measure the efficiency in various image sizes. Figure 8b,c adopt a fixed size of superpixel (about 1600 pixels per region on average) and a fixed superpixel number (expect 1000 per image on average) to partition different size of images, respectively. Theoretically, the time complexity of conventional SNIC is \(O(N\log(n))\), wherein \(\log(n)\) refers to the logarithm of the priority queue length. It means that the computational time is nearly linear in the number of pixels \(N\) in the image (as shown in Figure 8b). On the other hand, if there are a large number of unassigned elements in the priority queue, its sorting efficiency decreases significantly. For example, in Figure 8a, with the increasing expected number of superpixels, more unassigned neighboring pixels are inspected by additional seeds. It results in accumulation on the priority queue. It also can be proved by Figure 8b,c, where the difference of expected superpixel number is about 300 on \(1920\times 1080\) images. As a parameter-free strategy in the non-iterative clustering framework, AIR exhibits a scale-sensitive property for accelerating. If there are a small amount of pixels in each superpixels on average, AIR fails to show a significant promotion on SNIC. On the contrary, as the size of input images grows, the average pixel number of each superpixels becomes greater, it gradually becomes the main contributor for NICE. On \(1920\times 1080\) images with about 1300 superpixels in Figure 8b, 24.2% of queueing operations are eliminated by AIR on average, which improves the efficiency by a 14% reduction in execution time. Different from AIR, the result of EIR is determined by the parameter \(\sigma\) in Equation (4). As analyzed above, there is a balanced trade-off between runtime and accuracy by a proper \(\sigma\). In other words, efficiency boosting is contradictory with other evaluation metrics. Since AIR scarcely affects the accuracy of ANIC and NICE, a more comprehensive discussion between SNIC and ENIC is expanded based on the value of \(\sigma\). Table 4 shows the difference in terms of several metrics under various values of \(\sigma\) on BSDS500 images with fixed superpixel number 200. Apparently, when \(\sigma=0\), ENIC is equivalent to SNIC. Once \(\sigma\) becomes positive, EIR starts to promote the non-iterative clustering framework and dramatically reduce the repetitions of inspection. On the other hand, it would worsen the performance due to an accumulation of digital value causing color bias \(\sigma\) grows larger. In this experiment, \(\sigma=0.08\) can be regarded as a balance for the abovementioned trade-off, which speeds up by 25% while preserves the accuracy of conventional SNIC. It is notable that, for the resultant NICE, its speed-up ratio is greater than that sum of ANIC and ENIC. This indicates AIR together with EIR generates a synergetic effect that achieves more significant speed enhancement. Therefore, NICE only reduces the computation cost on small images, but lowers the slope of the required time for increasing image size.