# 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
In Figure 3f, non-edge background seeds and depth-based background seeds are further divided into three sub-sets: \(\Omega_{A}\), \(\Omega_{B}\), and \(\Omega_{\text{C}}\). It is obvious that the seeds in \(\Omega_{A}\) satisfy both background probability and depth with high values, while the seeds in \(\Omega_{B}\) and \(\Omega_{\text{C}}\) only satisfy the requirement of high background probability or high depth value, respectively. Then, for guaranteeing the diversity of the background and suppressing the background more effectively, we combine a small number of non-edge nodes with \(\Omega^{\prime}_{edge}\) and further form the final edge nodes \(\Omega_{f\_edge}\). These non-edge nodes are randomly composed of 50% \(\Omega_{A}\), 10% \(\Omega_{B}\), and 50% \(\Omega_{C}\). In the initial two-layer sparse graph, to reduce the geodesic distances of nodes, all edge nodes are simply connected together. However, it may be poorly robust to the case when salient objects touch the image boundaries. Therefore, instead of the rough connections, we use the final edge nodes \(\Omega_{f\_edge}\) connected in pairs to obtain a new two-layer sparse graph \(G_{new}\). In addition, to obtain more consistent salient regions, we introduce the non-local connection into the graph. Specifically, it first sorts the foreground prior \(S_{fp}\) and the region contrast prior \(S_{rc}\) of all nodes, the top 50% of both are selected as foreground seeds, and the bottom 50% are selected as background seeds. For each superpixel, we connect it to two nodes that are randomly chosen from the two seed sets respectively. This connection mechanism is more conducive to highlight the foreground objects and suppress the background regions. The improved two-layer sparse graph with the non-local connection is visualized in Figure 4e. Figure 4: The construction and comparison of the proposed graph model. (**a**) Input RGB image. (**b**) Input depth image. (**c**) Ground truth. (**d**) A diagram of the connections of one of the nodes based on initial two-layer sparse graph. A node (illustrated by a pink dot) connects to its adjacent nodes (blue dots and connections) and the most similar node (dark green dots and connections) sharing common boundaries with its adjacent nodes. All edge nodes are connected to pairs (yellow dots and local connections). (**e**) A diagram of the connections of one of the nodes based on improved two-layer sparse graph. Different from the initial graph, the new edge nodes first remove some foreground nodes which are in the image boundary (the nodes at the bottom edge of image), and further join a small number of non-edge background nodes (black nodes). Each pair of the new edge nodes connects to each other (yellow and black dots and connections). Additionally, each node connects to the background seeds (light green dots and connections) and the foreground seeds (purple dots and connections). Moreover, Figure 5 demonstrate the effects of the proposed background seed screening mechanism (BSSM) and non-local connection. In Figure 5e, it is clearly observed that the background is well suppressed by the improved two-layer sparse graph based on background seed screening mechanism (BSSM). Figure 5g illustrates that the non-local connection can achieve more complete and consistent salient regions.