# Salient Region Detection Using Diffusion Process with Nonlocal Connections
## 3 Experiment
### Parameter Analysis  
We conducted a series of experiments to investigate the influence of various factors on saliency detection. These factors or parameters include \(\sigma_{x}\), \(\sigma_{y}\) in Equations (10), (20), and (25); the updating time \(M\) in Equation (28); and the updating weight \(\varepsilon\), \(\tau\) in Equations (28) and (29); the graph with the nonlocal connections; and the integration of the feature-bias Gaussian model; the diffusion process with nonlocal connections; the single-layer updating and the multi-layer integration process. These experiments are processed in ASD dataset. (1) **Parameters**: The parameter \(\sigma_{x},\sigma_{y}\) decide the distribution amplitude of Gaussian model. To precisely refine the saliency map based on different cue, the \(\sigma_{x},\sigma_{y}\) in Equations (10), (20), and (25) should be different with each other. Compactness cue denotes the spatial variance of features, but the background may be wrongly highlighted, especially when the background also has a compact distribution. So the \(\sigma_{x},\sigma_{y}\) in Equation (10) should be lower than others. Figure 9a shows the precision-recall curves and the average precisions, recalls and F-measures using an adaptive threshold with different \(\sigma_{x},\sigma_{y}\) values in Equations (10), (20), (25). As we can see, the different values of \(\sigma_{x}(\sigma_{y})\) within the scope of the stated ranges have a similar result. Similarly, when the value of \(M\) and \(\varepsilon,\tau\) are varied, the performances change a small amount, which can be seen in Figure 9b,c. This means the performances are not sensitive to these two parameters. But to promote the recall and balance the performance, we set \(M=3\) and \(\varepsilon=\tau=0.08\). (2) **Graph Construction**: We expanded the nonlocal connections to 2-layer sparse graph. To validate it, we compared the performances of 2-layer neighborhood graph, 2-layer neighborhood graph with nonlocal connections, 2-layer sparse graph, and our proposed graph. Figure 10 shows the precision-recall curves and the average precisions, recalls and F-measures using an adaptive threshold. As is illustrated in Figure 10, the nonlocal connections can effectively promote the performance of the 2-layer neighborhood graph. Additionally, the result of the 2-layer sparse graph also has an improvement, whereas the progress may be slightly lower than 2-layer neighborhood graph. Respectively, the 2-layer sparse graph and the nonlocal connections can improve the topotaxy between different elements locally and globally. Generally, the local topotaxy may have a bigger impact of the results than the nonlocal topotaxy because of the closer spatial proximity. So as shown in Figure 10, the improvement of results via 2-layer sparse graph can be more obvious than the nonlocal connections. But the nonlocal connections can still improve the result of the 2-layer sparse graph by reducing the impact of the imprecise local connections. (3) **Component Analysis:** We combined the saliency-biased Gaussian model, the diffusion process with nonlocal connections, the single-layer updating and multi-layer integration process in our algorithm. To prove the efficiency of these components, a series of experiments were carried out. The precision-recall curves and the average precisions, recalls, and F-measures at an adaptive threshold are displayed in Figure 11. As is illustrated in Figure 11, the saliency-biased Gaussian model is effective in the improvement of precision, while the diffusion process with nonlocal connections mainly contributes to the recall. This can be explained logically. The saliency-biased Gaussian model can highlight the salient regions and compress the background, which means the high precision according to the Equation (31). Relatively, as the above mentioned, the diffusion process with nonlocal connections can obtain a more homogenous salient region, which leads to the high recall according to the Equation (32).