# Saliency Detection with Bilateral Absorbing Markov Chain Guided by Depth Information
## 2 Methodology
### Mid-Level Saliency Maps Generation by Bilateral Absorbing Markov Chain
#### 2.3.2 Background Seed Screening Mechanism  
Generally, traditional saliency detection models based on absorbing Markov chain [44; 45; 46] usually mirror image edge superpixels as absorbing nodes and simply connect all edge superpixels in pairs. However, as shown in Figure 2, when the salient object touches the image boundary, the mirroring will mistakenly regard the foreground nodes as background-based absorbing nodes, thus suppressing the saliency of the foreground regions or causing detection failure. Similarly, if the edge nodes contain foreground nodes, the full connections between them may be poorly robust. To overcome them, we propose a background seed screening mechanism (BSSM) for improving the two-layer sparse graph and selecting better background-based absorbing nodes. This mechanism removes the nodes that may belong to the foreground from the edge nodes. Furthermore, in order to increase the diversity of the background and restrain the background regions, a small number of random non-edge background nodes are selected to form a new edge node set and a background-based absorbing node set. Moreover, to obtain more homogeneous salient regions, we design the non-local connection similar to [47]. Next, we will introduce the construction process of the background seed screening mechanism and the non-local connections in detail. Figure 2: Traditional saliency detection models based on absorbing Markov chain. (**a**) RGB images. (**b**) Ground truth. (**c**) Saliency maps generated by [45]. (**d**) Saliency maps generated by [46]. (**e**) Saliency maps generated by [44]. To facilitate understanding, we provide a schematic diagram in Figure 3, which describes the main screening process of the background seeds. First, according to the attributes of saliency, position and depth, all nodes are classified as three categories. As shown in Figure 3a, based on the low-level background prior \(S_{bp}\), we divide all nodes into background seed set \(\Omega_{BG}\), foreground seed set \(\Omega_{FG}\) and others. \[\Omega_{BG}=\left\{i\big{|}S_{bp}(i)>0.9\right\} \tag{12}\]  
\[\Omega_{FG}=\left\{i\big{|}S_{fp}(i)>th_{FG}\right\} \tag{13}\]  
where \(S_{fp}\) represents the foreground prior,  
\[S_{fp}(i)=1-S_{bp}(i) \tag{14}\]  
\[th_{FG}>\frac{3\cdot mean(S_{fp})+\max(S_{fp})}{4} \tag{15}\]  
According to the position attribute, the nodes can be classified as edge node set \(\Omega_{edge}=\left\{i|i\in\text{edge}\right\}\) and non-edge node set \(\Omega_{non\_edge}=\left\{i|i\
otin\text{edge}\right\}\) as shown in Figure 3b. Considering that objects far away from the camera are likely to belong to the background, as shown in Figure 3c, we use the depth threshold to divide the nodes into depth-based background seed set \(\Omega_{Dep}\) and others. \[\Omega_{Dep}=\left\{i|d_{i}>1.2*th_{Dep}\text{ and }i\
otin\Omega_{FG}\right\} \tag{16}\]  
\[th_{Dep}>\frac{3*mean(d_{i})+\max(d_{i})}{4},i\in\Omega_{BG} \tag{17}\]  
To alleviate the boundary touch problem and select background seeds more accurately, we utilize k-means algorithm to filter out the foreground nodes in the background seed set \(\Omega_{BG}\) and edge node set \(\Omega_{edge}\). More specifically, we cluster the sets of \(\Omega_{BG}\), \(\Omega_{edge}\) and \(\Omega_{FG}\) to find the nodes that are similar with the foreground seeds \(\Omega_{FG}\). Figure 3d is the filtered result: new edge node set \(\Omega^{\prime}_{edge}\) and background seed set \(\Omega^{\prime}_{BG}\). In Figure 3e, we  
Figure 3: The process diagram of the background seed screening. (**a**) The node sets based on saliency attribute; (**b**) The node sets based on location attribute; (**c**) The node sets based on depth attribute; (**d**) The node sets after removing the foreground nodes; (**e**) The diagram of the comprehensive relationship between the three attributes; (**f**) The final node sets after classifying. take depth information into consideration in the process of background seed screening.